Mastering the Texas Assessment of Knowledge and Skills (TAKS

Diagnose Prescribe Practice Benchmark

Texas Assessment of Knowledge and Skills

Exit Level

Mastering TAKS_EL_SE_TP_877327-X1 1Mastering TAKS_EL_SE_TP_877327-X1 1 6/30/06 4:13:32 PM6/30/06 4:13:32 PM

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027

ISBN 13: 978-0-07-877327-3ISBN 10: 0-07-877327-X Mastering the TAKS: Diagnose–Prescribe–Practice–Benchmark, Grade 11

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 10 009 15 14 13 12 11 10 09 08 07 06

Test-Taking Tips• Go to bed early the night before the test. You will think more clearly

after a good night’s rest.

• Read each problem carefully, and think about ways to solve the problem before you try to answer the question.

• Relax. Most people get nervous when taking a test. It’s natural. Just do your best.

• Answer questions that you are sure about first. If you do not know the answer to a question, skip it and go back to that question later.

• Think positively. Some problems may seem hard to you, but you may be able to figure out what to do if you read each question carefully.

• If no figure is provided, draw one. If one is furnished, mark it in any way that will help you solve the problem.

• When you have finished each problem, reread it to make sure that your answer is reasonable.

• Become familiar with a variety of formulas and when they should be used.

• Make sure that the number of the question on the answer sheet matches the number of the question on which you are working in your test booklet.

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Mastering the TAKS, Grade 11 iii

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Road Map to TAKS SuccessAn Annotated Table of Contents

Diagnose Your Needs

Learn what mathematics skills are assessed on the TAKS.

Texas Essential Knowledge and Skills, Grade 11 . . . . . . . . . . .vi–ix

Take the Diagnostic Test fi rst.

Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1–10

Record your mastered skills.

Student Recording Chart for TAKS Mastery . . . . . . . . . . . . . . . . . .v

If you made a perfect score on your Diagnostic Test, proceed to Step 3 on the next page.

Prescribe Ways to Improve Your Skills

Use the information from your student Recording Sheet to determine which TAKS Practice pages you need to complete.

TFunctional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Properties and Attributes of Functions . . . . . . . . . . . . . . . . . . . . .16

Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

Linear Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . .33

Quadratic and Other Nonlinear Functions . . . . . . . . . . . . . . . . . . .39

Geometric Relationships and Spatial Reasoning . . . . . . . . . . . . .45

2-D and 3-D Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50

Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55

Percents, Proportions, Probability, and Statistics . . . . . . . . . . . . .64

Mathematical Processes and Tools . . . . . . . . . . . . . . . . . . . . . . . .70

Steps to Success Page(s)

continued on the next page

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iv Mastering the TAKS, Grade 11

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Practice Your Test Skills

Take the Practice Test to determine how you have improved your mathematics skills.

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . .76–85

Approximately 25 weeks before your test date, begin the Countdown to TAKS. This contains problems that are similar to those found on the TAKS.

Countdown to TAKS . . . . . . . . . . . . . . . . . .86–110

Work on the problems for each day unless your teacher instructs you to do otherwise. Each question tells which objective is being assessed.

Benchmark Your Progress

Monitor your progress as the year progresses by taking the Benchmark Tests. You can record your progress with each test.

Mastery of Objectives Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .x

Each Benchmark Test assesses the same concepts but is taken at a different time during the school year. Your test scores should improve with each test taken.

Benchmark Test 1 (take in late October) . . . . . . . . . . . . . . .112–121

Benchmark Test 2 (take in early January) . . . . . . . . . . . . . .122–131

Benchmark Test 3 (take in early February) . . . . . . . . . . . . .132–141

Steps to Success Page(s)

Road Map to TAKS SuccessAn Annotated Table of Contents

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Directions Mark a ✓ by each question from the Diagnostic Test that you answer correctly. If there are more than one or two questions not marked for a benchmark, write Yes in the Need Practice? box. Then complete the practice pages for that benchmark.

TEKS A.1(A) A.1 (B) A. 1.(C) A.1(D) A.1(E) A.2(A) A.2(B) A.2(C) A.3(A)

TAKS Objective 1 1 1 1 1 2 2 2 2

Test Questions 5 o 8 o 13 o 22 o 39 o 29 o 1 o 51 o 55 o

Need Practice?

Practice Pages 11 12 13 14 15 16 17 18 20

TEKS A.3(B) A.4(A) A.4(B) A.5(C) A.6(A) A.6(B) A.6(C) A.6(D) A.6(E)



Need Practice?

Practice Pages 21 22 23 25 26 27 28 29 30

TEKS A.6(F) A.6(G) A.7(A) A.7(B) A.7(C) A.8(A) A.8(B) A.9(B) A.9(C)



Need Practice?

Practice Pages 31 32 33 34 35 36 37 39 40

TEKS A.9(D) A.10(A) A.10(B) A.11(A) G.4(A) G.5(A) G.5(B) G.5(C) G.6(C)



Need Practice?

Practice Pages 41 42 43 44 45 46 47 48 51

TEKS G.7(A) G.7(B) G.7(C) G.8(A) G.8(B) G.8(C) G.8(D) G.9(D) G.10(A)



Need Practice?

Practice Pages 52 53 54 56 57 58 59 55 49

TEKS G.11(A) G.11(B) G.11(C) 8.3(B) 8.11(A) 8.11(B) 8.12(C) 8.13(B) 8.14(A)

TAKS Objective 8 8 8 9 9 9 9 9 10

Test Questions 47 o 56 o 32 o 15 o 28 o 45 o 57 o 59 o 6 10 o

Need Practice?

Practice Pages 60 61 62 64 65 66 68 69 70

TEKS 8.14(B) 8.14(C) 8.15(A) 8.16(A) 8.16(B)

TAKS Objective 10 10 10 10 10

Test Questions 21 o 2 o 44 o 54 o 52 o

Need Practice?

Practice Pages 71 72 73 74 75

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Student Recording Chart

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Texas Essential Knowledge and Skills

2A.1 FOUNDATIONS FOR FUNCTIONS.The student uses properties and attributes of functions and applies functions to problem situations. The student is expected to:(A) identify the mathematical domains and ranges of functions and determine reasonable

domain and range values for continuous and discrete situations; and

(B) collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

2A.2 FOUNDATIONS FOR FUNCTIONS.The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to:(A) use tools including factoring and properties of exponents to simplify expressions and

to transform and solve equations; and

(B) use complex numbers to describe the solutions of quadratic equations.

2A.3 FOUNDATIONS FOR FUNCTIONS.The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.(A) analyze situations and formulate systems of equations in two or more unknowns or

inequalities in two unknowns to solve problems;

(B) use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and

(C) interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

2A.4 ALGEBRA AND GEOMETRY.The student connects algebraic and geometric representations of functions. The student is expected to:(A) identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic

(f(x) = x2), exponential (f(x) = ax), and logarithmic (f(x) = logax) functions, absolute

value of x (f(x) = |x|), square root of x (f(x) = √__

x ), and reciprocal of x (f(x) = 1/x);C

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Texas Essential Knowledge and Skills for Mathematics, Algebra II

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(B) extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and

(C) describe and analyze the relationship between a function and its inverse.

2A.5 ALGEBRA AND GEOMETRY.The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to:(A) describe a conic section as the intersection of a plane and a cone;

(B) sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

(C) identify symmetries from graphs of conic sections;

(D) identify the conic section from a given equation; and

(E) use the method of completing the square.

2A.6 QUADRATIC AND SQUARE ROOT FUNCTIONS.The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to:(A) determine the reasonable domain and range values of quadratic functions, as well as

interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

(B) relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and

(C) determine a quadratic function from its roots or a graph.

2A.7 QUADRATIC AND SQUARE ROOT FUNCTIONS.The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to:(A) use characteristics of the quadratic parent function to sketch the related graphs and

connect between the y = ax2 + bx + c and the y = a(x - h)2 + k symbolic representations of quadratic functions; and

(B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a function in applied and purely mathematical situations.

2A.8 QUADRATIC AND SQUARE ROOT FUNCTIONS.The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:(A) analyze situations involving quadratic functions and formulate quadratic equations or

inequalities to solve problems;

(B) analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

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(C) compare and translate between algebraic and graphical solutions of quadratic equations; and

(D) solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

2A.9 QUADRATIC AND SQUARE ROOT FUNCTIONS.The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:(A) use the parent function to investigate, describe, and predict the effects of parameter

changes on the graphs of square root functions and describe limitations on the domains and ranges;

(B) relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

(C) determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

(D) determine solutions of square root equations using graphs, tables, and algebraic methods;

(E) determine solutions of square root inequalities using graphs and tables;

(F) analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and

(G) connect inverses of square root functions with quadratic functions.

2A.10 RATIONAL FUNCTIONS.The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:(A) use quotients of polynomials to describe the graphs of rational functions, predict the

effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

(B) analyze various representations of rational functions with respect to problem situations;

(C) determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

(D) determine the solutions of rational equations using graphs, tables, and algebraic methods;

(E) determine solutions of rational inequalities using graphs and tables;

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(F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and

(G) use functions to model and make predictions in problem situations involving direct and inverse variation.

2A.11 EXPONENTIAL AND LOGARITHMIC FUNCTIONS. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:(A) develop the definition of logarithms by exploring and describing the relationship

between exponential functions and their inverses;

(B) use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

(C) determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

(D) determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

(E) determine solutions of exponential and logarithmic inequalities using graphs and tables; and

(F) analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

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x Mastering the TAKS, Grade 11

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Directions Mark a ✓ by each question from the Benchmark Test that you answer correctly. The goal is to gain more ✓s with each Benchmark Test you take.

Test 1 Test 2 Test 3

Strand Date: Date: Date:

Objective 1 Questions:® 1 ® 15® 2 ® 30

Questions:® 2 ® 15® 1 ® 30

Questions:® 2 ® 15® 1 ® 30

Objective 2 Questions:® 5 ® 22 ® 43® 4 ® 25 ® 60® 10 ® 32

Questions:® 5 ® 22 ® 43® 4 ® 25 ® 60® 10 ® 32

Questions:® 5 ® 22 ® 43® 4 ® 25 ® 60® 10 ® 32


Questions:® 6 ® 23 ® 38® 13 ® 29 ® 57® 14 ® 33

Questions:® 6 ® 23 ® 38® 13 ® 29 ® 57® 14 ® 33

Objective 4 Questions:® 3 ® 44 ® 55® 24 ® 51

Questions:® 3 ® 44 ® 55® 24 ® 51

Questions:® 3 ® 44 ® 55® 24 ® 51

Objective 5 Questions:® 9 ® 34 ® 49® 11 ® 42 ® 53

Questions:® 9 ® 34 ® 49® 11 ® 42 ® 53

Questions:® 9 ® 34 ® 49® 11 ® 42 ® 53

Objective 6 Questions:® 7 ® 27 ® 41® 18 ® 35

Questions:® 7 ® 27 ® 41® 18 ® 35

Questions:® 7 ® 27 ® 41® 18 ® 35


Questions:® 12 ® 19 ® 54® 16 ® 48 ® 59

Questions:® 12 ® 19 ® 54® 16 ® 48 ® 59


Questions:® 8 ® 31 ® 56® 20 ® 39 ® 58® 26 ® 48

Questions:® 8 ® 31 ® 56® 20 ® 39 ® 58® 26 ® 48


Questions:® 17 ® 37 ® 46® 36 ® 40 ® 50

Questions:® 17 ® 37 ® 46® 36 ® 40 ® 50

Objective 10 Questions:® 21 ® 45® 28 ® 52

Questions:® 21 ® 45® 28 ® 52

Questions:® 21 ® 45® 28 ® 52

Mastery of Objectives Chart

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Perimeterrectangle P = 2� + 2w or

P = 2(� + w)

Circumferencecircle C = 2πr or C = πd

Arearectangle A = �w or A = bh

triangle A = 1 _ 2 bh or A = bh __ 2

trapezoid A = 1 _ 2 (b1 + b2)h or

A = (b1 + b2)h _______ 2

circle A = πr2

Surface Areacube S = 6s2

cylinder (lateral) S = 2πrh

cylinder (total) S = 2πrh + 2πr2 or

S = 2πr(h + r)

cone (lateral) S = πr�

cone (total) S = πr� + πr2 or

S = πr(� + r)

sphere S = 4πr2

Volumeprism or cylinder V = Bh*

pyramid or cone V = Bh*

sphere V = πr3

Piπ ≈ 3.14 or π ≈ 22 __ 7

Pythagorean Theorema2 + b2 = c2

Slope of a Line

m = y2 − y1 _____ x2 − x1

Standard Form of an EquationAx + By = C

Slope-Intercept Form of an Equationy = mx + b

Point-Slope Form of an Equationy − y1 = m(x − x1)

Distance Formulad = √

__________________

(x2 − x1)2 + (y2 − y1)

2

Midpoint Formula

M = ( x1 + x2 _____ 2 , y1 + y2 _____ 2 )

Quadratic Formula

x = -b ± √

________

b2 - 4ac ___________ 2a

*B represents the area of the base of a solid figure.

Mathematics Chart

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xii Mastering the TAKS, Grade 11

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LENGTH

Metric

1 kilometer = 1000 meters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

Customary

1 mile = 1760 yards

1 mile = 5280 feet

1 yard = 3 feet

1 foot = 12 inches

CAPACITY AND VOLUME

Metric

1 liter = 1000 milliliters

Customary

1 gallon = 4 quarts

1 gallon = 128 ounces

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 ounces

MASS AND WEIGHT

Metric

1 kilogram = 1000 grams

1 gram = 1000 milligrams

Customary

1 ton = 2000 pounds

1 pound = 16 ounces

TIME

1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Mathematics Chart

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Name Date

Mastering the TAKS, Grade 11 1

Diagnostic Test

Read each question and choose the

correct answer.

1 Which inequality best describes the domain of the function represented by the graph? A.2(B)

y

xO

A x ≥ 0B x ≤ 3C y ≥ 0D y ≤ 3

2 Esau wants to solve the equation 3y + 2 = 5 - y by graphing. Which method can he use to fi nd the solution for y? 8.14(C) F Graph the line x = 3y + 2 and fi nd

the y-intercept.G Graph the line x = 3y + 2 and fi nd

the x-intercept.H Graph the lines x = 3y + 2 and

x = 5 - y and fi nd the x-coordinate of the intersection.

J Graph the lines x = 3y + 2 and x = 5 - y and fi nd the y-coordinate of the intersection.

3 Which statement best describes what happens to the graph of y = ax2 when the value of a is changed from 2 to -2?A.9(B) A The graph translates 2 units down.B The graph translates 4 units down.C The graph translates 4 units up.D The graph is rotated 180°.

4 The line represented by the equation y = 2x - 1 is graphed below.

y

xO

Which of the following best describes the effect on the graph when the slope is halved? A.6(C) F The y-intercept increases.G The y-intercept decreases.H The x-intercept increases.J The x-intercept decreases.

5 Texas’s state sales tax rate is 6.25%. Which statement best represents the functional relationship between the tagged price of a taxable item and the total amount paid, including tax? A.1(A)

A The tagged price is dependent on the total amount paid.

B The total amount paid is dependent on the tagged price.

C The tagged price and the total amount paid are independent of each other.

D The relationship cannot be determined.

6 The area of a triangle is 72m4n9 square units. If the height of the triangle is 8m2n3 units, what is the triangle’s base? A.11(A) F 3m2n3

G 9m2n6

H 18m2n3

J 18m2n6

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Name Date

Diagnostic Test (continued)

2 Mastering the TAKS, Grade 11

7 Which of the following is a true statement about the net of the cube shown below, after it is folded to make a cube? G.6(C)

321

4

5 6

A Faces 1 and 2 are parallel.B Faces 1 and 3 are perpendicular.C Faces 2 and 3 are perpendicular.D Faces 2 and 4 are parallel.

8 Which equation best describes the relationship between x and y shown in the table below? A.1(B)

x y1 12 83 274 64

F y = 4xG x = 4yH x = y3

J y = x3

9 A tractor-trailer’s gas tank is fi lling at a rate that can be represented by the equation y = 15t + 10. What would an increase in slope indicate? A.6(F) A The tank is fi lling more slowly.B The tank is fi lling more quickly.C The tank started out with more gas in it.D The tank started out with less gas in it.

10 An engraved plaque costs $15 plus $0.49 per engraved character, with the 8th character provided for free. The Austin Bowling League orders 3 plaques with “1st Place,” “2nd Place,” and “3rd Place” engraved, respectively. What is a reasonable conclusion about p, the total price of all 3 plaques? 8.14(A) F 40 < p ≤ 45G 45 < p ≤ 50H 50 < p < 60J 60 < p ≤ 70

11 A manager at a department store calculated his commission c using the equation c = 0.002s + 25, where s is the total amount of sales. If the store sold between $100,000 and $120,000 in merchandise, the amount of the manager’s commission should be between which of these amounts? A.7(C) A $50 and $60B $75 and $85C $200 and $240D $225 and $265

12 A regular polygon is composed of equal-sized triangles. If you are given the base and height of each triangle, what additional information is needed to determine the area of the polygon? 8.14(A) F the area of each triangleG the length of each triangle’s third legH the length of one side of the polygonJ the number of triangles that make up

the polygon

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13 A long-distance phone call costs $1 for the fi rst minute and $0.15 for every minute thereafter. Which equation expresses c, the total cost of a long distance phone call in terms of m, the number of minutes used? A.1(C) A c = $0.15mB c = $1 + 0.15mC c = $0.15(m – 1)D c = $1 + $0.15(m – 1)

14 What is the approximate area of the unshaded part of the regular hexagon below if its horizontal line of symmetry measures 4 cm? G.8(A)

2 cm

F 1.7 cm2

G 3.5 cm2

H 6.9 cm2

J 8 cm2

15 Mark runs a 26-mile race in 3.5 hours. If Rose runs at the same speed, approximately how long will it take her to complete a 10-mile race? 8.3(B) A 1.25 hrB 1.35 hrC 7 hrD 9.1 hr

16 Find the slope of the line identifi ed by the equation 3x + 2y = 4. A.6(A) F –3

G – 3 _ 2

H 3 _ 2

J 4

17 Sharisse scored y points on her history test by answering 18 questions correctly. She scored an average of 8 points for each correct essay answer, and 2 points for each correct multiple choice answer. If x is the number of multiple choice questions Sharisse answered correctly, which equation can be used to fi nd y? A.7(A) A y = 2x + 8(x – 18)B y = 2x + 8(18 – x)C y = 8x + 2(x – 18)D y = 8x + 2(18 – x)

18 Use the table below to determine the expression that best represents the sum of the angle measures of a polygon with n sides. G.5(B)

Polygon Number of Sides

Sum of Angle Measures

Triangle 3 180°Quadrilateral 4 360°Pentagon 5 540°Hexagon 6 720°

F 60nG 90(n –1)H 120nJ 180(n – 2)


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19 Triangle FGH has vertices at (0, 2), (1, 4), and (4, 0). A triangle with which coordinates is congruent to triangle FGH? G.10(A) A (0, 0), (-1, 2), and (2, 2)B (0, 0), (1, 2), and (3, 2)C (1, 1), (2, 3), and (3, 4)D (1, 1), (2, 3), and (5, -1)

20 A pentagon is graphed on the coordinate grid. Which two coordinate points fall on the same line of symmetry? G.7(A)

y

xO

F (0, 0) and (2, 0)G (0, 0) and (0, 3)H (-2, -1) and (2, 1)J (-2, -2) and (2, -2)

21 A rectangle is shown below. 8.14(B)

4 cm

1.5 cm

How many of these rectangles can fi t together without any gaps to make a fi gure with a base of 12 cm and an area of 72 cm2?A 24B 12C 8D 6

22 The graph is the solution for which inequality? A.1(D)

y

xO

F y < 3 _ 2

x - 1

G y > 3

_ 2

x - 1

H y < 2 _ 3

x - 1

J y > 2 _ 3

x - 1

23 A carpeted square room measures 12 ft × 12 ft. Taye rips up the carpeting and puts it in a rectangular room with a length of 16 ft. If the new carpeting arrangement fi ts the rectangular room with none left over, what is the width of the room? G.4(A) A 3 ftB 9 ftC 32 ftD 36 ft

24 The graph of y = -x2 + c is a parabola with its vertex at (0, 1). Which of the following is true about the value of c? A.9(C) F c < 0G c > 0H c = 0J c = –1


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25 The ordered pair (- 1 _ 3 , 0) is a root of

which quadratic function? A.10(B)

A f(x) = 3x2 – 2x - 1

B f(x) = 3x2 - 1

C f(x) = x2 - 1 _ 3

D f(x) = x2 + 1 _ 9

26 Sweder’s Hardware carries k yards of oak, which sells for $3.75 a yard, and m yards of maple, which sells for $4.50 a yard. When a builder asks for a mixture of the two kinds of wood, Sweder’s sells him 50 yards at a price of $4.00 a yard. Which system of equations can be used to fi nd the number of yards of each kind of wood the builder received? A.8(A) F k + m = 50 375k + 450m = 4(50)G k + m = 50 3.75k + 4.50m = 4(50)H k + m = 50 450k + 375m = 4(50)J k + m = 50 4.50k + 3.75m = 4(50)

27 Which equation best represents the line on the graph? A.5(C)

y

xO

A 2y - x = -3B 2y + x = -3C 2y - x = -5D x - 2y = -3

28 A bag contains 5 red marbles, 6 blue marbles, and 9 green marbles. What is the probability that 2 red marbles will be drawn fi rst? 8.11(A)

F 1 _ 20 H 2 _ 19

G 1 _ 19 J 1 _ 10

29 Which graph best represents the function y = 1 – x2? A.2(A) A y

xO

B y

xO

C y

xO

D y

xO


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30 What are the coordinates of the x-intercept of the equation –2y = 7 – 3x? A.6(E)

F ( 0, – 7 _ 2 ) H ( 0,

3 _ 2 )

G ( – 7 _ 3 , 0 ) J ( 7 _ 3 , 0 )

31 Which two lines are perpendicular? G.7(B) A y = 3x + 5 and y = 6x + 2y = 0B y = 2x – 1 and 2x – 4y = 6C y = x – 7 and x – y = 7D y = 3 – x and 3y – 3x = 0

32 Right triangle ABC is similar to triangle FGH. The ratio of corresponding sides of triangle ABC and triangle FGH is 1:2. The height of triangle ABC is 4 in. and its area is 6 in.2. What is the length of the hypotenuse for triangle FGH? G.11(C) F 5 in. H 8 in.G 6 in. J 10 in.

33 The fi rst three stages of a fractal are shown below. G.5(C)

In the fourth stage of the fractal, how many triangles will be of the smallest size?A 3 C 9B 6 D 12

34 Which best represents the solution to the equation x2 – 1 = 0? A.4(A) F 1G –1H –1 and 1J 0

35 The equations of two lines are y = 2x and 2x – 4y = 12. Which of the following describes their point of intersection? A.8(B) A (–2, –4)B (–1, –2)C (0, 0)D There is no intersection.

36 The height of an electron in a cloud chamber, y, is related to its horizontal position, x, by the equation y = 100 – x – x2. If the electron is at a height of 28 units, what is its horizontal position? A.10(A) F 8G 9H 10J 28

37 A sphere has a diameter of 6 feet. What is the approximate volume of the sphere? G.8(D) A 27 ft3

B 113 ft3

C 452 ft2

D 904 ft3

38 What is the approximate length of QR¯¯¯ when the coordinates of its endpoints are (–2, –5) and (1, 2)? G.7(C) F 3.2 unitsG 5.4 unitsH 7.6 unitsJ 10.8 units


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39 The cost of oil increased over the fi rst 3 months of the year. It then remained steady over the next 3 months. Which graph best describes this situation? A.1(E) A

Co

st

Time

B

Co

st

Time

C

Co

st

Time

D

Co

st

Time

40 Which 3-dimensional fi gure has 4 faces? G.9(D) F rectangular prismG square pyramidH triangular prismJ triangular pyramid

41 A rectangle has a length of 12 cm. Its diagonal measures 15 cm. What is the area of the rectangle? G.8(C) A 54 cm2 C 135 cm2

B 108 cm2 D 180 cm2

42 The shaded area in the circle below represents the section of a circus ring that is roped off.

15 ft

75˚

What is the approximate area of the section of the circus ring that is NOT roped off? G.8(B) F 147 sq ft H 706 sq ftG 559 sq ft J 3,532 sq ft

43 Ms. Franklin’s students measured the growth of the Texas state insect, the monarch butterfl y, from egg to adult. Their data is shown in the table below.

Time (Days) Length (cm)

1 0.1252 0.2505 0.625

If the butterfl y continues to grow at the rate shown in the table, what is its approximate length in centimeters on day 15? Record your answer and fi ll in the bubbles in the answer grid below. A.6(G)

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0


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44 A mathematician determined the relationship between A, the area of a circle, and C, the circumference of a circle. Which equation represents this relationship? 8.15(A)

A A _ C = π

_ r C A _ C = r _ 2

B A _ C = 1 _ 2 D A _ C = 2 _ r

45 A carnival spin wheel has 16 equal sections marked either Win or Lose. If the spinner lands on Win six times out of 100 spins, which is the most likely number of Lose sections on the wheel? 8.11(B) F 1G 6H 10J 15

46 The graph below shows the height of a paper airplane from the time it is thrown until the time it hits the ground.

y

x

Heig

ht (f

t)

8

4

0

12 14 16

18 20

22

6

2

10

1 2 3 4

Time (sec)

How much time elapses while the paper airplane is 12 feet or higher in the air? A.9(D) A 2 secB 2.5 secC 5 secD 6 sec

47 Trapezoid FGHY is similar to trapezoid ABCD, which is shown below.

A B

CD

3 cm

6 cm 6 cm

9 cm

Which of the following could be the side lengths of trapezoid FGHY? G.11(A) F 6 cm, 9 cm, 9 cm, 12 cmG 5 cm, 8 cm, 8 cm, 11 cmH 4 cm, 6 cm, 6 cm, 12 cmJ 1 cm, 2 cm, 2 cm, 3 cm

48 Which equation represents the line that passes through the points at (2, –1) and (5, 0)? A.6(D)

A y = 1 _ 3 x – 2 _ 3

B y = 1 _ 3 x – 5 _ 3

C y = 1 _ 3 x + 1 _ 3

D y = 1 _ 3 x + 5 _ 3

49 The table below shows a pattern that continues infi nitely. A.3(B)

Input 3 4 5 6Output 3 8 15 24

Which expression can be used to determine the output in the nth step?F nG 2nH 4nJ n(n - 2)


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50 Which expression is equivalent to

1 _ 2 (2x + 6y) – (4y – 8x)? A.4(B)

A y – 3x C 5x + yB –7x – y D 9x – y

51 The graph below shows Olympic viewership, by age, for the 2006 Winter Olympics.

0

46–6

0

31–4

5

16–3

00–

15 60+V

iew

ers

(mill

ion

s)

Age Range

4

3

2

1

Which is the most reasonable conclusion about the data? A.2(C) F Viewers aged 60 and above watched the

least coverage.G Viewers 15 and under watched the least

coverage.H Viewership increased as age increased.J Viewership decreased as age increased.

52 Given: Two angles are complementary. The measure of one angle is 30° less than the measure of the other angle.

Conclusion: The measures of the angles are 105° and 75°. 8.16(B)

Which statement below is true?A The conclusion is contradicted by the

fi rst statement given.B The conclusion is verifi ed by the fi rst

statement given.C The conclusion invalidates itself

because a 75° angle cannot be complementary to another angle.

D The conclusion verifi es itself because 75° is 30° less than 105°.

53 What is the y-intercept of the line graphed below? A.6(B)

y

xO

F – 3 _ 2 H 2

G 3 _ 2 J 3

54 Raheem claimed that the area of a circle is always greater than its circumference. Which of the following examples disproves Raheem’s claim? 8.16(A) A a circle with a radius of πB a circle with a radius of 4C a circle with a radius of 1D Raheem’s claim cannot be disproven.

55 In 2004, the U.S. population was about 1,350,000 more than 13 times the population of Texas. If x represents the population of Texas, which expression can be used to determine the population of the U.S.? A.3(A) F 1,350,000 – 13x

G 13x + 1,350,000

H x _ 13 + 1,350,000

J 13x – 1,350,000


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56 A triangle has a height of 12 cm and an area of 60 cm2. What is the area of a similar triangle with a height of 6 cm? G.11(B) A 15 cm2 C 60 cm2

B 30 cm2 D 120 cm2

57 A circle graph of the survey data in the table below is constructed.

Voted forNumber of

Respondents

Incumbent 72Opponent 80Neither 36Undecided 12

What percent of the circle graph is represented by respondents who said “Neither”? 8.12(C) F 1.8%G 12%H 18%J 36%

58 Use the graph of y = 2 – 1 _ 2 x to solve the

equation for x when y = 0. A.7(B)

y

xO

A x = –2B x = 2C x = 3D x = 4

59 The table below shows the cost of a basket containing various numbers of apples. 8.13(B)

Number of Apples Cost

6 $3.0012 $5.4018 $7.2024 $8.00

Which conclusion can be made based on the information in the table?F A single apple costs $0.50.G Apples are always more than $0.35

apiece.H The cost of 20 apples would be $7.50.J The cost of 30 apples would be $10.00

or less.

60 Triangle XYZ, shown below, is a right triangle. If the length of its shortest side is 5 cm, what is the length of its hypotenuse? G.5(D)

12 cm

Y

X

Z

A 2.5 cmB 12 cmC 13 cmD 17 cm



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best answer.

1 Brazos County adds a local tax rate of 2% on top of the 6.25% levied by the state. Which statement best represents the functional relationship between the amount paid for a taxable item in Brazos County and the state/local tax rates? A The amount paid is dependent on only

the local tax rate.B The amount paid is dependent on only

the state tax rate.C The amount paid is dependent on both

the local and state tax rates.D The relationship cannot be determined.

2 The formula for the perimeter, P, of a square is P = 4s, where s is the length of a side. Which statement best describes the functional relationship represented by the formula? F P is an independent variable.G s is an independent variable.H P and s are both independent variables.J P and s are both dependent variables.

3 Carlos’ commission is 3% of his total sales. Which statement best represents the functional relationship between the total amount of Carlos’ sales and his commission?A His total sales are dependent on his

commission.B His commission is dependent on his

total sales.C His total sales and his commission are

independent of each other.D The relationship cannot be determined.

4 The formula for a line is y = mx + b, where m is the slope and b is the y-intercept. Which variable is dependent on all the others? F yG mH xJ b

5 Sheila earns $5.00 per hour babysitting and $6.50 per hour working the counter at the deli. Which statement best represents the functional relationship between the total amount of money Sheila earns in a month and the number of hours she works? A Her total monthly pay is dependent on

only the number of hours she babysits.B Her total monthly pay is dependent on

only the number of hours she works at the deli.

C The number of hours she works at each job is dependent on her total pay.

D Her total monthly pay is dependent on both the number of hours she babysits and the number of hours she works at the deli.

6 The formula for the area, A, of a triangle is

A = 1 _ 2 bh, where b is the base and h is the

height. Which statement best describes the functional relationship represented by the formula? F b is dependent on h.G h is dependent on b.H b and h are dependent on A.J A is dependent on b and h.

A.1(A) The student is expected to describe independent and dependent quantities in functional relationships.

TAKS PracticeOBJECTIVE 1

011-075_OB_TX_877327.indd 11011-075_OB_TX_877327.indd 11 6/28/06 3:53:04 PM6/28/06 3:53:04 PM

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best answer.

1 Which equation best describes the relationship between a and b shown in the table below?

a b

1 22 53 84 11

A b = 2a C b = 3a - 1

B a = 2b D a = 1 _ 2 b

2 The surface area, S, of a cube is represented by the function S = 6� 2, where � is the length of a side. What is the value of � when S = 24? F 2 H 576G 4 J 3456

3 A botanist measured a plant’s growth by using the data shown below.

Time, t(weeks)

Growth, g(mm)

0 0.01 2.52 10.03 22.5

Which equation best represents the relationship between g, the plant’s growth, and t, the passage of time? A g = 2.5t C g = 5tB g = 2.5t2 D g = t3 +1.5

4 The Texas Bake Shop sets its price for a dozen doughnuts according to the data shown below.

Time, t (hr) Price, p ($)

0 5.001 4.502 4.003 3.50

Which equation best represents the relationship between p, the price, and t, the time?

F p = 5 - t H t = p _ 5

G p = 5 - 1 _ 2 t J t = p _ 5 + 2

5 George has determined that his test scores, s, are represented by the function s = 68 + 2t, where t is the number of hours he sleeps the night before. If George slept 8 hours last night, what score is he most likely to receive on his math test today? A 68 C 80B 70 D 84

6 A San Antonio catering service has determined that the number of gallons of drink, d, they must provide is represented by the function d = √

__ g + 1, where g is

the number of guests. If the company is catering a party with 64 guests, how many gallons of drink do they need? F 8 H 3969G 9 J 6561

A.1(B) The student is expected to gather and record data and use data sets to determine functional relationships between quantities.


011-075_OB_TX_877327.indd 12011-075_OB_TX_877327.indd 12 6/30/06 9:28:48 AM6/30/06 9:28:48 AM


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best answer.

1 The total mass of a treasure chest full of gold bars is 150 pounds. The bars have an average mass of 3 pounds. Which equation expresses e, the mass of the empty chest, in terms of g, the total number of gold bars? A e = 150 + 3gB e = 150 - 3g

C e = 150

_ g

D e = 3g

2 At the beginning of a fundraiser, the cashbox contained $50. If each fundraising ticket cost $5, which equation best describes c, the total amount of cash in the cashbox after t tickets have been sold? F c = 50 + tG c = 50 - tH c = 50 + 5tJ c = 5t

3 Sharon must read a 400-page book in a month. If she reads about 25 pages each day, which equation best describes p, the number of pages she has left after d days of reading? A p = 25dB p = 400 - dC p = 400 + 25dD p = 400 - 25d

4 A full box of tomatoes weighs p pounds. The packing materials weigh 2 pounds. If there are 54 tomatoes in the box, which equation best describes t, the weight of a single tomato, in terms of p? F t = 54p

G t = p _ 54

H t = 54(p - 2)

J t = (p - 2)

_ 54

5 Jamar has observed that at dusk, the height of his shadow, s, is half his standing height, h. Which equation best represents this relationship?

A h = 1 _ 2 s

B s = 1 _ 2 h

C h = s - 1 _ 2

D s = h - 1 _ 2

6 An orchard owner has noticed that on average, a tree’s apple production, a, is triple its circumference, c. Which equation best represents this relationship? F a = c + 3G a = c - 3H a = 3c

J a = c _ 3

A.1(C) The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations.



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best answer.

1 Which graph best represents the inequality y - x > -1? A y

xO

B y

xO

C y

xO

D y

xO

2 The following graph is the solution for which inequality?

y

xO

F y < x - 2 H y ≤ x - 2G y > x - 2 J y ≥ x - 2

3 Which point falls in the solution of the inequality y ≥ 2x + 1? A (-1, -2) C (2, 0)B (1, 3) D not here

4 Which point falls in the solution of the

inequality y < 2 - 1 _ 2 x?

F (0, 3) H (1, 1)G (1, 2) J (3, 1)

5 Which point does NOT fall in the solution of the inequality y + 2x < 3? A (1, 1) C (-1, -1)B (0, 0) D (-2, -2)

6 Which point does NOT fall in the solution of the inequality x - y ≥ -1? F (-2, 0) H (0, 0)G (-1, 0) J (1, 0)

A.1(D) The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.




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best answer.

1 At the Texas Motor Speedway, the cars increased their pace until the caution fl ag was dropped 15 seconds into the race. They then decreased their pace until they hit caution speed, after which time their speed remained steady. Which graph best describes this situation? A

Spee

d

Time

B

Spee

d

Time

C

Tim

e

Speed

D

Tim

e

Speed

2 The tax, t, on a piece of property is represented by the equation t = 500 + 0.02a, where a is the property’s assessed value. Which is the best interpretation of the data? F A property with an assessed value of $0

is not taxed.G The tax on a piece of property is at

least $500.H The greater a property’s assessed value,

the less tax is owed.J The assessed value of a property is

dependent on the tax owed.

3 After applying the “curve,” the test scores, s, for Mr. Browden’s students were represented by the equation s = 5q + 15, where q was the number of questions answered correctly. How many questions did a student have to answer correctly to earn a perfect score of 100? A 3 C 17B 15 D 20

4 The average cost, c, of a used vehicle at Texas Trade-Ins is represented by the equation c = $20,000 - $1000y, where y is the age in years of the vehicle. Which is the best interpretation of the data? F All vehicles cost $20,000 or more.G A vehicle that is at least 20 years old is

free.H The older the vehicle, the more

expensive it is.J Texas Trade-Ins earns a profi t on all

used vehicles.

A.1(E) The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships.



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best answer.

1 Which equation is the parent function of the graph represented below?

y

xO

A y = xB y = √

_ x

C y = x2

D y = -x2

2 Which type of parent function is represented by the function graphed below?

y

xO

F absolute valueG exponentialH linearJ quadratic

3 Which equation is the parent function of the graph represented below?

y

xO

A y = �x�

B y = -xC y = xD y = -x2

4 Which type of parent function is represented by the function graphedbelow?

y

xO

F absolute valueG exponentialH linearJ quadratic

A.2(A) The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions.




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best answer.

1 Which inequality best describes the range of the function represented by the graph?

y

xO

A -2 < x < 2B -2 ≤ x < 2C -1 ≤ y < 3D -1 < y ≤ 3

2 What is the domain of the function shown in the graph?

y

xO

F y ≥ 0G y > 0H x ≥ -2J x > -2

3 What is the domain of the function y = x + 2 for the range -1 ≤ y ≤ 2? A 0 < x < 3B 0 ≤ x ≤ 3C -3 < x < 0D -3 ≤ x ≤ 0

4 What is the range of the function y = 2x - 1 for the domain 0 < x < 3? F -1 < y < 5G -1 ≤ y ≤ 5

H 1 _ 2 < y < 2

J 1 _ 2 ≤ y ≤ 2

5 What is the domain of the function y = x2 - 1 for the range 3 < y < 8? A -3 < x < -2B -3 < x < 3C -3 < x < 2D 2 < x < 3

6 What is the range of the function y = 2 - x2 for the domain -1 ≤ x ≤ 2? F -2 ≤ y ≤ 1G -2 < y < 1H -1 ≤ y ≤ 2J -1 < y < 2

A.2(B) The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete.



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best answer.

1 The graph below shows the decrease in Kris’ weight over a 6-month period while she was on a diet.

Wei

gh

t ( l

b)

145

155

135

0

165

175

Time (months)321 54 6

Which is a reasonable conclusion about Kris’ weight during the time shown on the graph? A Kris lost weight during every

consecutive month on the diet.B Kris’ weight decreased by 10 pounds

every month.C Kris gained weight between the 4th and

5th months.D Kris gained weight between the 5th and

6th months.

2 The graph below shows the increase in the cost of a gallon of gasoline over an 8-week period.

Co

st( $

)

150

200

1

0

250

300

Time (weeks)321 5 74 6 8

Which is a reasonable conclusion about the cost of gasoline during the time shown on the graph? F Its cost at 2 weeks was half its cost at

6 weeks.G Its cost at 1 week was twice its cost at

6 weeks.H It appreciated $0.50 every 2 weeks.J It depreciated $0.50 every 2 weeks.

3 A landscaper in Dallas received the bids shown in the graph below for cedar chips.

X X

X X

X X

X XX

Key:FennelGregoryHoweJacksonC

ost

/to

n( $

)

100

50

0

150

Weight (tons)321 54 6

If the landscaper needs 5 tons of cedar chips, which bidder is the cheapest? A Fennel C HoweB Gregory D Jackson

A.2(C) The student is expected to interpret situations in terms of given graphs or create situations that fi t given graphs.




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best answer.

1 The scatter plot below shows data collected by a doctor.

Hei

gh

t (i

n.)

20

30

10

0

40

50

60

Age642 108 12

Which is the patient’s most likely height at 12 years? A 58 in. C 72 in. B 63 in. D 75 in.

2 At the beginning of her speed-reading course, Bonnie could read 150 words per minute. At the course’s midpoint, she could read 225 words per minute. If her reading speed increased linearly throughout the course, what was Bonnie’s reading speed upon completion? F 150 words/min H 275 words/minG 225 words/min J 300 words/min

3 At the beginning of the track season, Rajiv’s hurdle time was 32 seconds. At the middle of the season it was 28 seconds. If his time decreased linearly throughout the season, what was Rajiv’s hurdle time at the end of the track season? A 24 sec C 32 secB 28 sec D 36 sec

4 Andrea collected the data shown in the table below.

Input 12 7 2 15Output 15 2 12 7

Which input value produced the greatest output value? F 2G 7H 12J 15

5 The scatter plot below shows April rainfall data collected by a meteorologist.

Rai

nfa

ll (i

n.)

2

3

1

0

4

5

6

Year

April Rainfall

2004

2003

2002

2006

2005

Which is the most likely rainfall for April 2007? A 2 in.B 3 in.C 4 in.D 5 in.

A.2(D) The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.



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best answer.

1 Let c represent the cost of a lunch in the school cafeteria. Let f(c) represent the total cost spent on lunches after d days. What is the best representation of f(c)? A c + dB c - d

C c _ d

D cd

2 Let c represent the cost of a bag of apples. Let f(a) represent the cost of a single apple if there are a apples in a bag. What is the best representation of the function f(a)? F a + cG c - a

H c _ a

J ac

3 Maya is 5 years younger than twice her brother’s age. If y represents Maya’s brother’s age, which expression can be used to determine Maya’s age? A y - 5B 2y - 5C 2yD 2y + 5

4 Jose sold 7 more than half as many raffl e tickets as Miriam did. If t represents the number of tickets Miriam sold, which expression can be used to determine how many tickets Jose sold? F 2t + 7G t + 7

H 1 _ 2 t

J 1 _ 2 t + 7

5 Let h represent Mrs. Abda’s height with shoes on. Let f(h) represent her height without shoes. If the height of her shoes is s, then what is the best representation of the function f(h)? A hs

B h _ s

C h - sD h + s

6 Let p represent the cost of a painting. Let f(p) represent the cost of the painting when it is framed. If the cost of the frame is f, then what is the best representation of the function f(p)? F p + fG p - fH pf

J p _

f

A.3(A) The student is expected to use symbols to represent unknowns and variables.




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best answer.

1 The table below shows a pattern that continues infi nitely.

Input 1 2 3 4Output -1 1 3 5

Which expression can be used to determine the output in the nth step? A -n C n - 1B 1 _

2 n D 2n - 3

2 The table below shows a pattern that continues infi nitely.

Gross Pay($)

100.00 150.00 200.00 250.00

Tax($) 25.00 37.50 50.00 62.50

Which expression can be used to determine the tax on $n? F n - 75 H n _

4

G 4n J n + 75

3 The pattern of circles shown below continues infi nitely, with more circles being added at each step.

Step 1 Step 2 Step 3

Which expression can be used to deter-mine the number of circles in step n? A n + 4 B 2(n + 1)C 4n D n2 + 2

4 In a trivia game, fi rst round questions are worth 2 points, second round questions are worth 5 points, third round questions are worth 10 points, and so on. Which expression can be used to determine the number of points for questions in the nth round? F n2 + 1G n2 - 1H 3nJ 3n + 1

5 On a dartboard, fi rst row hits are worth 1 point, second row hits are worth 3 points, third row hits are worth 5 points, and so on. Which expression can be used to determine the number of points an nth row hit is worth? A n + 1B 2n - 1C n2

D n2 - 1

6 Albert builds a model rocket that operates on compressed CO

2 cylinders. On the fi rst

test, his rocket reaches a height of 150 feet. On the second test, his rocket reaches 135 feet. On the third test, his rocket reaches 121.5 feet. Which expression can be used to determine the height of his rocket on the nth test? F 150(0.9)n

G 150(0.9)n-1

H 150(0.9)nJ 150(0.9)(n - 1)

A.3(B) The student is expected to look for patterns and represent generalizations algebraically.



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best answer.

1 Which best represents the solution to the equation 2x2 = x? A 0

B 1 _ 2

C 0 and 1 _ 2

D 0 and - 1 _ 2

2 What are the factors of 3x2 - x - 2 = 0? F (3x - 2) and (x - 1)G (3x + 2) and (x + 1)H (3x + 2) and (x - 1)J (3x - 2) and (x + 1)

3 Which best represents the solution to the equation x3 + 3x2 + 2x = 0? A 0, -2, -1B -2, -1C 2, 1, 0D 0

4 Which polynomial represents the factors (x + 2)(2x - 1)? F 2x2 - 2G 2x2 + 3x - 2H 2x2 + 4x - 2J 2x2 + 3x + 2

5 Which best represents the solution to the equation x2 = 4? A -2B 2C -2 and 2D 0

6 Which polynomial best represents the factors (3x - 1)(x - 3)? F 3x2 + 3G 3x2 + 10x + 3H 3x2 - 10x - 3J 3x2 - 10x + 3

7 What are the factors of 2x2 - 7x - 4? A (2x + 1) and (x - 4)B (2x - 1) and (x + 4)C (2x - 1) and (x - 4)D (2x + 1) and (x + 4)

8 Which polynomial best represents the factors (2x + 5)(x - 2)? F 2x2 – 10G 2x2 + x - 10H 2x2 - 9x - 10J 2x2 + 9x - 10

A.4(A) The student is expected to fi nd specifi c function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations.




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best answer.

1 Which expression is equivalent to (6 - 3x) + x(x + 1)? A 6 - xB x2 - 3x + 6C x2 - 2x + 6D x2 + 2x + 6

2 What is the area of the shaded region of the rectangle, reduced to simplest terms?

x

5 x

x + 5

F 4x2 + 25xG 5x2 + 25xH (5 + π)x2 +25xJ (5 - π)x2 + 25x

3 Which expression is equivalent to (x2 + 2)(x + 3)? A x2 + 5x + 6B 6x2 + 6C x3 + 5x2 + 6D x3 + 3x2 + 2x + 6

4 Jamil has y2 + 3y baseball cards. Arianna has 3y2 - 5 baseball cards. How many baseball cards do Jamil and Arianna have combined? F 3y4 + 9y3 - 5y2 -15yG 4y2 + 3y - 5H y2 + 6y - 5J 5 + 3y - y2

5 What is the area of the L-shaped fi gure, reduced to simplest terms?

x + 52x + 2

x

3x

A x2 + 5xB 4x2 - 6x - 10C 5x2 - x - 10D 6x2 + 6x

6 Mr. Downing must provide each of his students with 2x2 - 2x + 3 sheets of paper. If he has x students, how many sheets of paper does he need? F 3xG 2x2 - 2x + 3H 2x3 + x2

J 2x3 - 2x2 + 3x

A.4(B) The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions.



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best answer.

1 Which of the following sets of ordered pairs do NOT represent a linear function? A (0, -2), (1, -1), (2, 0), (3, 1)B (0, 0), (1, 1), (2, 4), (3, 9)C (0, 1), (1, 3), (2, 5), (3, 7)D (0, 3), (1, 2), (2, 1), (3, 0)

2 Which is the graph of a linear function? F

0

1

.5

321

G

0

1

2

321

H

0

1

23

4

321 4

J

0

1

23

4

321

3 Which of the following does NOT represent a linear equation? A y = 0B y = 1C y = xD y = (1 - x)(1 + x)

4 Which of the following sets of ordered pairs represents a linear function? F (-1, -16), (0, -7), (1, 2), (2, 11)G (-1, -2), (0, -3), (1, -2), (2, 1)

H ( -1, 1 _ 3 ) , (0, 1), (1, 3), (2, 9)

J (-1, 3), (0, 1), (1, 3), (2, 9)

5 Which of the following may be represented by a linear function? A rabbit population vs. timeB distance vs. time traveled at a constant

speedC area of a circle vs. its radiusD number of tomato plants planted vs.

side length of a square tomato patch

6 Which of the following can NOT be represented by a linear function? F circumference of a circle vs. its

diameterG gallons of gasoline used vs. distance

traveledH gallons of paint needed vs. feet of fence

to be paintedJ capacity of a spherical tank vs. its

height

A.5(A) The student is expected to determine whether or not given situations can be represented by linear functions.




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best answer.

1 Which linear equation best represents the verbal description “one-half y equals 4 more than twice x”? A y = x + 2B y = 2xC y = 2x + 4D y = 4x + 8

2 Which equation best represents the line on the graph?

y

xO

F y = 4x

G 1 _ 2 x + 2y = 0

H 2x - 1 _ 2 y = 0

J 2x + 1 _ 2 y = 0

3 Which linear equation best represents the verbal description “double x equals 3 less than quadruple y”? A 2x - 4y = 3B 2x + 4y = 3C 2x - 4y = -3D 2x + 4y = -3

4 Which linear equation best represents the data shown in the table below?

x -1 0 1 2y -1 2 5 8

F y + 3x = 2G y - 3x = 2H y - x = 0J x2 - y = -4

5 Which linear equation best represents the verbal description “three times x equals 2 less than y?” A y = 3x - 2B y = 3x + 2

C y = 1 _ 3 x - 2 _ 3

D y = 1 _ 3 x + 2 _ 3

6 Which linear equation best represents the data shown in the table below?

x -3 0 3 6y 1 0 -1 -2

F y = x _ 3

G x = y _ 3

H 3y - x = 0

J 3y + x = 0

A.5(C) The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.



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best answer.

1 What is the slope of the line graphed below?

y

xO

A -1B 1C 2D 3

2 What is the slope of the line represented by the table below?

x -2 -1 0 1y 3 5 7 9

F -2

G 1 _ 2

H 2J 7

3 Find the slope of the line identifi ed by the equation x - y = -5. A -5B -1C 1D 5

4 Find the slope of the line that contains the points (3, -2) and (0, 0).

F - 3 _ 2

G - 2 _ 3

H 2 _ 3

J 3 _ 2

5 What is the slope of the line graphed below?

y

xO

A -2B 0C 2D 4

6 What is the slope of the line represented by the table below?

x -1 1 3y -3 -1 1

F 0

G 1 _ 2

H 1J 2

A.6(A) The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations.




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best answer.

The drainage rate of a tub is a function of its capacity. The drainage time of 4 tubs with different capacities is shown in the table below. Use the table to answer Questions 1 and 2.

Capacity (gal)

Drainage Time (min)

5 110 220 425 5

1 If the data are graphed with drainage time on the horizontal axis and capacity on the vertical axis, what does the slope represent? A an average capacity of 15 gallonsB the capacity of the tub at a drainage

time of 0 minutesC a drainage rate of 5 gallons per minuteD the drainage time of the tub at 0

capacity

2 If the data are graphed with drainage time on the horizontal axis and capacity on the vertical axis, what does the x-intercept represent? F an average drainage time of 3 minutesG the capacity of the tub at a drainage

time of 0H the drainage rate per gallonJ the drainage time of the tub at

0 capacity

3 Find the y-intercept of the line identifi ed by the equation x - 2y = 4. A -4B -2C 2D 4

4 Find the y-intercept of the line identifi ed by the equation 3x - y = 7. F -7

G - 7 _ 3

H 7 _ 3

J 7

5 A line contains the point at (2, -1) and the y-intercept 3. What is the slope of the line? A -2B 1C 4D cannot be determined

6 A line contains the point at (-2, 5) and has

a slope of 1 _ 2 . What is the y-intercept of

the line? F -4G 4H 6J cannot be determined

A.6(B) The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.



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best answer.

Use this graph to answer Questions 1 and 2.

y

xO

1 Which of the following best describes the effect on the graph when the slope is multiplied by -1? A The y-intercept increases.B The y-intercept decreases.C The x-intercept increases.D The x-intercept decreases.

2 If the y-intercept decreases by 3, which linear equation represents this change? F y = -3x - 5G y = -1 - 3xH y = 3x - 5J y = 5 - 3x

3 In point-slope form, the equation for a

line is y + 2 = 1 _ 3 (x - 3). The y-intercept

is decreased by 1. What is the new y-intercept? A -4B -3C -2D -1

4 The equation for a line is 2y = 3x - 1. The slope is multiplied by -1. What is the new slope? F -3G -2

H - 3 _ 2

J -1

5 In point-slope form, the equation for a

line is y - 1 = -2 ( x + 3 _ 2 ) . The

y-intercept is increased by 2. What is the new y-intercept? A -2B -1C 0

D 7 _ 2

6 The equation for a line is -y = 3(x - 2). The slope is quartered. What is the new slope? F -3

G - 3 _ 4

H 3 _ 4

J 3

A.6(C) The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b.




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best answer.

1 Which equation represents the line that contains the point at (-3, 0) and has a y-intercept of 2? A y = x + 2

B y = 2 _ 3 x + 2

C y = 2x - 3D cannot be determined

2 Which equation represents the line that contains the point at (0, -2) and has an x-intercept of -1? F y = -2x - 2G y = -2x - 1H y = 2x + 1J cannot be determined

3 Which equation represents the line that passes through the points at (-2, -3) and (-1, 0)? A y = -x - 5B y = x - 1C y = 3x + 3D y = 3x + 9

4 Which function represents the line that

contains the point at (5, - 1 _ 2 ) and has a

slope

of 1 _ 2 ?

F f (x) = 1 _ 2 x - 5 _ 2

G f (x) = 1 _ 2 x - 3

H f (x) = 1 _ 2 x - 2

J f (x) = 1 _ 2 x + 5 _ 2

5 Which equation represents the line that contains the point at (1, -2) and has a y-intercept of -4? A y = -2x - 4B y = 2x + 4C y = 2x - 4D cannot be determined

6 Which equation represents the line that contains the point at (-3, -4) and has an x-intercept of -2? F y = 4x + 12G y = 4x + 8

H y = 2 _ 3 x - 2

J cannot be determined

A.6(D) The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept.



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best answer.

1 What are the coordinates of the x-intercept of the line that passes through points at (2, 2) and (5, 1)?

A ( 0, - 8 _ 3 )

B ( 0, 8 _ 3 )

C (-8, 0)

D (8, 0)

2 What are the coordinates of the y-intercept of the line that passes through the points at (-4, 1) and (2, -2)? F (0, -2)G (0, -1)H (-2, 0)J (-4, 0)

3 What are the coordinates of the x-intercept of the equation 3x = 1 - 2y? A (0, 1)

B ( 0, 1 _ 2 ) C ( 1 _

3 , 0 )

D ( 1 _ 2 , 0 )

4 What are the coordinates of the y-intercept of the equation 3y - x = 8?

F ( 0, 8 _ 3 )

G ( 0, - 8 _ 3 )

H (-8, 0)J (8, 0)

5 What are the coordinates of the x-intercept of the line that passes through the points at (2, -3) and (-1, 3)? A (2, 0)

B ( 1 _ 2 , 0 )

C (0, 1)D (0, -2)

6 What are the coordinates of the y-intercept of the line that passes through the points at (7, 2) and (-1, -1)?

F ( 0, - 5 _ 8 )

G (0, 0)

H ( 0, 3 _ 8 )

J ( 5 _ 3 , 0 )

A.6(E) The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations.




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best answer.

Use the graph below to answer Questions 1 and 2.

Co

st

$1.00

$1.50

$0.50

0

$2.00

Time (min)321 54 6

1 What change would cause the slope of the graph to decrease? A The cost per minute remains the same.B The cost per minute increases.C The cost per minute decreases. D The call is disconnected.

2 What change would cause the y-intercept to increase? F The phone company charges a fee for

calls that never go through.G The cost per minute increases.H The duration of the call increases. J The duration of the call decreases.

The graph below shows the deceleration of a race car at different times. Use the graph to answer Questions 3, 4, and 5.

Spee

d( m

ph

)

50

75

25

0

100

150

Time (sec)642 108 12

3 What change would cause the slope of the graph to increase? A The car decelerates more slowly.B The car decelerates more quickly.C The deceleration remains the same.D The starting speed is slower.

4 What change would cause the y-intercept to decrease? F The time to stop is shorter. G The starting speed remains the same.H The starting speed is higher.J The starting speed is lower.

5 If the initial speed AND the rate of deceleration were both doubled, how would the time to reach zero mph be affected? A It would be unaffected.B It would double.C It would be cut in half.D There is not enough information to

answer this question.

A.6(F) The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations.



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best answer.

1 In a trivia bowl game, Aubrey typically answers 14 out of 15 questions correctly. If Aubrey were asked 100 questions, approximately how many would she answer correctly? A 93 C 87B 91 D 85

2 The number of cookies Joachim burned varies directly with the total number of cookies he baked. It is estimated that he burned 1 out of 9 cookies. If he burned a total of 12 cookies, how many cookies did he bake? F 108 H 95G 101 J 89

3 Mr. Walker’s class measured the temperature at various intervals throughout the day. Their data is shown in the table below.

Time Temperature (°F)

8:30 A.M. 489:00 A.M. 519:30 A.M. 5410:30 A.M. 60

If the temperature continues to rise at the rate shown in the table, what will the approximate temperature be at noon? A 66°F C 72°FB 69°F D 75°F

4 The number of free throws Sandra scores varies directly with the number of free throws she attempts. It is estimated that she scores 6 out of every 10 free throws attempted. If during the basketball season she attempts 55 free throws, how many free throws does she score? F 22G 33H 44J 110

5 Mrs. Celeski’s science class is conducting an evaporation experiment with a beaker of water. The results are shown in the table below.

Time(days)

Water Level(in)

1 3.002 2.6255 1.5

If the water continues to evaporate at the rate shown in the table, what will its level be on day 7?

Record your answer and fi ll in the bubbles in the answer grid below.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

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A.6(G) The student is expected to relate direct variation to linear functions and solve problems involving proportional change.




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1 Kamil swam x laps over the weekend. He swam twice as many laps on Saturday as he did on Sunday. If � is the number of laps he swam on Saturday, which equation can be used to fi nd x?

A x = 3 _ 2 � C x =

3 _ 2 (� - 2)

B x = 3� D x = 3(� - 2)

2 Annika must earn at least d dollars to attend the band trip. She can earn this money by selling 300 raffl e and/or dinner concert tickets at a profi t of $2 apiece. If she sells r raffl e tickets, which inequality can be used to fi nd d? F d ≤ 2r + 2(300 - r)G d ≥ 2r + 2(300 - r)H d ≤ 2r + 2(r - 300)J d ≥ 2r + 2(r - 300)

3 Didi used at most g gallons of gas on her 3-hour trip to Dallas. She used an average of 2 gallons per hour on the interstate highway and 1.5 gallons per hour the rest of the way. If h is the number of hours she spent on the interstate, which inequality can be used to fi nd g? A g ≥ 1.5h + 2(3 - h)B g ≤ 1.5h + 2(3 - h)C g ≥ 2h + 1.5(3 - h)D g ≤ 2h + 1.5(3 - h)

4 Gabby scored p points in last night’s basketball game by hitting 8 shots. She scored 3 points for each outside shot and 2 points for each inside shot. If n is the number of outside shots she scored, which equation can be used to fi nd p? F p = 3n + 2(8 + n)G p = 3n + 2(8 - n)H p = 2n + 3(8 + n)J p = 2n + 3(8 - n)

5 Xavier weighs 10 pounds less than Yanni. Zeb weighs 15 pounds less than twice Xavier’s weight. If Yanni weighs y pounds, which equation can be used to fi nd Zeb’s weight, z? A z = 2(y - 10)B z = 2y - 25C z = 2(y - 10) - 15D z = 2(y - 25)

6 Corrine must read a book of at least 300 pages in one week. She reads p pages each day from Monday to Saturday. Which inequality can be used to fi nd at least how many pages she must read on Sunday, s? F s ≥ 300 - 6pG s ≤ 300 - 6pH s ≥ 300 - pJ s ≤ 300 - p

A.7(A) The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems.



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best answer.

1 The solution to the inequality 3x - 6 y ≤ 0 falls in which quadrants? A I and IIB I, II, and IIIC I, III, and IVD I and IV

2 Mr. Storper explained to his Economics class that a car’s current cost, c, is at least $2500 more than triple the cost 30 years ago. If the cost of a car 30 years ago was $4000, which inequality represents the cost today? F c ≤ $14,500 H c ≤ $12,000G c ≥ $14,500 J c ≥ $12,000

3 Use the graph of x - 2y = 4 to solve the equation for y when x = -2.

y

xO

A y = -3 C y = 0B y = -2 D y = 8

4 Pilot Johansen determined that the total number of gallons of fuel used on a fl ight, f, could be represented by the equation f = 20h + 25, where h is the number of hours the fl ight takes. If 125 gallons of fuel were used, how long did the fl ight last? F 5 hrG 6.25 hrH 7.5 hrJ 8 hr

5 Mrs. Blackwell explained that the cost of a book, b, at the bookmobile would be at most $0.50 less than $0.02 per page. If a book contains 400 pages, which inequality represents its cost? A b ≤ $8.50B b ≥ $8.50C b ≤ $7.50D b ≥ $7.50

6 The solution to the inequality x ≤ -y falls in which quadrants? F I and IIG I and IVH II, III, and IVJ I, II, and IV

A.7(B) The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities.




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best answer.

1 The number of nails, n, hammered by a carpenter in a day can be represented by the inequality 15h + 75 < n < 35h - 15, where h represents the number of hours worked. If a carpenter works 9 hours, which of the following is a reasonable number of hammered nails? A 200 C 300B 250 D 305

2 An accountant estimates the tax, t, on a short-term investment gain to be t = 0.40d - 25, where d is the difference between the selling price and the buying price. What is a reasonable estimate of the tax on a short-term investment with a buying price of $5000 and a selling price of $6250? F $20G $475H $500J $1250

3 Kianti uses the equation t = 0.15s - 500, where s is her salary after deductions, to estimate her self-employment tax. If her salary after deductions is between $30,000 and $35,000, what is the range of Kianti’s self-employment tax? A $4000 to $4500B $4000 to $4750C $4500 to $5250D $4750 to $5250

4 The Texas Regional Fair Association estimates that the number of fair attendees, a, is represented by the inequality 5000d + 500 ≤ a ≤ 6000d - 250, where d is the number of days the fair runs. Which of the following is a reasonable number of attendees if the fair runs 10 days? F 49,000 H 55,000G 50,000 J 60,000

5 The value of y is represented by the inequality 50x - 8 < y < 75x + 10. Which of the following is NOT a reasonable estimate for y when x = 8? A 392 C 500B 400 D 589

6 A lawyer estimates c, his contingency fee on a lawsuit, to be c = 0.35s + $1000, where s is the settlement amount. What is a reasonable conclusion about the contingency? F If the settlement amount is $0, the

lawyer will earn no contingency.G The lawyer will earn a contingency

of at least $1000, regardless of the settlement amount.

H The lawyer will earn a contingency of at most $1000, regardless of the settlement amount.

J To earn a contingency, the settlement amount must be at least $2858.

A.7(C) The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities.



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1 At a doughnut shop, Manuel bought a box of 18 that contained g glazed doughnuts and j jelly doughnuts. If the number of glazed doughnuts was 2 less than twice as many jelly doughnuts, which system of linear equations could be used to determine the number of each kind? A g + 2j = 20 g + j = 18B g + 2j = 18 g + j = 20C 2j - g = 2 g + j = 18D 2j - g = 20 g + j = 18

2 The ages of Shelby and her father combined equals 50. Shelby’s father’s age, f, is 1 less than triple Shelby’s age, s. Which system of linear equations could be used to determine the ages of Shelby and her father? F 3s - f = 1 s + f = 50G 3s - f = 1 f - s = 50H 3s + f = 60 s + f = 50J 3s + f = 1 f - s = 50

3 Fudgie’s Fudge Shop sells peanut butter fudge, p, for $6.75 a pound and walnut fudge, w, for $7.50 a pound. A customer asks for a 3-pound mixture of both kinds of fudge, which costs $7.00 a pound. Which system of linear equations can be used to fi nd the number of pounds of each type of fudge in the mixture? A 7.50p + 6.75w = 7.00(3) p + w = 3B 7.50p + 6.75w = 7.00(3) p + w = 7.00C 7.50w + 6.75p = 7.00(3) p + w = 7.00D 7.50w + 6.75p = 7.00(3) p + w = 3

4 The price of a new digital camera, n, is $50 less than twice the cost of a refurbished camera, r. The difference in price between the two cameras is $150. Which system of linear equations can be used to determine the price of each camera? F 2r - n = 50 r - n = 150G n - 2r = 50 n - r = 150H 2r - n = 50 n - r = 150J 2r - n = 0 n - r = 150

A.8(A) The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems.




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1 The table below gives the slope and y-intercept of two lines.

m -1 2y-intercept 3 -3

What is the solution to this system of linear equations? A (2, 1)B (3, 0)C (6, -3)D No solution

2 Which of the following is the solution for

the system of linear equations y = 1 _ 4 x - 4

and 2x - 2y = -4? F (0, 4)G (0, -4)H (-8, 6)J (-8, -6)

3 The equations of two lines are y = 3x + 2 and 2x + y = 4. Which of the following describes their point of intersection? A (2, 0)

B (2, 16)

C ( 2 _ 5 , 16

_ 5 ) D no intersection

4 The graph of the equation y = 3 - x is given below.

y

xO

If the graph of y + x = 6 is added to the diagram, what would be the solution to this system of equations? F (-3, 6) H (3, 0)G (0, 3) J no solution

5 The table below gives the slope and y-intercept of two lines.

m 1 _ 2 - 1 _ 2

y-intercept -2 3

What is the solution to this system of equations?

A ( -1, 7 _ 2 ) C ( 5, 1 _ 2 )

B ( 1, - 3 _ 2 ) D no solution

6 Which of the following is the solution for the system of linear equations x - y = 1 and y = 2 - x?

F ( 1 _ 2 , 3 _ 2 ) H (3, 2)

G ( 3 _ 2 , 1 _ 2 ) J no solution

A.8(B) The student solves systems of linear equations using concrete models, graphs, tables, and algebraic methods.



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best answer.

1 The price of a designer wedding gown, d, is $150 less than triple the price of a knock-off, k. The difference in price between the two dresses is $750. Which is a reasonable estimate for the price of the designer gown? A $150B $450C $750D $1200

2 Pietta and Bob’s combined weights total 305 pounds. Bob’s weight, b, is 5 pounds

more than 3 _ 2 Pietta’s weight, p. Which is a

reasonable estimate for Bob’s weight? F 105 lbG 120 lbH 185 lbJ 200 lb

3 A senior class ring costs $200 plus $5 per engraved character. Characters 11 and above are free. Amita wants to engrave her class year on the inside of the ring. What is a reasonable conclusion about r, the total cost of her ring? A $200 ≤ r < $20B $200 < r ≤ $255C $250 < r ≤ $255D $255 < r < $260

4 A fast food restaurant sells chicken sandwiches, c, at $4 apiece and fi sh sandwiches, f, at $3 apiece. A customer orders a mixture of 6 sandwiches. The restaurant charges $20 (tax excluded) for all 6 sandwiches. Which is a reasonable estimate for the number of chicken sandwiches ordered? F 2G 3H 4J 5

5 The price for a fl oor model lamp, f, is $10 more than half the price of an in-box model, i. The difference in price between the two models is $24. Which is a reasonable estimate for the price of the fl oor model? A $34B $44C $58D $68

6 When Karl and Shaina’s ages are combined, the sum is 64. Karl’s age, k, is 19 years more than two-thirds Shaina’s age, s. What is a reasonable estimate of Shaina’s age? F 27G 37H 67J 96

A.8(C) The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations.




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1 If the graph of y = ax2 opens down, which of these statements is NOT true? A The graph of y = -ax2 opens up.B The coeffi cient of the quadratic term, a,

is negative.C The vertex is below the origin.D The graph of y = -ax2 would be

refl ected across the x-axis from the graph of y = ax2.

2 The equation y = -4x2 is shown on the graph.

y

xO

What happens to the parabola if the coeffi cient of the quadratic term is changed to 2? F It opens upward and widens.G It opens upward and narrows.H It still opens downward but widens.J It still opens downward but narrows.

3 Dane applies for a summer internship in the Antarctic. He will study whether ice drift, d, might be related to the water’s force by the formula d = aw2. He believes that a shift in currents might increase a by a factor of 2. If that happens, what would change in the way the drift responds to the water’s force? A The constant cannot change.B The drift would be halved from its

previous amount.C The drift would double from its

previous amount.D The drift would quadruple from its

previous amount.

4 Which equation describes the narrowest parabola? F y = -3x2

G y = x2

H y = 3x2

J y = 6x2

5 Carolyn notices that the sand dunes on Padre Island have a parabolic shape. If y = 0 is set as sea level, she believes that the formula determining the dune’s formation could be h = -af 2, where h is the height of the dune and f is the force of the wind. What happens to the dunes if the constant a decreases due to an overgrowth of dune grass? A The form is no longer parabolic and the

dunes fail to form.B The wind digs out the sand instead of

forming dunes.C The dunes widen.D The dunes narrow.

A.9(B) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax2

+ c.



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best answer.

1 How would Sonya change the constant coeffi cient of the equation y = x2 + 5 if she wanted to move the vertex below the origin? A Changing the constant coeffi cient has

nothing to do with the position of the vertex.

B She would remove it.C She would decrease the constant

coeffi cient to 0.D She would replace it with a negative

number.

2 Daniel has a summer job as a window washer on the 64th fl oor of Houston’s Williams Tower. The wind vibrates the scaffolding at a rate of 3 vibrations per second. When he steps away from the center of the platform in either direction, the vibrations, v, increase as a quadratic function of x, with x the distance away from the center. Which equation would graph the way the vibrations, v, are related to x? F x = v2 + 3 vibrationsG v = x2 + 3 vibrationsH v = x2 + 64 vibrationsJ v = -x2 - 3 vibrations

3 What happens to the graph of the equation y = x2 + 1 when the constant coeffi cient is changed to 4? A The parabola widens.B The parabola narrows.C The parabola is translated 4 units higher.D The parabola is translated 3 units higher.

4 Stephanie, a gymnast, typically holds her handstand on the balance beam for 10 seconds. If she places her thumbs incorrectly, the time drops as a quadratic function of the distance her thumbs are off center. The equation t = -x2 + 10 describes the relationship, with t being the time in seconds that she can hold the handstand and x being the distance in centimeters her thumbs are off center. If she could typically hold her handstand 20 seconds instead of 10, how would the constant coeffi cient change? F It would double.G It would increase by a factor of 100.H It would increase by a factor of 400.J It would not change.

5 How does the graph of y = x2 - 6 differ from the graph of y = x2 - 3? A The graph of y = x2 - 6 is translated

3 units lower.B The graph of y = x2 - 6 is translated

3 units higher.C The graph of y = x2 - 6 is translated

3 units to the left.D The graph of y = x2 - 6 is wider.

A.9(C) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c.




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1 Sonya caught the bouquet after her sister’s wedding ceremony. The graph shows the bouquet’s height as a function of time.

Hei

gh

t( m

)

2

3

1

0

4

5

6

Time (sec)321 5 74 6 8

Which conclusion is NOT true? A Sonya’s sister stood on a balcony

about 3 meters above the fl oor of the reception hall to toss the bouquet.

B The bouquet reached its maximum height 2 seconds after being tossed.

C Sonya caught the bouquet in the air.D The graph has no negative values

for the range because the bouquet could not drop below the fl oor of the reception hall.

2 Velvet ropes hang between the poles that line the red carpet at a movie opening. Their shape is parabolic. If the origin of a coordinate plane is set at fl oor level halfway between 2 poles, x would represent the distance from that center point and y would represent the rope’s height from the ground. Which statement is true of the quadratic equation meant to represent the rope’s curve? F The coeffi cient of the quadratic term is

negative.G The minimum value for the range is

found at the two poles.H The constant coeffi cient is negative.J The domain extends from -x to x, with

x being half the distance between poles.

3 The graph shows a parabola. Which equation is graphed?

y

xO

A 2y = -2x2 - 2B 2y = 2x2 - 2C y = 0.5x2 - 4D y = -0.5x2 - 4

A.9(D) The student is expected to analyze graphs of quadratic functions and draw conclusions.



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best answer.

1 Juanita deposits her savings in an account that compounds interest. If she leaves the money in the account for 2 years, the fi nal value of her deposit is a quadratic function of the interest rate. The relationship is shown in the table.

r FV

2% $260.103% $265.234% $270.405% $275.63

Which equation does the table represent?A FV = 250(1 + r)2

B FV = 250(1 - r)2

C FV = 250(r)2

D FV = 250 + (1 + r)2

2 Using the difference of two squares method, what would be the fi rst step in solving the equation x2 - 25 = 0?

F x = √ ___________

02 - 4(1)(25)

G x = -0 ± √

__________

02 - 4(1)25 __

2(1)

H (x - 5)(x + 5) = 0J (x - 25)(x + 25) = 0

3 Candace calculates that the milk sales from her family’s Brenham dairy farm are described by the formula s = -30p2 + 510p, where s is sales and p is the price charged. What should the family charge for its product if the goal is to make $1800 in sales? A either $0.20 or $0.08B either $5 or $12C either $10 or $24D either $300 or $720

4 Given an equation y = 2x2 - 3, which of the following statements is true about the vertex? F The vertex is at the origin, so that the

solution of the equation would be x = 0.G The vertex is at the minimum value for

y, below the origin, meaning that the graph has 2 x-intercepts and 2 solutions.

H The vertex is at the maximum value for y, below the origin, and there are no x-intercepts and no solutions.

J The vertex is translated 3 units to the left of the origin, and there are 2 x-intercepts and 2 solutions, both negative.

A.10(A) The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods.




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1 A function has roots at x = 0.5 and 2.5. Which graph could represent that function? A y

xO

B y

xO

C y

xO

D y

xO

2 Metal fatigue experienced by a ship can be expressed as a quadratic function of its speed. A theoretical example might be the function f(x) = 0.5x2 for x ≥ 0, where x is the speed and f(x) is the metal fatigue factor. A graph of the function is shown.

Met

al F

atig

ue

Fact

or

2

3

1

0

4

5

6

7

8

Speed (knots)1 2 3 4 5 6 7 8

Which statement is true of the graph?F There is one y-intercept, but no x-intercept.G The solution of the graphed function

represents the point at which the ship is not moving and the metal fatigue factor is 0.

H There is no solution to the graphed function.

J The graphed function has no roots.

3 If the coordinate pairs (4, 0) and (6, 0) represent the solutions of a quadratic function, what are the roots of that function? A x = 0, 0B y = 0, 0C x = 4, 6D y = 4, 6

A.10(B) The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.



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best answer.

1 The table shows the radii of a series of spheres.

Sphere Radius

1 3r2 9r 2

3 27r 4

4 81r 8

Which of these spheres has a volume of 26,244πr12? A Sphere 1B Sphere 2C Sphere 3D Sphere 4

2 If a species of bird has an initial population of 200, population growth may be determined by the formula p

n = 200(2.8)3.2n, where p is the population

and n is the year. If conditions do not change, which expression tells the predicted population of that species of bird in 8 years? F 200(2.8)25.6

G 200(2.8)11.2

H 200(2.8)(25.6)J 200(2.8)3.2(8)

3 Simplify the expression (r2 - z2)5

__ (r2 - z2)4(r - z)

.

A (r2 - z2)9

_ r - z

B r + zC r - zD (r - z)2

4 A savings account at Sarah’s bank adds interest every day to her $500 deposit. The expression that would tell her how much she would have after t years is $500(2.718)rt, where r is the interest rate earned, expressed as a decimal. Which expression shows how much her account would be worth after 5 years if she earns a 5% interest rate? F 500(2.718)(25)G 500(2.718)(0.25)H 500(2.718)25

J 500(2.718)0.25

5 Medical research has shown that when death rates are plotted as a function of blood pressure and cholesterol levels, a J-shaped curve is produced, similar to the graph shown below.

2

3

1

0

4

5

6

7

8

1 2 3 4 5 6 7 8

Which of the following functions created this J-shaped curve? A y = 0.1x4

B y = 0.1x4 for x ≥ 0C y = 0.2x3

D y = x4 for x ≥ 0

A.11(A) The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations.




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best answer.

1 Courtney starts at point A and walks 5 feet before making a left-hand turn of 72°. She walks another 5 feet before making a right-hand turn of 144°. She repeats this pattern until she returns to point A. What shape has Courtney walked? A

B

C

D

2 A square is broken into 2 triangles as shown. What are the measurements of the interior angles of �ABC?

A B

D C

F 30°, 60°, 90° H 90°, 90°, 90°G 45°, 45°, 90° J 90°, 120°, 180°

3 A pie is cut into 12 equal pieces. The tip of each piece forms what angle? A 20° C 30°B 25° D 40°

4 Right triangle XYZ has an interior angle of 30°. What are the measurements of all of the interior angles? F 30°, 60°, 90° H 30°, 45°, 45°G 30°, 45°, 90° J 30°, 90°, 180°

5 Marcus has an old circular patio in his backyard with a radius of 25 feet. He removes the border of bricks that encircles the patio, which he then uses to make the border of a square greenhouse in his backyard. What is the approximate side length of the greenhouse? A 39 ft C 45 ftB 42 ft D 50 ft

G.4(A) The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.



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best answer.

1 Marcia compares the number of sides of a regular polygon to the measurements of each angle. Which chart would best represent her fi ndings? A

Sides Angle Measurement

3 60°4 90°5 108°6 120°

B Sides Angle

Measurement

3 60°4 90°5 108°6 180°

C Sides Angle

Measurement

3 45°4 90°5 180°6 120°

D Sides Angle

Measurement

3 60°4 90°5 72°6 120°

2 Which of the following measures for 3 sides of a polygon could NOT be the 3 sides of a triangle? F 21, 28 and 35 H 2.5, 3 and 5G 8, 9 and 17 J 2, 3.5 and 4

3 A family visits the Beaumont Botanical Gardens. The group walks along the path and makes 5 right turns before returning to the starting point. The relationship between a, the number of angles turned, to s, the number of sides of the fi gure walked, is a = s. What is the shape of the family’s path? A square C pentagonB rectangle D hexagon

4 The formula that provides the measurement of the interior angle of a

regular polygon is (s - 2)(180°)

__ s , where s is

the number of sides. What is the measure of each of the interior angles of a polygon with 35 sides? F 169.71° H 190.29°G 180° J 190.90°

5 Leon made a fence around his garden. Each vertex had an interior angle measurement of 144°. If the fence formed a regular polygon, which is the shape of the fence? A hexagon C octagonB heptagon D decagon

G.5(B) The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar fi gures and solids, and angle relationships in polygons and circles.




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best answer.

1 Which set of polygons can be tiled infi nitely? A

B

C

D

2 See the shaded fi gure. Through what angle can this shape be repeatedly rotated in order to generate the fi gure shown?

F 180° H 72°G 90° J 45°

3 Mel made 5-pointed tin stars for the Annual Big Spring Craft Show. She used translations of only one shape. Which shape did she use? A

B

C

D

G.5(C) The student is expected to use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations.



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1 Natasha uses the Pythagorean Theorem to solve for the length of side b in a right triangle. If the lengths of sides a, b, and c are Pythagorean triples and a and c are odd numbers, what can be assumed about b? A It is an odd number.B It is an even number.C It is a negative number.D No assumption can be made.

2 Which of the following sets of numbers is NOT a Pythagorean triple? F 3, 4, 5G 8, 15, 17H 11, 60, 61J 20, 21, 27

3 A 30-60-90 triangle’s shortest side has a measurement of x. What is the measurement of the other side that includes the right angle? A x √

_

2 B 30xC 2xD x √

_

3

4 Brett built a skateboard ramp that was a triangle with angles of 45°, 45°, and 90°. If the height of the ramp is h, which formula tells him the length, �, of the skateboard ramp?

Skateb

oard

Ramp

45˚

F h2 = �G h2 = �2

H � = h √

_

2 J h = � √

_

2

5 A wire from the top of a transmission tower to the ground is 250 feet long. The wire makes a 45° angle with the ground. About how tall is the transmission tower? A 167.8 ftB 176.8 ftC 186.7 ftD 187.6 ft

G.5(D) The student is expected to identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.




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best answer.

1 Which pair of the following polygons is congruent?

A

B

C

D

A polygons A and BB polygons A and CC polygons B and C D polygons B and D

2 The 2 fi gures shown are congruent. What are 2 corresponding segments?

A B

T U

V

W

M

NO

P

QR

S

C

DE

F

G

H

IJ

KL

F ____

AB and ____

ST G

____ BC and

_____ MW

H ____

DE and ____

PQ J

____ JK and

____ QP

3 The graph shows quadrilateral ABCD.

A B

CD

y

xO

Which set of coordinates below represents a congruent fi gure? A (-1, 3), (2, 3), (2, -1), (-1, -1)B (-2, 3), (1, 3), (2, -1), (-1, -1)C (-2, 4), (1, 3), (2, -2), (-1, -1)D (-2, 5), (1, 4), (2, -1), (-1, 0)

4 See the fi gure below.

80˚

80˚

C

A

D

EB

Which of the following would be enough information, added to what is already known from the fi gure, to justify that �ABC and �EBD are congruent? F ∠CBA congruent to ∠DBEG ∠BAC congruent to ∠BED H

____ AC congruent to

____ BC

J ____

BC congruent to ____

BD

G.10(A) The student is expected to use congruence transformations to make conjectures and justify properties of geometric fi gures including fi gures represented on a coordinate plane.



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best answer.

1 The container shown has to be taken apart and stored fl at.

Which diagram below shows the same container? A

B

C

D

2 Anthony assembles a TV stand. He lays the pieces out as shown. What will be the height of the TV stand once assembled?

36 in.

17.5 in. 17.5 in.

24 in.

32 in.

Back

BottomSide A Side B

Top

Door A Door B

F 17.5 in. H 28 in.G 24 in. J 32 in.

3 See the net of a rectangular prism below.

base 1

base 2

2 cm

2 cm

2 cm

2 cm

2 cm

2 cm

4 cm

What is the surface area of the prism? A 12 cm2 C 24 cm2

B 16 cm2 D 40 cm2

G.6(B) The student is expected to use nets to represent and construct three-dimensional geometric fi gures.




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1 Marissa made a table out of sugar cubes for her sister’s dollhouse.

How many sugar cubes are needed to construct the table? A 15 C 20B 17 D 23

2 Kelsey works for her uncle, an architect, during the summer. She studies the blueprints shown.

Kitchen

Dining

LivingRoom

GarageStudy

Which home could be built from these blueprints?

F

G

H

J

G.6(C) The student is expected to use orthographic and isometric views of three-dimensional geometric fi gures to represent and construct three-dimensional geometric fi gures and solve problems.



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best answer.

1 A hexagon is shown.

y

xOQ

P

Which are the coordinates of the vertex 1 unit above and 2 units to the left of vertex P? A (6, 0)B (0, 6)C (2, 0)D (0, 2)

2 Which pairs of line segments contain parallel sides on the hexagon below?

y

xO

Q

S

TV

P

R

F ____

PQ and ____

QR G

____ PQ and

____ RS

H ____

PQ and ____

ST J

____ RS and

____ ST

3 The graph shows two line segments.

y

xO

( 3, 0) (0, )

(0, 4)Q

Q'

P'

43

( 1, 0)

P

Which coordinate pairs for vertices T and T' would complete two similar triangles PQT and P'Q'T'? A T'(-3, 6), T(-3, 6)B T'(-1, 2), T(-3, 6)C T'(0, 3), T(0, 6)D T'(1, -1), T(1, -3)

4 The coordinates on a number line of the endpoints of line segment

___

AB are –4 and +3. What are the two possible end point coordinates of a congruent segment with one endpoint at –6? F –7 and –5G –10 and –2H –9 and –3J –13 and + 1

G.7(A) The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays. line segments, and fi gures.




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1 Ryan promised to help his mom paint a series of stripes that parallel the staircase. The equation defi ning the staircase is 10y = 8x, for 0 ≤ x ≤ 12, and the equation of the fi rst stripe is y = mx - 1. What is the value for m? A 0.1B 0.8C 1.25D 8.00

2 The line 4y = -5x - 4 contains one of the parallel sides of a trapezoid. Which of the following lines could contain the other? F 10y = -8x + 11G y = -0.8x + 7H y = 1.25x - 5J -y = 1.25x - 6

3 Friends intend to go mountain biking in Palo Duro Canyon. Some will take Highway 87, a north-south highway, while others will take 4th Avenue, an east-west road. If the map of the area were superimposed on a coordinate grid and Highway 87 followed the graph of the equation 2x = 12, what could be an equation for 4th Avenue? A x = 6B x = -6C y = 4D y = 2x + 3

4 Two sides of a rhombus are shown below.

y

xO

Which equation might contain one of the other two sides of the rhombus? F 3y = -4x + 1G 3y = -4x + 3H 3y = 4x + 3J 4y = -3x + 4

5 See the line graphed below.

y

xO

Which equation describes a line perpendicular to the graphed line? A y = 0.5x + 2B y = -2x + 3C 2y = x - 2D 4y = 2x + 2

G.7(B) The student is expected to use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons.



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1 In San Antonio, Megan’s family walks from the Instituto Cultural Mexicano to the Spanish Governor’s Palace. If the two were plotted on a coordinate plane, the Instituto might be at (0, 1) and the palace at (-2, 0), with 1 unit equaling 1 block. If Megan could take a bird’s straight fl ight path from one site to the other, what would the distance be? A 1.41 blocks C 2.24 blocksB 1.73 blocks D 2.42 blocks

2 After seeing the Four Seasons Garden at Fort Worth, Justin decides that a four seasons garden would make a perfect wedding present for his older sister. He plans the garden as shown, with the coordinates (6,5.5) and (2.5,5) marking a line that forms the diameter of the garden.

Chrysanthemum

Daylily

Iris

Daylily

(2.5, 5)

(6, 5.5)

Justin plans to place a small fountain at the center of the garden. What would be its coordinates? F (1.5, 5.75) H (4.25, 3)G (1.75, 2.5) J (8.5, 6)

3 Padma wants to build an arbor across a sidewalk that angles from her house to the street. When she lays out the plot plan for the house and grounds, the endpoints of the sidewalk are located at (-5, -2) and (6, 3), as shown.

(6, 3)

( 5, 2)

The arbor will be built at the midpoint of the sidewalk’s length. Which coordinate pair marks the midpoint? A (0.5, 2.5) C (1, 1)B (0.5, 0.5) D (5.5, 2.5)

4 The diameter of a circle is shown below.

( 8, 4)

(1, 2)

What is the length of the circle’s diameter? F 6.71 units H 10.82 unitsG 8.24 units J 12.37 units

G.7(C) The student is expected to derive and use formulas involving length, slope, and midpoint.




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best answer.

1 Jonelle plays a game with her younger sister. A bag contains several prisms. Each has an identical match in the bag. The fi rst prism her sister fi nds is the one shown below.

Which prism matches the one Jonelle’s sister has? A an oblique hexagonal prismB an oblique pentagonal prismC a right octagonal prismD a right regular pentagonal prism

2 Two cubes of the same size are joined together to make a right square prism. Which statement best describes the relationship between the cubes and the prism they form? F The volume of the right square prism is

3 times the volume of 1 cube.G The base of the right square prism has

an area 2 times the base of 1 cube.H The lateral sides of the prism have a

length 2 times the sides of 1 cube.J The surface area of the right square

prism is 4 times the surface area of 1 cube.

3 Chelsea needs to know the surface area of a prism with regular hexagonal bases. She has already calculated the area of the bases. What should she do now? A Multiply the area of one of the bases by

the height of the prism.B Find the area of 1 side of the prism,

multiply it by 5, and then add that fi gure to the area of the 2 bases.

C Find the area of 1 side, multiply that number by 6, and add it to the area of the two bases.

D Multiply the area of 1 base by 6.

4 The top of a downtown Austin building forms a pyramid. Imagine the pyramid is removed, the building is re-roofed, and the building becomes a prism with 5 surfaces. What type of prism does the building form? F triangular prismG rectangular prismH pentagonal prismJ hexagonal prism

5 Colby assembles a storage container, but the container appears to be missing a piece. He has two pieces that measure 2 feet by 6 inches, two pieces that measure 3 feet by 6 inches, and one piece that measures 2 feet by 3 feet. What is the most likely shape of the resulting prism after he locates the missing piece? A triangular prismB cubeC rectangular prismD pentagonal prism

G.9(D) The student is expected to analyze the characteristics of polyhedra and other three-dimensional fi gures and their components parts based on explorations and concrete models.



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best answer.

1 Tiffany wants to make a superhero cape for her little sister. The pattern is shown below.

Cros

swis

e Fo

ld

radius of smallcutout = 4 in.

45 in.

45 in.

If the shaded area is not counted, what is the approximate area of cloth used for the cape? A 1540 in.2 C 1590 in.2

B 1577 in.2 D 2025 in.2

2 The graph shows a parallelogram.

y

xO

(0, 2)P

Q R

S( 5, 2)

( 2, 2) (3, 2)

What is the area of the parallelogram? F 16 units2 H 25 units2

G 20 units2 J 32 units2

3 The Travis Central Appraisal District divided land into more than 175,000 polygons. The possible shape and dimensions for one are shown.

325 ft 425 ft

450 ft

250 ft

Which is the area of this parcel? A 111,250 ft2 C 174,357 ft2

B 168,750 ft2 D 181,250 ft2

4 Joshua’s family woke one morning to fi nd that mysterious crop circles had fl attened portions of his family’s corn crop. The fi eld and circles are shown below.

300 ft

200 ft

75 ft

150 ft

r = 60 ft

r = 30 ft

How much of the family’s corn crop was NOT fl attened by the circles? F 27,120 ft2 H 38,424 ft2

G 30,870 ft2 J 40,967.40 ft2

G.8(A) The student is expected to fi nd areas of regular polygons, circles, and composite fi gures.




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1 Katie works for a caterer in Grapevine on the weekends. The diagram shows a 12-inch-round platter of different cheeses she assembled.

FarmhouseCheddar

Gruyere

Morbier

Shropshire Blue

144˚

What is the surface area of the platter that the Farmhouse Cheddar occupies? A 15.07 in.2

B 45.22 in.2

C 90.43 in.2

D 180.86 in.2

2 When Andrew visits his brother at Texas Tech, he runs around the outer lane of the track at the top of the dome. The dome is 300 feet in diameter. How many times does he have to circle the track if he wants to run a mile? F 5.6G 11.2H 13.4J 17.6

3 A group of singers is arranged on the school’s stage as shown.

25 ft

30˚

How long is the portion of the stage’s circumference where the singers are standing? A 3.27 ftB 6.54 ftC 13.08 ftD 40.89 ft

4 The dome of an old building provides a panoramic view of the city. A visitor standing in the center of the dome has a 12° view through one window. What is the approximate diameter of the dome if the window is 18 inches wide? F 1.43 ftG 7.17 ftH 14.33 ftJ 171.97 ft

G.8(B) The student is expected fi nd areas of sectors and arc lengths of circles using proportional reasoning.



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1 Lourdes works at a frame shop after school. She put together 4 frames. All corners need to measure 90°. Which of the four frames has corners that all measure 90°? A

13 units

9 units

16.01 units

B

10 units

9 units

13.52 units

C

3 units

9 units 9.49 units

D

15 units

8 units18 units

2 See ____

PQ shown below.

y

xO

P(-5, 1)Q(1, 2)

Using the Pythagorean Theorem, which coordinates for vertex R would create a right triangle? F (1, 4) H (0.577, -0.288)G (0.577, -0.115) J (-5, -3)

3 Amber wants to drive from her home in Corpus Christi to visit a friend in Waco. An Internet search turns up the distances between Corpus Christi and Galveston and between Galveston and Waco. Amber notices that the 3 cities form a triangle as shown.

CorpusChristi

Galveston

DallasTexas

10

10

37

Waco

Austin

SanAntonio

212 miles

180 miles

Houston

What does Amber estimate as the approximate distance between Corpus Christi and Waco? A 112 mi C 278 miB 196 mi D 392 mi

G.8(C) The student is expected to derive, extend and use the Pythagorean Theorem.




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1 A company wants to introduce a smaller container for its salt. The new cylinder will have a diameter of 6 centimeters and a height of 10 centimeters. Which will be the volume of the new container? A 90 cm3

B 118.4 cm3

C 282.6 cm3

D 1130.4 cm3

2 Radha shares a room with her younger sister. For privacy, she hangs a canopy of beaded netting around the chair in her half of the room.

3 m

1 m

What is the volume of space that Radha enclosed? F 3.14 m3

G 6.28 m3

H 12.56 m3

J 18.84 m3

3 Brian does not want the helium balloons he bought for his girlfriend’s birthday fl ying all around his car while he drives. He fi nds a box in his trunk and fi ts them in as shown.

1 m

What is the volume of each balloon if the 3 are identical in size? A 0.01939 m3 C 0.1163 m3

B 0.1150 m3 D 0.5817 m3

4 A pyramid of honeycomb is placed in the center of a table. If that honeycomb had a square base of 5 inches and a height of 6 inches, and if 1 fl uid ounce (oz) is equal to 1.8 cubic inches, how many ounces of honeycomb might be on the table? F 27.78 oz H 82.12 ozG 33.25 oz J 90.23 oz

5 For a craft activity at the community center where she volunteers, Danielle provides spherical balloons infl ated to 5 inches in diameter. The children will cover them with papier-mâché. What is the surface area each child will cover? A 15.7 in.3 C 78.50 in.3

B 65.42 in.3 D 314 in.3

G.8(D) The student is expected to fi nd surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these fi gures in problem situations.



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1 A builder designs a room as shown.

Then the builder makes changes to the design, as shown.

Which change did the builder make? A He refl ected the design across a

vertical axis.B He refl ected the design across a

horizontal axis.C He dilated the design.D He translated the design to the right.

2 Dario recreates an 1862 map of Texas for his bedroom wall. The original is 16.5 inches by 24.5 inches, but Dario wants his representation to be larger. Which of the following might be the size of Dario’s enlargement, if it is mathematically similar? F 20.53 in. by 30.63 in.G 24.75 in. by 36.75 in.H 32.00 in. by 49.00 in.J 41.25 in. by 62.15 in.

3 Alika collects pottery bowls of different sizes but with shapes similar to the one shown.

h = 8

r = 12

Which of these bowls would NOT belong in her collection? A

h = 2.5 r = 3

B

h = 4

r = 6

C h = 1

r = 1.5

D

h = 2 r = 3

4 A scalene triangle lies completely in the fi rst quadrant. Which transformation is not equivalent to the other three? F 180° clockwise rotation about the

originG refl ection in y-axis followed by

refl ection in x-axisH refl ection in x-axis followed by

refl ection in y-axisJ translation across x-axis followed by

translation across y-axis

G.11(A) The student is expected to use and extend similarity properties and transformations to explore and justify conjectures about geometric fi gures.




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1 Forbidden Gardens in Katy has 1 _ 3 -scale replicas of the fi rst Chinese emperor’s 6000-piece terra cotta army. The original terra cotta army features soldiers of varying heights and in various postures. If a replica in Katy is 22 inches in height, how tall would the original in China be? A 3.67 in. C 7 ft 4 in.B 5 ft 6 in. D 66 ft

2 Rectangle PQRS is shown.

y

xO

P S

Q R

Rectangle P'Q'R'S' is a dilation of PQRS by a scale of 2. What is the area of rectangle P'Q'R'S'? F 25 units2 H 100 units2

G 50 units2 J 625 units2

3 Ariana and her father build a 0.08-scale model of her grandmother’s cottage in Greece as a present for her mother. If the scale model has a square footage of 7.68 square feet and if one side is 3.2 feet long, what is the square footage of her grandmother’s cottage? A 0.049 ft2 C 2240 ft2

B 1200 ft2 D 3840 ft2

4 �PQR and �STV are similar. The triangles and some of their dimensions are shown.

3 cm

h = 2.91 cm

R P

Q

T

S V

8 cm

Which is the area of �STV? F 1.64 cm2 H 11.6 cm2

G 3.27 cm2 J 16 cm2

5 An isosceles trapezoid is shown.

y

xO

For any trapezoid, the area A is defi ned by

the formula A = 1 _ 2 h(b1 + b

2), where h is

the height of the trapezoid, b1 is the length

of one of the parallel bases and b2 is the

length of the other. If a second trapezoid is

a 1 _ 5 contraction of the one shown, what is

its area? A 1.2 units2 C 6 units2

B 4 units2 D 30 units2

G.11(B) The student is expected to use ratios to solve problems involving similar fi gures.



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best answer.

1 A triangle has sides of the following lengths: 150, 150 √

_

2 , and 150 millimeters. Which of the following triangles could NOT be similar to this triangle? A a triangle with 2 equal sides 2 inches

longB a triangle with 1 side with a length

of 20 meters, 1 angle of 90°, and a hypotenuse of 28.28 meters

C a triangle with two 45° anglesD a triangle with a right angle and another

angle of 30°

2 Amir and his brother each build ramps for their bikes on the family property. Each ramp includes one 90° angle, as shown.

One brother decides to build a steeper ramp with a 45° slope. Which describes the steeper ramp? F a ramp with the length equal to √

_

2 times its height from the ground.

G a ramp with sides of 4 √

_

3 , 4, and 8H a ramp with one side 2 times the length

of the otherJ a ramp with one 30° angle

3 A right triangle has sides of 3, 4, and 5 centimeters. Which triangle would be similar? A a triangle with two 60° anglesB a right triangle with sides of 50, 80, and

94.34 cmC a right triangle with sides of 45, 60, and

75 in.D a right triangle with sides of 3, 5, and

5.83 ft

4 Two right triangles have sides that are Pythagorean triples. Which other condition or conditions must exist for them to be similar to each other? F None, since all triangles with sides that

are Pythagorean triples are similar to each other.

G If one has sides of lengths a, b, and c, the other must have sides of ka, kb, and kc, where k is a constant.

H One side of each triangle must be divisible by 5.

J The hypotenuse must be an odd number.

5 At a Kerrville quilt shop, Katie fi nds a quilt pattern she wants to expand and paint on her wall. If the original pattern has a pieced right triangle with sides of 3, 4, and 5 inches, which similar measurements might she paint on her wall? A a right triangle with sides of 5 ft, 6 ft 8

in., and 8 ft 4 in.B a right triangle with two sides of 16 in.C a right triangle with a hypotenuse of

30 in. and one side of 25 in.D a right triangle with a hypotenuse of

30 in. and one side of 20 in.

G.11(C) The student is expected to develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods.




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best answer.

1 A builder chooses between 4-inch Venetian tiles and 16-inch Venetian tiles. How many more tiles will the builder have to grout if she chooses the 4-inch tiles? A 4 times as manyB 8 times as manyC 16 times as manyD 64 times as many

2 Amy intends to use Texas limestone for a retaining wall on her property. She can choose blocks that are 6 inches wide, 12 inches long, and 6 inches wide, as shown.

6 in.

6 in. 12 in.

Top Surface

Amy can also choose similar blocks that are a dilation by a scale factor of 2 of the smaller block. She intends to use the top of the wall as a bench. How much larger is the area of the top surface of the larger block than that of the smaller one? F 2 times as largeG 4 times as largeH 8 times as largeJ 64 times as large

3 The volume of a cube is 8 times that of a second cube. The second cube is a contraction of the fi rst. Which is the scale factor of the contraction?

A 1 _ 32

C 1 _ 4

B 1 _ 8 D 1 _

2

4 Two similar triangles are shown.

7 cm1 cm

b

The area of the smaller triangle is what fraction of the area of the larger?

F 1 _ 7 H 1 _

49

G b _ 7 J b _

49

5 The Sun’s radius is about 109 times as large as Earth’s. By which factor would the Sun’s circumference be larger than Earth’s? A 109 C 11,881B 218 D 1,295,029

G.11(D) The student is expected to describe the effect on perimeter, area, and volume when one or more dimensions of a fi gure are changed and apply this idea in solving problems.



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1 Guidelines from the government suggest that a 17-year-old female who exercises between 30 and 60 minutes a day should consume 17.5 cups of vegetables per week. The breakdown between vegetable groups is as follows: 3 cups of dark green vegetables, 2 cups of orange vegetables, 3 cups of dry beans and peas, 3 cups of starchy vegetables and 6.5 cups of other vegetables. Which of the pie charts shows the correct percentages of vegetables suggested? A Dark

Green

Dry

StarchyOrange

Other

B DarkGreen

DryStarchy

OrangeOther

C DarkGreen

Dry

Starchy

OrangeOther

D DarkGreen

Dry

Starchy

OrangeOther

2 Ahren has $30.02 this week to spend on CDs. His employer deducts 5% of his total earnings for taxes and other costs. Ahren allows himself to spend only 20% of his take-home pay on CDs. What were his total earnings? F $1.58 H $158.00G $5.70 J $300.20

3 Jennifer and her father are aviation fans. One summer they toured aviation museums in Schulenburg, Addison, and Houston, among others. The admission price for one was $10. The admission price for a second was 80% of the admission of the fi rst. The admission price for the third was 25% of the admission price for the second. What was the admission price for the third museum? A $1.50 C $2.50B $2.00 D $50.00

4 A cylindrical container holds 25 bath beads. A similar container has a radius and height that are twice that of the fi rst container. About how many bath beads will the second container hold? F 50 H 200G 100 J 250

5 Two rotors of the same diameter spin at different rates. The fi rst rotor spins at a rate of 120 rotations per minute and completes 2400 more rotations in an hour than the second rotor. What is the speed of the second rotor? A 60 rpm C 80 rpmB 70 rpm D 90 rpm

8.3(B) The student is expected to estimate and fi nd solutions to application problems involving percents and other proportional relationships such as similarity and rates.




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1 Sponsors for a cheerleading squad hand out lunch bags to the 15-member group before they board the bus for a game. Four of the bags have orange juice and the rest have tropical punch. J.C. picks up bags for himself and a friend. What is the probability that both bags have orange juice?

A 2 _ 35

C 101 _ 210

B 2 _ 15

D 8 _ 15

2 Justin’s family wants to go deep-sea fi shing. Justin picks 5 different ports and writes each one on a slip of paper. He puts the slips into a bag for his brother to draw from. If Justin’s brother picks a slip but then returns it to the bag, what is the probability that Justin will draw the same slip himself?

F 1 _ 25

H 2 _ 5

G 1 _ 5 J 9 _

20

3 A teacher puts topics for senior papers in a basket on her desk and asks each student to choose one. Five students will be asked to write papers on Thoreau, 5 on Maya Angelou, and 12 on T.H. White. Kenny’s best friend is absent, so he draws fi rst for himself and then for his friend. Expressed as a percentage, what is the probability that both will be writing papers on Angelou? A 4.3% C 17.4%B 11.4% D 45.5%

4 When gathering for graduation practice, students are handed a number from 1 to 10, directing them to a certain line. When they reach the head of their assigned lines, they will be given either a red or a black robe, with the color assigned at random. What is the probability that a student will be directed to line number 3 and receive a red robe, with the probability expressed as a decimal? F 0.05 H 0.15G 0.06 J 0.6

5 At the end of the year, students with perfect attendance are awarded coupons for either a local coffee or movie rental shop. Eighteen students had perfect attendance. The principal holds 15 coupons for the coffee shop and 15 for the movie rental shop, to be given out randomly. What is the probability that the fi rst two students receive coupons for the coffee shop?

A 1 _ 210

C 7 _ 29

B 1 _ 15

D 29 _ 30

6 A sack contains 13 butterscotch candies, 3 strawberry candies, and 8 chocolate candies. Marvin takes a candy at random and then passes the sack to his friend, Joe. Joe takes a candy at random, and passes it to George, who does the same. What is the probability that none of the 3 friends choose a chocolate candy?

F 14 _ 253

H 70 _ 253

G 7 _ 53

J 1 _ 3

8.11(A) The student is expected to fi nd the probabilities of dependent and independent events.



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1 During basketball practice, James broke the index fi nger on his left hand. He has to type a paper. He counts two lines of a previously written paper and fi nds the results for various keystrokes shown in the table.

Keystroke TimesFound Keystroke Times

Found

A 6 M 1B 3 N 5C 2 O 3D 2 P 1E 9 R 4F 2 S 5G 1 T 3H 2 U 1I 6 X 1J 1 Y 1K 1 Space 17L 3 Shift 3

The keystrokes that require him to use his broken fi nger are 4, 5, B, F, G, R, T or V. What is the probability that a given keystroke on the paper will NOT require the use of his broken fi nger?

A 1 _ 13

C 13 _ 70

B 13 _ 83

D 70 _ 83

2 Kayla checked her cell phone records. Out of the last 60 calls placed to her phone, she concludes that the probability that the next

call will be from her mother is 2 _ 15 and the

probability that the next call will be from

her best friend is 1 _ 3 . Based on this

experimental evidence, what is the probability that the next call will be from someone other than her mother or best friend?

F 3 _ 15

H 8 _ 15

G 7 _ 15

J 13 _ 15

3 Aisha’s senior thesis must average 265 words a page to meet the school’s requirements. The table below shows her average words per page on previous high school papers.

Words Per Page

256 261 268268 267 263267 259 255258 253 266247 260 268

Based on these experimental results, what is the probability that the paper Aisha has just completed will have an average of 265 or more words per page?

A 2 _ 15

C 2 _ 5

B 1 _ 3 D 3 _

5

8.11(B) The student is expected to use theoretical probabilities and experimental results to make predictions and decisions.




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1 For health class, Carl was required to record the number of calories he consumed per day during the school week. His results are shown in the table.

Day Calories

Monday 3210Tuesday 2430Wednesday 2950Thursday 3190Friday 2500

One source suggests that Carl can consume an average of 3044 calories a day to maintain his current weight. Which measure of central tendency will best tell him if he is consuming enough calories? A mean C modeB median D range

2 The Sandwich Board has developed 5 new sandwiches. After testing them out for several months, what measure of central tendency could they use to determine the best sandwiches to keep on the menu? F mean H modeG median J range

3 Orlando has worked for the same grocery store chain for several years. His monthly salary tends to fl uctuate, depending on the hours he works. By the end of the next year, he hopes to have saved about 10% of his yearly salary. What is the best way to determine how much he should take out of each month’s paycheck? A He should fi nd the range of his

paychecks over the last year, and then save 10% of the highest value of the range from each month’s paycheck.

B He should fi nd the mode for the last year and save 10% of that amount from each month’s paycheck.

C He should divide a year’s salary by 12 to fi nd the mean and save 10% of that amount from each month’s paycheck.

D He should fi nd the median for the last year, and save 10% of that amount from each month’s paycheck.

4 Celeste received the following grades in history class: 95, 89, 99, 87, and 92. What measure of central tendency should she use to determine her grade in the class? F range H medianG mode J mean

8.12(A) The student is expected to select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation.



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1 The Wilson family plants fl owers in the front yard. Mr. Wilson plants 35% of the fl owers. Mrs. Wilson plants 15% of the fl owers. Two children each plant 20%. The third child plants 10%. Which circle graph represents this information? A

Mr.Wilson

Child 1

Child2

Child 3

B

Mr.Wilson

Mrs.Wilson

Child 1

Child2

Child 3

C

Mr.Wilson

Mrs.Wilson

Child1

Child2

Child 3

D Mr. Wilson

Mrs.Wilson

Child 1

Child 2 Child 3

2 A list of colleges and universities in Texas shows 75 community colleges, 57 private universities, and 41 public universities. Which chart represents this information? F

100500

Public

Community

Private

Number of Colleges

G

100500

Public

Community

Private

Number of Colleges

H

100500

Public

Community

Private

Number of Colleges

J

6020 400

Public

Community

Private

Number of Colleges

8.12(C) The student is expected to select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.




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1 Trent tracks his average grades for each month over a school year. During the months of December, January, and February, Trent worked at a part-time job. During the month of October, Trent missed several days of school.

Nov

.

Oct

.

Sept

.

Aug

.

10

20

30

40

50

60

70

80

90

100

0

Ave

rag

e G

rad

e

Dec

.Ja

n.Fe

b.M

ar.

Apr

. M

ay

Month

Which information is NOT a correct conclusion? A Trent’s grades were likely affected by

his after-school job.B Trent’s grades improved from March

through May.C Trent’s grades were affected by his

absences. D Trent’s highest average was the fi rst

month of school.

2 The graph below shows the average rainfall each month for the past year in Kilgore, Texas.

Nov

.

Oct

.

Sept

.

Aug

.

1

2

3

4

5

6

0

Rai

nfa

ll( i

n.)

Dec

.

Jan.

Feb.

Mar

. A

pr.

May

Jun.

Jul.

Month

What can be concluded from the graph? F Average rainfall decreased over the

year.G Average rainfall was the lowest in

March.H Average rainfall was the highest in

June.J Kilgore had an unusual amount of rain

during the last year.

3 New books will be purchased for the school library. The school needs to know the percentage of books currently held that were purchased last year, 2 years ago, 5 years ago, and 10 years ago. What is the best method to represent this information? A a circle graph showing the percentages

of each categoryB a scatterplot with 1 point for each

category, with the point showing the percentage of books in that category

C a line drawing showing the number of books in each category

D a bubble chart with one bubble for each category, with the bubble representing the number of books in that category

8.13(B) The student is expected to recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.



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1 A Texas state sales tax of 6.25% is levied on all retail purchases except food. Corrine bought a magazine, a loaf of bread, and a T-shirt at the local convenient store. Before tax, her total came to $16.97. What additional information is needed to determine the amount of tax Corrine paid? A the price of the magazineB the price of the T-shirtC the price of the loaf of breadD All necessary information has been

given.

2 Parking at Main Street Garage costs $2.00 for the fi rst hour, $1.50 for the second and third hours, and $1.00 every hour thereafter. Josette parks in the garage 20 days a month for the same number of hours each day. What additional information is needed to determine Josette’s monthly parking fee? F the number of days in the monthG the number of hours she parks in the

garage each dayH the time she leaves the garage each dayJ All necessary information has been

given.

3 Sean’s swimming lap time linearly decreased over the course of the swim season. At the end of the season his lap time was 25 seconds. What additional information is needed to determine the rate at which Sean’s lap time decreased each day throughout the season? A his lap time at the beginning of the

seasonB his lap time the day before the end of

the seasonC the kind of stroke he was swimmingD the number of days in the swim season

4 A line contains the point at (0, 5). What additional information is needed to determine the equation of the line? F the y-intercept of the lineG whether the line passes through the

originH the equation of a line that does not

intersect itJ the slope of the line

5 Ms. Harrison wants to carpet her classroom before the new school year starts. Carpeting costs $4 per square foot plus 6.25% sales tax. The width of her classroom is 25 feet. What other information is needed to determine the cost of carpeting the classroom? A the length of the roomB the total cost of each square foot of

carpetingC the number of desks in the classroomD the store’s discount policy for private

organizations

8.14(A) The student is expected to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.



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1 Ms. Bradshaw and Mrs. Cornell split their coffee shop bill. They ordered 4 coffees at $3.00 apiece plus $0.10 per creamer. If Mrs. Cornell’s portion of the bill came to $6.25, how many creamers did they use? A 2.5 C 7.5B 5 D 10

2 A telephone call costs $0.50 for each of the fi rst 5 minutes and $0.15 per minute thereafter. The total cost of a call was $5.50. How many minutes did the call last? F 11 H 25G 20 J 36

3 Boris’ radio fell off his desk and the antenna bent as shown below.

X

16

The antenna’s original height above the radio was 20 inches. After it was bent, the top of the antenna touched the radio 16 inches from the base. How tall is the part of the antenna left standing? A 3.6 in.B 4 in.C 12 in.D 16.4 in.

4 A square is shown below.

3 cm

How many of these squares can fi t together without any gaps in order to make a similar fi gure with an area of 144 square centimeters? F 4G 16H 24J 48

5 Jaya, Barry, and Cal split the cost of their parking fee. The cost for parking is $1.00 for the fi rst hour and $0.50 per hour thereafter. If Cal’s portion of the bill was $2.00, how many hours was their car parked? A 3B 5C 10D 11

6 Lucinda bought 3 identical tablecloths. The tax on the tablecloths was 6%. Her total, with tax, came to $39.75. How much did 1 tablecloth cost? F $8.28G $12.50H $12.99J $13.25

8.14(B) The student is expected to use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.



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1 Andy had a box of crayons. He gave three-quarters of the crayons to his little brother, Pete. Pete lost half of his crayons and then gave one-sixth of the crayons left back to Andy. If Pete still has 10 crayons, how many were in the box to begin with? A 12 C 32B 24 D 48

2 Louie inherited a sum of money. He put half of it in the bank. He then set aside one third of the remaining amount for charity. He divided that amount among four different charities. If each charity got $2,000, how much money did Louie inherit? F $8,000 H $24,000G $12,000 J $48,000

3 Jimmy wants to solve the equation 7 - 3x = 2x - 3 by graphing. Which method can he use to fi nd the solution for x? A Graph the lines y = 7 - 3x and

y = 2x - 3 and then fi nd the x-coordinate.

B Graph the lines y = 7 - 3x and y = 2x - 3 and then fi nd the average of the x-intercepts.

C Graph the line 7 - 3x + 2x - 3 = yand then fi nd the y-intercept.

D Graph the line 7 - 3x - 3 - 2x = y and then fi nd the y-intercept.

4 How many disks with a radius of 2 units and a thickness of 1 unit can be stacked inside a cylinder with a base of 4π square units and a height of 8 units? F 4 H 16G 8 J 32

5 Polly has a bag of chips. She gives onehalf of them to Quentin. Quentin then gives one third of his chips to Raoul. Raoul, in turn, gives one quarter of his chips to Santo. If Santo has 5 chips, how many chips were in the bag at the start?


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6 Sandivar loses one-third of his change on the bus. When he gets to school, he uses two-thirds of his remaining change to pay for lunch. From the money left over, he puts one half in the library’s charity tin. At the end of the day, Sandivar has $0.72 in change. How much change did he start with? A $2.16 C $4.32B $2.86 D $6.48

8.14(C) The student is expected to select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systemic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.




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As part of a classroom assignment, Kevin was given a geoboard to model the y-intercept and slope of the line 6x + 3y = 6. Use the geoboard to answer Questions 1 and 2.

4

0

3

2

1

01 2 3 4

5

6

5 6

A B

C

DE F

G

1 If the peg in the lower left-hand corner represents the origin on a coordinate plane, which peg represents the y-intercept? A peg AB peg BC peg CD peg F

2 If the peg in the lower left-hand corner represents the origin on a coordinate plane, where would Kevin place a rubber band to represent the slope of the line? F origin to peg DG origin to peg EH origin to peg GJ not here

3 Zoe wanted to fi nd 3 consecutive even numbers that totaled 102. She wrote the equation (n - 4) + (n - 2) + n = 102. What does the variable n represent in the equation? A the least of the three even numbersB the middle of the three even numbersC the greatest of the three even numbersD the average of the three even numbers

4 An astrophysicist determined the relation-ship between V, the volume of a sphere, and S, the surface area of a sphere. Which equation represents this relationship?

F V _ S = r _ 3 H V _

S =

16 _ 3r

G V _ S =

16r _ 3 J V _

S =

1 _ 3r

5 A carpet installer mathematically expressed the dimensions of a room in square footage. Which of the measurements below did he report? A the room’s perimeterB the room’s areaC the room’s surface areaD the room’s volume

6 Anise wanted to fi nd 4 consecutive odd numbers that totaled 309. She wrote the equation (n - 2) + n + (n + 2) = 309. What does the variable n represent in the equation? F the least of the three odd numbersG the middle of the three odd numbersH the greatest of the three odd numbersJ the sum of the least and greatest of the

three odd numbers

8.15(A) The student is expected to communicate mathematical ideas using language, effi cient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.



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1 Not including the years ending in double zeroes, those that are divisible by 4 have 366 days. All others have 365 days. Which year has 366 days? A 2106 C 2364B 2310 D 2402

2 A townhouse builder used arrangements of toothpicks to describe his latest plan to a coworker. The diagram below shows the toothpick arrangement he used for 1 and 2 townhouses.

Which expression can be used to determine the number of toothpicks the builder will need to represent y connected houses? F 6y H 5yG 6y - 1 J 5y + 1

3 Zach claimed that the square root of a number is always less than or equal to the number. Which of the following examples disproves Zach’s claim?

A √ __

1 _ 4

B √

_

1 C √

_

4 D Zach’s claim is true.

4 If the sum of a number’s digits is divisible by 3, that number is divisible by 3. Which number is NOT divisible by 3? F 100,000,002G 100,000,011H 311,000,003J 432,000,000

An ice cream shop surveyed 200 customers to determine their favorite sundae topping or combination of toppings. Use the Venn diagram below to answer Questions 5 and 6.

HotFudgeCherry

WhippedCream

70

30 50

8

10

12 20

5 How many of the customers surveyed picked a combination of 2 toppings as their favorite? A 8B 20C 42D 50

6 How many people surveyed picked whipped cream as at least one of their favorite toppings? F 110G 102H 90J 70

8.16(A) The student is expected to make conjectures from patterns or sets of examples and nonexamples.




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Use the circle graph below to answer

Questions 1 and 2.

A

B

C D

1 The circle graph most accurately represents which of the following situations? A In a recent survey about favorite

subjects, 50% of those surveyed chose discrete math, 30% chose chemistry, 20% chose biology, and 10% chose algebra.

B On a history test, parts A, B, C, and D comprised equal portions of the overall score.

C In a class election, Amy received 3% of the votes, Brian received 12%, Carl received 25%, and Deondrea received 60%.

D On a test, Part A comprised 5%, Part B comprised 15%, Part C comprised 35%, and Part D comprised 45%.

2 Which portion of the graph represents

more than 1 _ 5 but less than 1 _ 3 ? F A H CG B J D

3 ‹

____ › AB is parallel to

‹

____ › DE . Which conclusion

can be drawn? A The two lines intersect at some point C.B

‹

____ › AB ⊥

‹

____ › DE

C Points A, B, D, and E are collinear.D The two lines never intersect.

Use the diagram below to answer Questions 4 and 5.

Q

Y W

ZX

4 What conclusion can be drawn about ‹

_____ › WX

and ‹

____ › YZ ?

F ‹

_____ › WX and

‹

____ › YZ are parallel.

G ‹

_____ › WX and

‹

____ › YZ are perpendicular.

H ‹

_____ › WX and

‹

____ › YZ are supplementary.

J No conclusion can be drawn.

5 What conclusion can be drawn about ∠YQX and ∠WQZ? A They are complementary.B They are supplementary.C They have an equal measure.D No conclusion can be drawn.

6 ∠ABC and ∠DEF are vertical angles. The measure of ∠ABC is 90°. What conclusion can be drawn? F ∠ABC and ∠DEF are complementary.G ∠ABC and ∠DEF are supplementary.H ∠ABC and ∠DEF are perpendicular.J ∠ABC and ∠DEF are parallel.

8.16(B) The student is expected to validate his/her conclusions using mathematical properties and relationships.




best answer.

1 The formula for the circumference, C, of a circle is C = πd, where d is the diameter. Which statement best describes the functional relationship represented by the formula? A C is a dependent variable.B π is a dependent variable.C d is a dependent variable.D C, π, and d are all independent

variables.

2 Mrs. Whitson determined that the total cost of the class fi eld trip, t, could be represented by the equation t = 45s + 495, where s is the number of students going on the trip. If the trip costs $1845, how many students are going? F 30G 18H 11J 8

3 What is the area of the shaded region of the square, reduced to simplest terms?

x + 2

x

3x

3x

A 9x2

B 9x2 – x – 2C 8x2 + 2xD 8x2 – 2x

4 The estimated number of persons over age 65 in San Marcos varies directly with the city’s total population. It is estimated that on average, 7 out of every 100 San Marcosans are over age 65. If San Marcos’s total population is approximately 43,000, about how many residents are over age 65?


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5 Amil is 5 years older than Bette. Craig

is 4 _ 3 as old as Amil. If Bette is b years

old, which equation can be used to fi nd c,

Craig’s age?

F c = 4 _ 3 b H c = 4 _ 3 (b + 5)

G c = 4 _ 3 b + 5 J c = 4 _ 3 (b – 5)

6 Which polynomial best represents the area of a circle with a radius of x – 3? A π(x2 + 9) B π(x2 – 6x – 9)C π(x2 – 6x + 9)D π(x2 – 6x) C

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Practice Test

076-085_PT_TX_877327.indd 76076-085_PT_TX_877327.indd 76 6/30/06 9:44:59 AM6/30/06 9:44:59 AM

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Practice Test (continued)

7 A labor study reveals that the average lifetime income, d, of people who possess a college degree is twice as great as the average lifetime income, n, of their non-degree counterparts. Which equation represents this relationship?

F d = 1 _ 2 n H d = 2n

G d = n + 2 J n = 2d

8 Cory took a 3-day bike trip. On day 1 he biked 20 miles more than half the distance he biked on day 2. On day 3 he biked 40 miles less than twice the distance he biked on day 2. What additional information would make it possible to determine how far Cory biked each day? A his acceleration each dayB his speed each dayC the time he spent biking each dayD the total distance he biked

9 Which equation will produce the narrowest parabola when graphed?

F y = –x2

G y = – 1 _ 2 x2

H y = 1 _ 4 x2

J y = 2x2

10 The area, A, of a circle is represented by the function A = πr2, where r is the radius of the circle. What is the approximate value of r when A = 154? A 7B 12.4C 23,716D 74,536

11 Shape ABCDE is congruent to shape FGHIJ. What are the coordinates of point G?

y

x1 2 3 4 5 1 2 3 4 5

5

3 4

2 1

A

B

C

D

F

G

H

IJE

F (–3, –4)G (–3, –2)H (–2, –3)J (3, 4)

12 Which of the following patterns will NOT fold to form a cube?

A

B

C

D


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13 What is the range of the function shown on the graph?

y

x1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

5

3 4

2 1

F –1 < y < 3G –1 ≤ y ≤ 3H –2 < x < 2J –2 ≤ x ≤ 2

14 Which of the following represents a linear function? A 2x

B x4 + 1C 3 – 3xD x2

15 In right triangle ABC, the interior angle C measures 60°. Which shows the measure of all three interior angles of triangle ABC? F 30°, 60°, and 90°G 60°, 60°, and 60°H 60°, 90°, and 210°J 60°, 150°, and 150°

16 FG has endpoints at (–3, 4) and (1, –2). What are the coordinates of the midpoint of FG ? A (–2, 3)B (–1, 1)C (0, 0)D (3, –2)

17 The front, side, and top views of a solid built with cubes are shown below. How many cubes are needed to construct this solid?

Top view Left view Front view Right view

F 3 H 6G 5 J 11

18 The Amarillo Florist Shop sells roses, r, at approximately $3 apiece and carnations, c, at $1.50 apiece. A customer orders a mixed bouquet of the two fl owers. The bouquet contains 12 fl owers. The shop charges approximately $24 for the bouquet. Which is a reasonable estimate for the number of roses in the bouquet? A 4 C 8B 6 D 12

19 Line p contains the points at (1, 3) and (–2, –3). Which equation best represents a line parallel to line p? F y = 6x + 2G y = –6x + 3H y = 2x – 5J y = –2x + 1

076-085_PT_TX_877327.indd 78076-085_PT_TX_877327.indd 78 6/28/06 3:57:28 PM6/28/06 3:57:28 PM

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20 Which graph best represents the inequality x – y ≥ 2? A y

xO

B y

xO

C y

xO

D y

xO

21 A winter coat that costs $100 has been marked down 30%. Approximately what percent of the discounted price is the original price? F 70%G 130%H 143%J 333%

22 The pattern of Xs shown below continues infi nitely, with more Xs being added at each step.

X X X X X X

X X X X X

X X X

Step 1 Step 2 Step 3

Which expression can be used to determine the number of Xs in Step n?A n + 2B 2nC 2n + 3D n2

23 A circular spinner with a diameter of 6 inches is divided into 3 sections: Move Forward, Roll Again, and Lose a Turn.

MoveForward= 240°

Lose aTurn

RollAgain= 95°

What is the approximate length of the arc of the Lose a Turn section of the spinner? F 1.3 in.G 5 in.H 6.3 in.J 18.8 in.


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24 Quadrilateral ABCD ~ quadrilateral WXYZ. What is the length of Y Z ?

1 cm

3 cm

2 cm 2 cm 3 cm

C

A B

D Y

W X

Z

A 2 cm C 6 cmB 4.5 cm D 9 cm

25 A square is shown below.

3 cm

How many of these squares can fi ttogether without gaps in order to make a similar fi gure with a perimeter of 36 cm? F 4G 9H 12J 16

26 Find the slope of the line identifi ed by the equation 3x + 2y = 4.

A –1 C 2 _ 3

B – 3 _ 2 D 1

27 The radius of a sphere is tripled. What is the change on the sphere’s volume?F It is tripled.G It is increased by a factor of 9.H It is increased by a factor of 18.J It is increased by a factor of 27.

28 What are the coordinates of the y-intercept of the line represented by the equation 2x – 3y = 9?

A (0, –3) C ( 2 _ 3 , 0)

B (0, 3) D (9, 0)

29 Shanice’s daily net take-home pay after expenses for parking and lunch is represented by the equation p = 8h – 20, where h is the number of complete hours she works. What is the least number of hours Shanice must work to earn take-home pay? F 1 H 3G 2 J 12

30 The rectangle R represents 500 Texans surveyed about their pet ownership. Circle C represents the 175 surveyed who own cats. Circle D represents the 325 surveyed who own dogs.

R

100 250

DC

75

How many surveyed own neither a cat nor a dog? A 0 C 100B 75 D 250


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31 Start with the isosceles trapezoid shown below. In each iteration, Step 2 occurs for the smallest unshaded triangles resulting from the previous iteration.

Step 1: Divide each new shape into equilateral triangles.Step 2: Shade only the center triangles.

What fraction of the trapezoid remains unshaded after the second iteration?

F 1 _ 3 H 2 _

3

G 1 _ 2 J 3 _

4

32 The price, u, of a laptop computer at Store A is $175 more than half the price, �, of the same computer at Store B. The difference in price between the computer at Store A and Store B is $250. Which system of equations can be used to determine the price of the computer at each store?

A u + 1 _ 2 � = 175 C u – 1 _ 2 � = 250

u + � = 250 � – u = 175

B u – 2� = 250 D u – 1 _ 2 � = 175

� – u = 175 � – u = 250

33 Which ordered pair represents one of the roots of the function f(x) = 3x2 – 8x + 4?

F ( 2 _ 3 , 0 ) H (3, 0)

G (2, 0) J (4, 0)

34 How does the graph of y = x2 – 2 differ from the graph of y = x2 + 2? A y = x2 – 2 is 4 units below y = x2 + 2.B y = x2 – 2 is 4 units above y = x2 + 2.C y = x2 – 2 is 4 units to the left of

y = x2 + 2.D y = x2 – 2 is 4 units to the right of

y = x2 + 2.

35 The cost of a pumpkin is a function of its weight. The cost for four different pumpkins is shown in the table.

Weight (lb) Cost

2 $1.005 $2.50

10 $5.0025 $12.50

If the data are graphed with weight on the horizontal axis and cost on the vertical axis, what does the slope represent? F the total cost per pumpkinG a cost of $0.50 per poundH an average weight of 10 pounds

per pumpkinJ a total of 5 pounds between pumpkins


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36 Which type of parent function is represented by the function graphed below?

y

xO

A absolute valueB exponentialC linearD quadratic

37 The graph of the equation y = 1 _ 2 x – 1 is

given below. Graph y = 2 – x on the grid.

y

xO

What is the solution to this system of equations? F (0, 0) H (2, 0)G (0, 2) J no solution

38 How many boxes that are 6 inches long, 4 inches wide, and 3 inches tall can fi t in a 12-inch cube? A 6 C 18B 12 D 24

39 A rectangle has a width of 3 feet and a perimeter of 16 feet. What is the perimeter of a similar rectangle with a length of 15 feet? F 15 ft H 80 ftG 48 ft J 135 ft

40 The function for force, F, is represented by the equation F = ma, where m represents the mass and a represents the acceleration. If F = 32 and m = 4, which is the value of a? A 4 C 28B 8 D 32

41 Which function represents the line that contains the point at (–3, 2) and has a slope of –1? F f(x) = –x – 1 H f(x) = –x + 5G f(x) = –x – 3 J f(x) = –x + 1

42 Nina threw a coin from the second story of the mall into the fountain on the ground fl oor below. The table below shows the relationship between the elapsed time and the coin’s height above the bottom of the fountain.

Time (sec) Height (ft)

0 640.5 601.0 481.5 282.0 0

If the height of the coin is a quadratic function of time, which equation best represents the height, h, at time, t?A h = 64 – 16t2

B h = 64 – t2

C h = 48t2

D h = t2 + 64


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43 Brady rolls a number cube. What is the probability that he will roll a 1 or an even number?

F 1 _ 12

H 2 _ 3

G 1 _ 10

J 23 _ 30

44 An equilateral triangle has a side length of 6 cm. What is the approximate area of the triangle? A 5.2 cm2 C 20 cm2

B 15.6 cm2 D 27 cm2

45 ‹

___

› AB and

‹

___

› CD form a right angle at point Z.

Which statement must be true? F ∠AZD is complementary to ∠BZD.G

‹

___

› AB is perpendicular to

‹

___

› CD .

H ‹

___

› AB is parallel to

‹

___

› CD .

J Points A, B, C, and D are collinear.

46 The graph below shows the percent of each animal cracker in a bag.

Camels20%

Rhinos38%

Elephants26%

Giraffes 16%

Which of the following is a reasonable conclusion about the data? A Camels and rhinos accounted for more

than half the crackers. B Elephants and camels accounted for

more than half the crackers.C The bag contained fewer camels than

any other animal.D The bag contained more elephants than

any other animal.

47 Bowser is on a leash that is staked to the ground 4 feet away from him, so that the end of his leash is 1 feet above the ground. Lady is also on a leash attached to the same stake. She stands four times as far away from the stake as Bowser, and the end of her leash is twice as high as the end of Bowser’s leash. If leashes are stretched tight, how does the slope of Lady’s leash compare to the slope of Bowser’s leash?

F It is 1 _ 4 as great.

G It is 1 _ 2 as great.

H It is twice as great.

J It is four times as great.

48 A right triangle with a hypotenuse of 13 inches is to be cut from a rectangular piece of paper that measures 8 inches × 11 inches as shown below.

13 in. 8 in.

11 in.

Which is the closest amount of paper that will be left over after the triangle is cut out? A 11 in.2

B 39 in.2

C 50 in.2

D 77 in.2


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49 The number of students absent from school the past 10 days was 2, 24, 24, 33, 35, 40, 53, 62, 89, and 103. What is the best measure of central tendency if school offi cials want to determine the average number of students absent on any given day? F meanG medianH modeJ range

50 Sphere X has a surface area of approximately 200.96 in.2. Sphere Y is similar to sphere X. The ratio of the corresponding radii of spheres X and Y is 1:2. What is the radius of sphere Y? A 2 in.B 4 in.C 8 in.D 16 in.

51 Which linear equation best represents the data shown in the table?

x –2 0 2 4y 0 1 2 3

F y = 1 _ 2 x H x = 1 _ 2 y + 1

G x = 1 _ 2 y J y = 1 _ 2 x + 1

52 The vertices of triangle ABC are (0, 0), (–1, 3) and (–3, 1). If the triangle is rotated clockwise 270° about the origin, in which quadrant will it appear? A Quadrant IB Quadrant IIC Quadrant IIID Quadrant IV

53 The base of a cylinder has a radius of4 cm. The height of the cylinder is 10 cm. What is the approximate volume of the cylinder? F 25 cm2

G 50 cm2

H 250 cm2

J 500 cm2

54 The table below shows the responses of 250 gardeners when asked to name their favorite fl ower.

Favorite Flower Gardeners

Rose 110Lily 75Hydrangea 55Daffodil 10

If a bar graph of the data is constructed, what would be the best label for the vertical axis? A Favorite FlowerB Number of GardenersC Total Gardeners SurveyedD Flower Shop Conducting Poll

55 A carpenter mathematically expressed the amount of space occupied by a wooden storage cube. Which of the cube’s measurements did she report? F perimeterG areaH surface areaJ volume


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56 The graph of a line is shown below.

y

xO

If the slope of the line is tripled and the y-intercept increases by 2 units, which linear equation represents these changes? A y = –3x – 1B y = –3x + 1C y = 3x – 1D y = 3x + 1

57 The graph below shows the depth of a diver from the time she leaves the diving board until the time she resurfaces, with “0” being the water level. Approximately how much time elapses between the moment she reaches the maximum underwater depth and the moment she resurfaces?

y

x

912

36

30

6

1 2 3Time (seconds)

Dep

th (

feet

)

F 0.5 sec H 1.5 secG 1 sec J 2 sec

58 A circle with a diameter of 4 cm is to be cut from a rectangular piece of paper that measures 4 cm by 9 cm as shown below.

9 cm

4 cm

Which is closest to the amount of paper that will be left over after the circle is cut out? A 5.24 cm2

B 12.6 cm2

C 23.4 cm2

D 36 cm2

59 A botanist estimates that a tree’s age, a, in years is represented by the inequality 2r –5 < a < 2.5r – 10, where r is the number of rings in the trunk. Which of the following is a reasonable age for a tree with 40 rings? F 70 yr H 92.5 yrG 80 yr J 95 yr

60 In 1999, the median household income

for Amarillo was about 7 _ 8 the median

household income for Texas. If t represents the median household income for Texas, which expression can be used to determine the median household income for Amarillo?

A 1 _ 8 t C 7 _

8 t

B 1 _ 7 t D 8 _

7 t


Name Date

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25 Weeks to TAKS

Monday Tuesday

1 What is the sum of all of the numbers in the table?

14 68 31 64 9186 32 69 36 9

A 481B 498C 500D 517

2 Variables h and t are related bythe equation h = t 2 + 1. Which statement describes how h and t are related?

F Variable h depends on t.G Variable t depends on h.H Variables h and t are independent of

each other.J The relationship cannot be determined.

Wednesday Thursday

3 Jamie has a ribbon that is 100 feet long. She needs to cut it into a number of short, 2-foot strips and long, 5-foot strips. Let s be the number of short strips and t be the number of long strips. Which inequality best relates s and t? A s + t ≤ 100B s + t + 7 ≤ 100C 2s + 5t ≤ 100D 5s + 2t ≤ 100

4 How does the graph of y = 3x + 1 compare to the graph of y = 2x + 1?

F The graph rises faster as x increases.G The graph rises slower as x increases.H The whole graph is shifted higher

by 1 unit.J The whole graph is shifted lower

by 1 unit.

Friday

5 On a map of Texas, the scale is indicated to be 1 inch : 25 miles. Let f(d) denote the actual distance corresponding to a distance of d on the map. What kind of function is f ? A absolute valueB constantC linearD quadratic

086-110_CD_TX_877327.indd 86086-110_CD_TX_877327.indd 86 6/28/06 4:03:11 PM6/28/06 4:03:11 PM

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Monday Tuesday

1 Which choice gives the relationship between x and y shown in the table?

x y

2 –14 –36 –58 –7

A y = –x – 1B y = –x + 1C y = –x + 3D y = –2x + 3

2 Which type of function is the parent function of the graph shown?

y

x

m

O

F absolute valueG linearH quadraticJ square root

Wednesday Thursday

3 Let a, b, and c represent numbers. Which expression represents the sum of the squares of these numbers? A a + b + cB 2(a + b + c)C a2 + b 2 + c 2 D (a + b + c ) 2

4 How does the graph of y = –2 x 2 compare to the graph of y = 2 x 2 ? F It is the refl ection in the x-axis.G It is the refl ection in the y-axis.H It is narrower.J It is wider.

Friday

5 A group of students went on a hiking trip in Big Bend National Park. Their progress is shown in the chart. The students stopped for lunch in the middle of their trip. Based on the chart, for how many hours were the students actually moving? A 0.75B 2C 2.75D 4.25

Mile

s

y

x

Time (Hours)

51 2 3 4

2

0

4

6

1

3

5

7

24 Weeks to TAKS


Name Date

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23 Weeks to TAKS

Monday Tuesday

1 How can one obtain the graph of y = x 2 + 40 from the graph of y = x 2 – 40? A.9 (C) DA Shift the graph 80 units down.B Shift the graph 40 units down.C Shift the graph 40 units up.D Shift the graph 80 units up.

2 Evaluate the expression

( 52 × 1 _ 4 � 1 _ 13 × (5 + 19) � ) . A.4 (B) G

F 19

G 24H 260J 312

Wednesday Thursday

3 What is the midpoint between the points at (7, –11) and (–3, –5)? G.7 (C) CA (–2, –3)B (–1, –8)C (2, –8)D (5, –3)

4 A storage company in Austin has rooms that are 15 feet by 12 feet by 14 feet. What is the volume of a room? G.8 (D) GF 2180 cubic ftG 2520 cubic ftH 2710 cubic ftJ 3000 cubic ft

Friday

5 Which equation represents the relation between x and y as shown in the table? A.5 (C) B

x y

–3 0–1 41 83 12

A y = 2x + 2B y = 2x + 6C y = 4x + 6D y = 4x + 12


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22 Weeks to TAKS

Monday Tuesday

1 Which equation best describes the relationship between x and y shown in the table?

x 1 2 3 4y –1 –4 –9 –16

A y = – x 2 B y = (–x ) 2 C y = x 2 D x = – y 2

2 A company allocated a fi xed amount of money to purchase computers and printers. In fact, p = 90 – 8c, where p is the number of printers and c is the number of computers. Thinking of p as a function of c, what is the largest possible domain for this function? F integers c that satisfy 0 ≤ c ≤ 11G integers c that satisfy 0 < c ≤ 11H integers c that satisfy 0 < c < 11J real numbers c that satisfy 0 ≤ c ≤ 11

Wednesday Thursday

3 An airplane is landing at Dallas/Fort Worth International Airport. The plane follows a straight-line path from 3 miles out until it lands. If the slope of the descent is –0.11, what was the approximate altitude of the plane at the beginning of the descent? A 0.33 ftB 1740 ftC 3300 ftD 5280 ft

4 The variable y is linearly dependent on x. The table shows a few values of this dependency. If the line is graphed, what would be its slope?

x 1 2 3 4y 6 –1 –8 –15

F –9G –8H –7J –6

Friday

5 Mia is boiling water in a pot. The pot contains 24 ounces of water. Mia has to be careful that the water does not completely boil off because this would destroy the pot. If water evaporates at the rate of 2 ounces every 3 minutes, for how many minutes can Mia let the water boil? A 12 minB 24 minC 36 minD 48 min


Name Date

Countdown to TAKS

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21 Weeks to TAKS

Monday Tuesday

1 Simplify the expression (x + 2)(x + 6) + x 2 – 5. A 2 x 2 + 3x + 7B 2 x 2 + 8x + 7C 2 x 2 + 3x + 12D 2 x 2 + 8x + 12

2 The point at (3, 6) is on the graph of y = x 2 + c. Which of the following points is on the graph of y = x 2 + c – 7?F (–3, 6)G (3, –1)H (3, 13)J (10, 6)

Wednesday Thursday

3 A group of friends decided to have a pizza party. The cost of each pizza is $8. Delivery costs $5 plus $0.50 per pizza. How many pizzas can the friends buy if they have $60 total? A 4B 5C 6D 7

4 The point at (8, –11) is on a line with slope –10. What is the y-coordinate of the point on this line that has x-coordinate 6? F –31G –21H –1J 9

Friday

5 Orson has two maps that show the same region of Galveston. The scale of one map is 1 inch : 1200 feet. The scale of the other map is 1 inch : 1800 feet. If two points on the larger map are 6 inches apart, how far apart should they be on the smaller map? A 4 in.B 4.75 in.C 5.5 in.D 6 in.


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Name Date

Countdown to TAKS


Monday Tuesday

1 A policeman pulled over a driver for speeding. The driver protested that he could not have been going over the 65 mph speed limit because he “just came from the cinema two minutes ago!” Assume that this statement is correct and the cinema is a mile and a half down the road. Which of the following is the greatest speed that can be proven to have been exceeded? A 35 mphB 45 mphC 65 mphD 75 mph

2 An architect sketches the cross-section of a house on a sheet of graph paper. A sloping roof is represented as part of a line. Assuming that the slope remains the same, what effect is made by increasing the y-intercept of this line by 2 units?F The fl oor will be raised by 2 units.G The ceiling will be raised by 2 units.H The ceiling will become steeper.J The ceiling will be lowered by 2 units.

Wednesday Thursday

3 What is the equation of a line with slope 9 and y-intercept –9? A y = –9x – 9B y = –9x + 9C y = 9x – 9D y = 9x + 9

4 The solutions to the equation –4x + 2y = 9 are graphed on the xy-coordinate plane. What is the slope of the resulting line? F –2G –1H 1J 2

Friday

5 A photographer wants to take a picture of the San Jacinto Monument in La Porte. The monument is a tower 15 feet higher than the Washington Monument. The photographer would like to be as far from the monument as √

_

3 times its height. At that distance, what angle would the line of sight to the tip of the monument make with the horizontal? A 30°B 45°C 60° D 90°

20 Weeks to TAKS

086-110_CD_TX_877327.indd 91086-110_CD_TX_877327.indd 91 6/30/06 9:50:33 AM6/30/06 9:50:33 AM

Name Date

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Monday Tuesday

1 Callie needs to solve the quadratic equation x 2 + 20x + 99 = 0 by factoring the left-hand side. What is this factorization? A (x – 9)(x – 11)B (x + 10)2

C (x + 2)(x + 18)D (x + 9)(x + 11)

2 A cell culture has 212 cells in it. After fi ve more doublings, how many cells will there be in the culture? F 5 × 2 12

G 10 × 212

H 217

J 260

Wednesday Thursday

3 In a poll asking 120 people to name their favorite card game, the results were: Poker: 44, Hearts: 28, Bridge: 21, Euchre: 15, Other: 12. If this data were represented on a circle graph, how many degrees would the sector representing Euchre be? A 15° B 45° C 54°D 60°

4 Which data best describes the line shown in the graph?

y

xO

F slope –3 and y-intercept 8G slope –3 and y-intercept 5H slope 3 and y-intercept 2J slope 3 and y-intercept –8

Friday

5 A corporate sign maker is hired to make the letters for the word “TEXAS.” The design for the “X” is shown below. Which choice most accurately describes the shape of the shaded part of the letter? A parallelogramB quadrilateralC rectangleD trapezoid

19 Weeks to TAKS


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Countdown to TAKS


18 Weeks to TAKS

Monday Tuesday

1 The table lists the x- and y-coordinates of a few of the points on a line. What is the y-intercept of this line?

x y

–12 –25–3 211 4420 71

A 5B 8C 11D 14

2 An endangered gulf turtle species began a slow but steady recovery in 2001. Based on the chart, what do you estimate will be the size of the turtle population in 2010 if current trends continue?

Est.

Po

pu

lati

on

(t

ho

usa

nd

s)

y

x

Year

’05’01 ’02 ’03 ’04’00

1

0

2

3

F 2500G 5000H 7500J 10,000

Wednesday Thursday

3 Use substitution to discover which point satisfi es the linear inequality 5x – 7y > 10. A (–22, –17)B (20, 13)C (26, 17)D (34, 23)

4 Martin needs to solve a system of linear equations where the fi rst equation is 3x – 5y = 11 and the second is 6x + y = 8. By what must Martin multiply the fi rst equation so that the variable x is eliminated when the result is added to the second equation? F –2G –1H 0J 2

Friday

5 The ratio of the areas of two equilateral triangles is 100. The side length of the smaller triangle is 1000 units. What is the side length of the larger triangle?A 10 units C 1000 unitsB 100 units D 10,000 units


Name Date

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17 Weeks to TAKS

Monday Tuesday

1 In downtown San Antonio, a city clerk surveyed the 12 parking garages and discovered that at noon there were between 250 and 550 cars parked in any one garage. Which of the following could be the number of cars parked in all the garages combined? A 500B 1000C 2000D 4000

2 The graph shows a cross-section of a radio telescope. How wide is the dish?

y

x10 20 30 40

10

10

O

F 10 unitsG 20 unitsH 30 unitsJ 40 units

Wednesday Thursday

3 The fi rst, second, and third arrangements of bricks are shown in the fi gure. If the pattern is continued, how many brickswould be needed in the nth arrangement?

A nB 4nC n 2 D n 2 + n

4 Which two fi gures are congruent? y

A B

C D

xO 4 4

4

4

F A and CG A and DH B and DJ C and D

Friday

5 A solid is created by starting with a cone sitting on its base and pointing up. A cylindrical hole is drilled through the cone along its axis. The radius of the hole is half the radius of the base of the cone. What is the side view of the resulting object? A an isosceles trapezoidB an isosceles triangleC a rectangleD a ring


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Name Date

Countdown to TAKS


16 Weeks to TAKS

Monday Tuesday

1 What is the equation of the line that passes through the points at (9, 1) and (10, 20)? A y = 9x – 80B y = 19x – 170C y = 20x – 190D y = 20x – 200

2 What is the largest root of the function f(x) = 2 x 2 – 5x – 3? F –0.5G 0.5H 3J 3.5

Wednesday Thursday

3 A triangular prism has 5 faces. If a prism has an n-sided polygonal base, how many faces does it have? A n + 2B 2nC 2n + 2D n 2 + 2

4 Rhea and Luke live in a suburb of Dallas. To get to Rhea’s house from his home, Luke must walk due south for 50 yards then walk due east for 120 yards. How far apart are the two houses? F 110 ydG 130 ydH 150 ydJ 170 yd

Friday

5 During one month, Brad earned d dollars and spent s dollars. If he started the month with x dollars, how much did he have at the end of the month? A x + d + sB x + d – sC x – d + sD d + s – x


Name Date

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15 Weeks to TAKS

Monday Tuesday

1 Bridget must toss a tool up to her friend, Rachel, who is working on the roof. The height of the tool if Rachel misses is shown in the graph. Rachel can catch the tool any time it is above 12 feet. How much time will Rachel have to catch the tool? A 0.5 secB 1 secC 1.5 secD 2 sec

2 A pattern is made by overlapping equilateral triangles each of area 4 square units. To extend the pattern, the next triangle is placed so that it covers one fourth of the area of the last triangle. The fi gure shows a pattern with 5 triangles. Which describes the visible area of such a pattern if it consists of n triangles? F 3n – 3 G 3n – 1H 3n + 1J 4n

Wednesday Thursday

3 Carol tossed 7 coins, one after the other. What is the probability that the fi rst and last coins showed heads and the middle coin showed tails? A 0.125B 0.25C 0.375D 0.5

4 Luke is hired to track the number of yo-yos sold monthly at a toy store. He needs to know how many digits to allocate for the number. What number should he compute from past data to fi gure out what he needs? F meanG medianH modeJ range

Friday

5 The net shown is missing a single polygon. What single polygon should be located at the question mark so that the resulting net will represent a three-dimensional solid? A an equilateral triangleB a 45-45-90 triangleC a squareD a regular pentagon

y

x1 2

8

16

OHei

gh

t (f

eet)

Seconds

?


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Name Date

Countdown to TAKS


Monday Tuesday

1 For a large origami convention, organizers decide that they should bring at least 50 sheets of origami paper per participant. They also decide to bring an additional 1250 sheets just in case. What is the maximum number of participants if organizers ended up purchasing 6650 sheets? A 100B 108C 133D 145

2 Sarah is thinking of two numbers. Their sum is 19. If the smaller is subtracted from the larger, the result is 5. What is the smaller number? F 3G 5H 7J 9

Wednesday Thursday

3 Which object can have rectangular top and front views and a triangular side view? A a cubeB a sphereC a triangular prismD a triangular pyramid

4 The Houston Rockets play on a rectangular court that measures 54 feetby 90 feet. Approximately how long is the diagonal of this court? F 99 ftG 101 ftH 103 ftJ 105 ft

Friday

5 Maryanne builds a circular fence 240 meters in diameter around her Texas ranch. She places 40 evenly spaced poles along the perimeter. What is the approximate length of each arc between neighboring poles? A 6 mB 11 mC 15 mD 19 m

14 Weeks to TAKS


Name Date

Countdown to TAKS

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13 Weeks to TAKS

Monday Tuesday

1 Which formula gives a solution to the

equation 1 _ 2 x 2 – 5x + 7 = 0?

A x = 5 – √

__

11

B x = 5 – √

__

–3 C x = –5 – √

__

11 D x = –5 – √

__

–3

2 Jane wants to tile her bathroom wall. The wall is a rectangle 10 feet by 8 feet. Each tile is a square with a side length of 4 inches. How many tiles should she order? F 80G 240H 720J 1280

Wednesday Thursday

3 Marcos wants to know how many cars most families own. He polls 100 families and records the number of cars in each. What should he compute from his data to get the information he desires? A meanB medianC modeD range

4 A right triangle has one leg 48 units long and is similar to an 8-15-17 right triangle. What is the length of its hypotenuse? F 60 unitsG 72 unitsH 90 unitsJ 102 units

Friday

5 See the shaded quadrilateral. Through what angle can it be repeatedly rotated in order to generate the fi gure shown? A 24°B 30°C 36°D 45°


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Name Date

Countdown to TAKS


12 Weeks to TAKS

Monday Tuesday

1 Which choice represents the dimensions of a rectangular prism that is NOT similar to one with dimensions 20 × 24 × 40? A 10 × 12 × 20B 30 × 36 × 50C 40 × 48 × 80D 50 × 30 × 25

2 The fi gure shows the cross-section of a box fi lled with soil. Six earthworms are found to be present in the region of the highlighted square. Assuming that the highlighted region is representative of the whole, how many earthworms do you estimate are present in the entire cross-section?

F 6 G 12H 30J 60

Wednesday Thursday

3 Which inequality is shown in the graph? A y < 2x + 1 B y ≤ 2x + 1C y > 2x + 1D y ≥ 2x + 1

4 The entire graph of the function f(x) is shown. What is the range of f? F –4 < x < 2G –4 ≤ x ≤ 2H –1 < y < 4J –1 ≤ y ≤ 4

Friday

5 On a street map of Houston, Main Street can be modeled by the graph ofy = 1.25x – 20 and Capitol Street by the graph of y = – 0.8x + 21. What are the coordinates of their intersection on this map? A (8, –10)B (20, 5)C (20, 37)D (25, 1)

y

x1 2 3 4 1 2 3 4 1 2

4 3

3

2

4

1

y

x

3

5

5 5 O


Name Date

Countdown to TAKS

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11 Weeks to TAKS

Monday Tuesday

1 The variables g and s are related by a function. When g is 2, s is 4. When g is – 4 or g is –8, s is 2. How are s and g related? A Variable s depends on g.B Variable g depends on s.C Variables g and s are independent.D The relationship cannot be determined.

2 Which function has parent function x 2 ? F f(x) = 5x + 3G f(x) = 5x2 + 3H f(x) = |5x + 3|J f(x) = 2x

Wednesday Thursday

3 A patient must be transferred from Plaza Specialty Hospital to Riverside General Hospital in Houston. To do this, one drives 1.3 miles down Fannin Street, makes a 90° right turn onto Elgin Street, and stays on Elgin for 1.2 miles. Which is the approximate distance between the two hospitals? A 1.52 miB 1.77 miC 2.12 miD 2.5 mi

4 The graph shows the difference in altitude between hot air balloon 1 and hot air balloon 2. How many times were the balloons at the same altitude?

h

t20 40 60 80

100

50

100

50

O

F 1G 2H 3J 4

Friday

5 How does the graph of y = –5 x 2 compare to the graph ofy = –15 x 2 ? A It is narrower.B It is wider.C It is shifted up 10 units.D It is shifted down 10 units.


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Name Date

Countdown to TAKS


10 Weeks to TAKS

Monday Tuesday

1 When it began to rain, the water level in a shallow part of Lake Waco was 52 inches. Every hour, half an inch of rain fell. How many hours did the rain fall if the water level in the same part rose to 55 inches? A 4 hrB 5 hrC 6 hrD 7 hr

2 Which equation best describes the relationship between x and y shown in the table?

x 1 2 3 4y 3 7 12 18

F y = x 2 + 3x

_ 2

G y = x 2 + 5x

_ 2

H y = x 2 + 2xJ y = x 2 + x + 2

Wednesday Thursday

3 Which column depends linearly on x?

x A B C D

1 3 –1 1 42 0 2 1 33 3 –3 2 24 0 4 2 1

A column AB column BC column CD column D

4 Which pair of points are separated by √

__

74 units? y

x1 2 3 4 1 2 3 4 1 2

4 3

3

2

4

1

P Q

SR

F P and QG R and SH P and SJ Q and R

Friday

5 An aquarium must display some lionfi sh and some cuttlefi sh. A condition is that there must be equal numbers of lionfi sh and cuttlefi sh. Which additional requirement is possible in the sense that both conditions can be met at the same time? A There must be at least 3 cuttlefi sh for every lionfi sh.B The number of lionfi sh must be a third as much as 4 plus the number

of cuttlefi sh.C The number of cuttlefi sh must be one more than twice the number

of lionfi sh.D There must be 6 more lionfi sh than twice the number of cuttlefi sh.


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Countdown to TAKS

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9 Weeks to TAKS

Monday Tuesday

1 The diagonals of a regular pentagon are drawn dividing the regular pentagon into 11 regions. If these regions are sorted into sets of congruent shapes, which is the minimum number of such sets needed? A 2 B 3C 4D 5

2 Martha started hiking in the Hueco Tanks near El Paso. She began by hiking 1 kilometer. Each day, she increased her hiking distance by 1 kilometer. By the end of which day had she hiked 78 kilometers in total? F day 6G day 9H day 12J day 15

Wednesday Thursday

3 Let f(x) = x 2 – 31

_ 45 x + 2 _ 27 . If one root of f

is 5 _ 9 , what is the other root?

A 1 _ 45

B 2 _ 15

C 5 _ 9

D 2 _ 3

4 Line � has equation y = mx + b. What can be done to change the line so that it passes through P? F Reduce b

by 7.G Reduce b

by 11.H Increase m

by 3.J Increase m

by 5.

Friday

5 The bar chart shows the number of new and departing members each year in a social club. From 2001 through 2004, what was the net change in club membership? A The club lost members.B Membership remained unchanged.C The club gained members.D There is not enough information to decide.

y

x

P

‘02‘01

10

5

0

Nu

mb

er o

f Pe

op

le

‘03 ‘04Year

Key: New members Leaving members


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Name Date

Countdown to TAKS


8 Weeks to TAKS

Monday Tuesday

1 Let a < 0, b < 0, c > 0, and d < 0. What does the line segment connecting (a, b) with (c, d) intersect? A the positive x-axisB the positive y-axisC the negative x-axisD the negative y-axis

2 Let S be the set of integers that have fewer than 5 factors (including 1 and itself). Which number is NOT in S? F 16G 27H 35J 65

Wednesday Thursday

3 The playing area of a miniature golf hole looks like a rectangle sandwiched between two 45-45-90 right triangles in such a way that the hypotenuse of each triangle completely contains a short side of the rectangle and the vertices of all three shapes are distinct. How many sides does the playing area have? A 6B 8C 10D 12

4 Leon tosses two number cubes without looking at them. A friend tells Leon that the total came out to be an odd number. What is the probability that the total is 7?

F 1 _ 6

G 2 _ 9

H 1 _ 3

J 1 _ 2

Friday

5 See the triangle below. What is x? A 4B 6C 7.5D 9

312

x


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7 Weeks to TAKS

Monday Tuesday

1 A long square prism is passed through the center of a cube as shown. How many faces does the resulting solid have? A 10 B 12C 14D 16

2 The fi gure below is the net of a three-dimensional object. Which two points correspond to the same point on the object? F A and B

B

D

A CG B and CH C and DJ D and A

Wednesday Thursday

3 A cylinder has a radius of x 2 units and a height of x 3 units. What is the volume of the cylinder? A πx 7 B π x 8 C π x 9 D π x 12

4 David and Jessica are running toward each other. They are initially separated by 55 meters. If Jessica runs 20% faster than David, how far will Jessica have run when they meet? F 27.5 mG 30 mH 35 mJ 44 m

Friday

5 Which of the following points, together with points P and Q, will form the vertices of an isosceles triangle? A (–2, –2)B (0, 5)C (3, 0)D (5, 5)

y

xOP

Q


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Name Date

Countdown to TAKS


6 Weeks to TAKS

Monday Tuesday

1 A jungle gym has a large cube frame made out of strong metal poles. How many ways are there to get from one vertex of the cube to the opposite vertex while traveling along exactly 3 edges, as shown? A 3 B 6C 9D 12

2 The vertices of a triangle are A(1, 5), B(–3, –4), and C(6, –1). What is the equation of the line that contains the altitude to vertex A? F x – 3y = 9G x + 3y = 16H 3x – y = –2J 3x + y = 8

Wednesday Thursday

3 The polygon shown contains squares A and C, equilateral triangle B, and an isosceles triangle. What is the area of the polygon?

A 4 + √

_

3 _

2 s 2

B

A Cs

B (2 + √

_

3 ) s 2

C 3 s 2

D (4 + √

_

3 ) s 2

4 The population of Dallas is about 1.2 × 1 0 6 . The population of Austin is about 7 × 1 0 5 . If all you know is that a person lives in Dallas, Austin, or Houston, then the probability that the person does not live in Austin is about 0.82. Which is the approximate population of Houston? F 1.2 × 1 0 6 G 1.6 × 1 0 6 H 2.0 × 1 0 6 J 3.2 × 1 0 6

Friday

5 Sam needs to buy 2 toothbrushes, dental fl oss, and toothpaste. He only has time to go to one store. Given the information in the table, which store would be cheapest?

Store Toothbrush Floss Toothpaste

A $2.34 $3.59 $4.69B $2.19 $3.49 $4.99C $2.49 $3.99 $4.85D $2.49 $3.89 $5.01

A store AB store BC store CD store D


Name Date

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5 Weeks to TAKS

Monday Tuesday

1 Three similar solids have side lengths in the ratio 1 : 2 : 3. Which of the following is equivalent in volume to one of the large solids? A 1 small and 1 medium solidB 1 small and 2 medium solidsC 2 small and 2 medium solidsD 3 small and 3 medium solids

2 A cylinder of height 2 meters and base radius 3 meters is altered by doubling its base radius. By how much does its surface area increase? F 30π m2

G 48π m2

H 60π m2

J 66π m2

Wednesday Thursday

3 The equation of a line is 3x + 7y = 42. The vertices of a right triangle consist of the origin and the x- and y-intercepts of the line. What is the area of this triangle? A 1 sq. unitB 21 sq. unitsC 42 sq. unitsD 882 sq. units

4 A cone has base radius 5 meters and height 10 meters. Approximately what is its lateral surface area? F 79 m2

G 176 m2

H 254 m2

J 314 m2

Friday

5 Points A(2, 8), B(–2, 0), and C(4, –2) form the vertices of a triangle. What is the equation of the line that contains the midsegment parallel to

−− AB ?

A x + 3y = 12B 2x – y = 3C 3x + 2y = 8D 5x + y = 4


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Name Date

Countdown to TAKS


4 Weeks to TAKS

Monday Tuesday

1 Which is the approximate area of a regular octagon with a side length of 5 feet? A 121 square feetB 144 square feetC 146 square feetD 242 square feet

2 Amy has twice as much money as Barry. Barry has $10 less than Celia. Don has $5 less than what Amy and Barry have together. All four together have $145. If 2x + x + (x + 10) + (3x – 5) = 145, who has x dollars? F AmyG BarryH CeliaJ Don

Wednesday Thursday

3 City planners were going to build a bridge from point A to point B as shown. However, the actual bridge built has a slope twice that of the planned bridge. Approximately how much longer is the actual bridge than the planned bridge? Each unit represents 100 meters. A 200 m y

x1 2 3 4123412

43

3

2

4

1

B 287 mC 329 mD 566 m

4 A nesting of squares is created by starting with a square, then inscribing a square rotated by 45° within, and then repeating this process as shown in the fi gure for 4 squares. If n squares are so nested, into how many regions is the original square divided? F 4n – 4 G 4n – 3H 4nJ 4n + 1

Friday

5 Patricia collected data in the form of a sequence of zeroes and ones shown below.

11110011101111110011001111111011111100101011101111111001110

Which pattern is contradicted by the data? A There are never more than 2 consecutive zeroes.B An even number of consecutive ones is followed by 2 zeroes.C Two consecutive zeroes are followed by at least 2 ones.D There are never more than 7 consecutive ones.


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3 Weeks to TAKS

Monday Tuesday

1 Which of the following is a more succinct way of describing a number that has an odd number of factors (including one and itself)? A It is prime.B It is odd.C It is a perfect square.D It is a perfect cube.

2 The point at (p, q) is 85 units away from the point at (–90, 80). Which of the following points must be 85 units away from the point at (–p, q)? F (–90, 80)G (0, 0)H (80, –90)J (90, 80)

Wednesday Thursday

3 Richard is applying for jobs. One company advertises an average salary of $69,000 per year. Based on this information, what can Richard expect his salary to be if he gets a job at that company? A less than $69,000, but certainly more

than $34,500B at least $50,000C about $69,000D It is impossible to estimate and could

even be less than $34,500.

4 A completely fi lled water container is shaped like an upside-down cone with base diameter equal to its height. A hole appears in the side of the container and half of the water leaks out. Approximately how high is the hole as a percentage of the height of the cone? F 50%

Hole

G 71%H 79%J 85%

Friday

5 A lattice triangle is a triangle in the coordinate plane whose vertices have integer coordinates. Given the four triangles shown, which conjecture is true?

xO

A The area of a lattice triangle is an integral multiple of 0.5.B The area of a lattice triangle is an integer.C The interior points of lattice triangles cannot have integer coordinates.D All lattice triangles have area less than 50.


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Name Date

Countdown to TAKS


Monday Tuesday

1 A snowman consists of three spherical snowballs. The ratio of their volumes is 64 : 125 : 512. The snowman is 170 centimeters tall. What is the radius of its head, which corresponds to the smallest of the three snowballs? A 4 cmB 17 cmC 20 cmD 40 cm

2 What are the coordinates of the intersection of � and m shown in the graph below? F (–20, 10) G (–17, 11)H (–14, 8)J (–11, 5)

Wednesday Thursday

3 The area of the circle below is 60 square units, and point P is its center. What is the area of the overlap between the regular pentagon and the circle? A 12 sq. units

PB 15 sq. unitsC 18 sq. unitsD 20 sq. units

4 A nesting of squares is created by starting with a square, then inscribing a square rotated by 45° within, and then repeating this process as shown in the fi gure for 4 squares. If n squares are so nested, what is the ratio of the side lengths of the largest and smallest squares in the pattern? F √

___

2 n–2 G √

___

2 n–1 H √

__

2 n

J √

____

2 n+1

Friday

5 Rachel must prove that given two polygons of the same area, either one can be cut into pieces and rearranged to form the other. As she works on the problem, she makes 4 statements (not necessarily in the order given). Which statement is false? A “The result follows, if I can prove it for any two triangles.”B “The result follows, if I can prove it assuming that one of the polygons is a square.”C “Any triangle can be cut into 3 pieces that can be formed into a rectangle.”D “I can assume the area is 1 square unit, without loss of generality, by scaling if

necessary.”

2 Weeks to TAKS

y

x

m

O


Name Date

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1 Week to TAKS

Monday Tuesday

1 Consider the statement “Any quadratic function whose range is a subset of the integers must have integer coeffi cients.” Which function contradicts this?

A f(x) = x + 5B f(x) = x 2 + x + 1

C f(x) = 1 _ 2 x 2

D f(x) = x(x + 1)

_ 2

2 The 20 students in Ms. Hawthorne’s class were asked to pick a whole number between 1 and 5 (inclusive). The average of the numbers picked was 2 and the range was 4. Which shows the minimum number of students who must have picked 1? F 1G 3H 5J 7

Wednesday Thursday

3 Let f(x) = x 2 – 36. Which of the following prime numbers is the smallest factor of f(7913) other than 1? A 6667B 7027C 7907D 7919

4 Mark wants to determine the number of triangles n that have integer side lengths and perimeter p for any integer p. For example, there is only one triangle whose perimeter is 3 and whose side lengths are integers. He decides to investigate by making a table. Which numbers complete the bottom row?

p 3 4 5 6 7 8n 1 0 1 ? ? ?

F 1, 2, 1G 1, 2, 2H 1, 2, 3J 2, 2, 3

Friday

5 Let f(n) = n 2 + 1 with the domain being the set of positive integers. Which of the following statements is true? A f(n) is divisible by n.B f(n) is always a prime number.C f(n) + 2n is a perfect square.D For some n in the domain, f(n) = n.


111-121_BT1_TX_877327.indd 111111-121_BT1_TX_877327.indd 111 6/28/06 4:11:19 PM6/28/06 4:11:19 PM

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correct answer.

1 The height h of a tossed ball above the ground is given by the equation h = 20 + 32t – 16t2, where t is time measured in seconds. Which statement best represents the functional relationship between the variables h and t?A The height h is dependent on the time t.B The time t is dependent on the height h.C The height h and time t are independent

of each other.D The relationship cannot be determined.

2 A bookstore in Dallas uses a storage room to store overstock. Let n be the number of boxes in the storage room. Each box can contain up to 12 books. Let b represent the number of books in the storage room. Assuming that all the books in the storage room are contained in boxes, which inequality relates b to n?F b ≤ n H 12b ≤ nG b ≤ n + 12 J b ≤ 12n

3 The graphs of the equations y = 2x + 5 and y = –0.5x are shown. Based on the graph, what is a solution to both equations?

m

y

xO

A x = –2, y = –1 C x = –1, y = –2B x = –2, y = 1 D x = –1, y = 2

4 The graph shows the altitude of an airplane during part of its fl ight one morning from El Paso to Austin. Which of the following statements is true?

Alt

itu

de

(ft.

)

2000

3000

1000

0

4000

5000

6000

7000

Time9 A.M. 10 A.M. 11 A.M.

F The airplane landed at 10:30 A.M.G The airplane traveled a total of

1500 feet.H The airplane lost 1500 feet of altitude

between 9 A.M. and 11 A.M.J The airplane was rising at a rate of

1000 feet per hour at 9:45 A.M.

5 Justin placed a glass of water on his desk. The table shows the height of the water level each day at noon. Which equation best represents the relationship between h and d?

Day (d) Height of Water (h)

1 10 cm2 8 cm3 6 cm4 4 cm

A h = 4 + 2d C h = 10 – 2dB h = 10 – d D h = 12 – 2d

6 The points at (3, 5) and (5, 3) are both on line �. What is the slope of �?F –1 H 1G 0 J 1.6

Benchmark Test 1



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Benchmark Test 1 (continued)

7 To make a wooden side panel for a bench, Juanita takes a 2-foot by 3-foot rectangular piece of wood. She then removes and discards an isosceles right triangle with area 0.5 square feet from a corner. What is the area of the side panel?A 3 ft2

B 4 ft2

C 5.5 ft2

D 6 ft2

8 Which choice gives the side lengths of a right triangle similar to the one shown?

12 15

9

F 2, 3, 4G 3, 4, 5H 5, 12, 13J 6, 9, 12

9 How does the graph of y = 3x2 compare to the graph of y = -3x2?A One graph is the mirror image of the

other about the x-axis.B One graph is the mirror image of the

other about the y-axis.C One graph can be obtained by rotating

the other around the origin by 90°.D One graph is a translation of the other

graph.

10 Let f(x) = 3x2 - 2x + 1. What is f(–2)?

F –17 H 9G –7 J 17

11 The quadratic equation x2 - 3x - 28 = 0 has two solutions a and b. What is (a - b)2 ?A 64 C 121B 100 D 144

12 What is the equation of the line that is the perpendicular bisector of the segment with endpoints at (1, 0) and (7, 2)?F y = –3x + 11G y = –3x + 13H y = 3x + 11J y = 3x + 13

13 Stunt organizers set up a ramp as shown in the graph below. The top of the ramp runs along the dashed line and meets the ground at the coordinate (–6, 0). The organizers determine that to succeed they have to increase the slope of the ramp by 50%. If the new ramp also runs from (–6, 0) to the y-axis, where will the top of the new ramp touch the y-axis?

y

xO

A (0, 4) C (0, 5)B (0, 4.5) D (0, 5.5)


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14 The lines in the graph represent streets in downtown Houston. Line � is the graph of the equation y = –0.5x + 1. Which line has the same slope as �, but a y-intercept of 4, instead of 1?

y

xO

d

ca b

F line a H line cG line b J line d

15 What equation best describes the relationship between x and y shown in the table below?

x 0 1 3 6 10y 10 9 7 4 0

A y = –x + 10 C x = –y2 + 10B y = –x – 10 D y = –x2 + 10

16 What approximately is the distance between points P and Q?

y

xO

Q

P

F 10 unitsG 14 unitsH 14.14 unitsJ 100 units

17 The table shows the numbers of each type of housing in Amanda’s town. She wants to make a circle graph based on this data. A sector of what measure would represent the duplex housing?

HousingType Number

Home 110Duplex 40

Townhouse 15Apartment 35

A 20°B 40°C 72°D 144°

18 Howard takes a square piece of paper and cuts it along its diagonals to produce four congruent 45-45-90 triangles. The side length of the original square was 10 inches. What is the approximate perimeter of one of the resulting triangles?

10 in.

F 14.14 in. H 24.14 in.G 20 in. J 28.28 in.




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19 Which best describes the three-dimensional solid whose net is shown below?

A cubeB cylinderC triangular prismD triangular pyramid

20 The top of a proposed tower for a park in Austin is a square pyramid. The base of the pyramid has a side length of 12 feet and the height of the pyramid is 20 feet. What is the volume of the pyramid?F 960 ft3 H 1920 ft3

G 1440 ft3 J 2880 ft3

21 The table below shows the remainders that result when one divides a perfect square by 4. Which choice is a reasonable conjecture that can be made based on the information in the table?

n n 2 Remainder of n 2 divided by 4

1 1 12 4 03 9 14 16 05 25 1

A Perfect squares are always divisible by 4.B Perfect squares are never divisible by 4.C One plus a perfect square is always

divisible by 4.D One plus a perfect square is never

divisible by 4.

22 Which equation is the parent function of the graph shown below?

y

xO

F y = √

__ x

G y = xH y = x2

J y = | x |

23 The distance d in feet of Nathan’s car from his home after t seconds is given by the equation d = 88t + 140. This is a linear equation with slope 88 and y-intercept 140. Assume that Nathan is driving along a straight road. What does the slope represent?A the number of feet Nathan’s car travels

every secondB the number of feet Nathan’s car was

initially from his homeC the number of feet Nathan’s car was

from his home after 1 secondD the top speed of Nathan’s car

24 For one week in January, the number of hours h that the sun shone each day in Houston satisfi ed the inequality 4 < h < 10. Which of the following is NOT a possible number of hours that the sun shone during that entire week?F 40 hrG 50 hrH 60 hrJ 70 hr


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25 The water level begins rising in an artifi cial basin. Without intervention, the water level h in inches would be given by h = 8t + 34, where t is the number of hours after it began raining. A supervisor must open a drainage valve whenever the water level reaches 54 inches. How many hours after the rain begins can the supervisor wait before opening the drainage valve?A 2 hr C 4.25 hrB 2.5 hr D 6.75 hr

26 The fi gure shows a regular pentagon with lines drawn from its center to each of its vertices. Based on the information in the fi gure, what is the area of the pentagon?

9 yd2

F 9 yd2 H 45 yd2

G 27 yd2 J 63 yd2

27 A car drives along the road as shown. Through what sections of the road is the car undergoing a pure translation?

A

B

C D

E

A B and D C A, C, and EB A and C D A, B, C, D, and E

28 Marcos is asked to sketch a circle in such a way that it both contains and is tangent to the existing circle. Which circle accomplishes this purpose?

A C D EB

F the circle that passes through B with center at A

G the circle that passes through C with center at A

H the circle that passes through D with center at A

J the circle that passes through E with center at A

29 Which equation represents a line that passes through the point at (–3, 1) and has a slope of 3?A y = –3x + 1B y = –3x + 3C y = 3x + 1D y = 3x + 10

30 At a raffl e held at the Frank Buck Zoo in Gainesville, each person is allowed to purchase no more than 10 tickets. Let t be the number of tickets purchased and let n be the number of people who bought tickets. Which statement best represents the relationship between t and n?

F t = 10nG t < 10nH t > 10nJ t ≤ 10n

111-121_BT1_TX_877327.indd 116111-121_BT1_TX_877327.indd 116 6/30/06 10:03:00 AM6/30/06 10:03:00 AM


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31 The two fi gures shown are similar to each other. What is the value of x?

11

20

15

12

x

A 6 3 _ 5

B 8 4 _ 5

C 9D 16

32 A Fort Worth company has 10 employees. Of the 10 employees, N of them have a salary of D dollars per year and the rest have a salary of 2D dollars per year. Which expression gives the amount of money the company spends each year on salaries?

F NDG 3NDH D(20 – N)J D(20 + N)

33 The table shows a linear relationship between x and y. For what value of x would y be equal to 0?

x y

–6 –36–2 –204 46 12

10 28

A 0B 1C 2D 3

34 To obtain the graph of y = x2 + 5 from the graph of y = x2 + 2, which option should be used?F Shift the graph to the left by 3 units.G Shift the graph to the right by 3 units.H Shift the graph up by 3 units.J Shift the graph down by 3 units.

35 Let n points be given in a plane. Let s(n) denote the number of line segments that can be formed by joining 2 of the n points. Using the table, which is an expression for s(n)?

n 1 2 3 4 5s(n) 0 1 3 6 10

A n(n - 1)

_ 2 C

3n(n - 1) _

2

B n(n - 1) D 2n(n - 1)

36 Organizers at the Dallas Convention Center estimate that 40% of attendees will sign up for the fi nal banquet. If 720 people attended the convention, how many people do you expect will attend the fi nal banquet?


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37 Kate fl ips a coin 4 times in a row. What is the probability that at least 3 consecutive heads appear?

A 1 _ 16

C 3 _ 16

B 1 _ 8 D 1 _ 4

38 Four different equations are shown in the coordinate plane. Which one corresponds to the graph of a linear function?

y

xO

c

b

d

a

F a H cG b J d

39 The fi gure shows two concentric circles, one with a radius twice that of the other. The area of the shaded region is 21 square centimeters. What is the area of sector AOB?

A O

B

21 cm2

A 10.5 cm2 C 31.5 cm2

B 28 cm2 D 42 cm2

40 A company uses the advertisement shown to attract customers. In what way could the advertisement be misleading?

We Cost LESS!

Them Us496

498

Co

st t

o C

lien

t ($

)

500

Company

F The vertical axis shows the cost to the client as opposed to the company.

G The horizontal axis is mislabeled.H In fact, the company charges more than

the others.J Although the company charges less,

because of the range of values shown on the vertical axis, the difference is visually exaggerated.

41 Lucia made 50 Texas fl ags out of wire. For the fi ve-pointed star, she made the design below by bending a wire 20 inches long into shape. She wants to make 50 congruent copies of the star in total. How much wire will she need to make all 50 stars?

A 70 in.B 100 in.C 1000 in.D There is insuffi cient

information to answer this question.



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42 Find the positive root of the function f(x) = 2x2 - 2x - 12.F 1 H 3G 2 J 4

43 What is the range of the function f(x) = -x2 + 4x - 1?A (–∞, –5] C (–∞, 3]B (–∞, –1] D (–3, ∞)

44 Suppose x and y satisfy the two equations 3x – y = –1 and 5x + y = 17. Which shows the correct fi gure for y?F 1 H 5G 3 J 7

45 Walter is mailing books on the history of Texas as presents to his friends. Each book costs $2.90 to mail. Walter has a $20 bill. If Walter mails as many books as he can using his $20 bill, how much money should he have left?A none C $1.40B $0.90 D $2.60

46 A pair of number cubes is rolled 360 times. How many times would you expect the 2 cubes to show the same number?F 30 H 72 G 60 J 90

47 Corey has a rectangular prism with dimensions 6 units × 12 units × 24 units. Which set of dimensions corresponds to a rectangular prism similar to Corey’s?A 8 units × 2 units × 4 units B 3 units × 6 units × 9 unitsC 12 units × 4 units × 3 unitsD 1 unit × 2 units × 3 units

48 Which choice shows the right side view of the 3-dimensional fi gure shown below?

F

G

H

J


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49 The following sequence of numbers is obtained by starting with 1, and then multiplying each term by 2 and adding 1 to get the next term: 1, 3, 7, 15, 31, etc. Which formula gives the nth term in the sequence?A 2n – 1B 2n2 – 1C 2n – 1

D 2n – 1

50 An exercise shop in Galveston sells jump ropes in a number of lengths. Every time someone buys a jump rope, the store manager records its length. What should the manager compute using this data to determine the most popular jump rope length?F meanG medianH modeJ range

51 Paula prepares a bath for her dog. The temperature T of the water in the bath is initially 95°F. For the fi rst hour after the bath is prepared, the temperature of the water can be modeled by the equation

T = - 1 _ 3 m + 95, where m is time in

minutes. The dog is most comfortable if the water temperature is above 89°F. How much time does Paula have to bathe her dog comfortably?A 15 minB 18 minC 24 minD 30 min

52 Jason is asked to determine for which values of n is 4n + 1 divisible by 3. He decides to make the table shown. Based on the table, what would be a reasonable conjecture for the answer?

n 4n + 11 52 93 134 175 216 257 298 33

F n = 2, 5, and 8G n = 3k + 1 for some integer kH n = 3k + 2 for some integer kJ No value of n works.

53 The graph of a quadratic function f(x) = ax2 + bx + c is shown. Based on the graph, which statement is true?

y

xO

A a < 0B a = 0C 1 > a > 0D a ≥ 1

54 Which three-dimensional fi gure has exactly 2 triangular faces?F square pyramidG triangular prismH triangular pyramidJ cylinder



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55 A pet shelter only has dogs and cats. The total number of dogs and cats is 50. There are 12 more cats than dogs. How many dogs are in the shelter?A 16 C 22B 19 D 25

56 The fi gure shows three equilateral triangles erected on the sides of a right triangle. What is the area of the unknown equilateral triangle?

2 m2

8 m2

?

F 6 m2 H 10 m2

G 2 √

___

17 m2 J 68 m2

57 Part of the path of a Texas Eagle train makes the straight line shown below in the graph. Which statement best describes this line?

y

xO

l

A a line with slope –1.5 and y-intercept –1

B a line with slope - 2 _ 3 and y-intercept 1

C a line with slope –1.5 and y-intercept 1

D a line with slope –1.5 and y-intercept 2 _ 3

58 William bought a set of drinking glasses. The glasses are shaped like cylinders and come in two sizes. The circular bases of both sizes are 3 inches in diameter. The large glasses are 8 inches in height and the small glasses are height 5 inches in height. The amount of water that the small glasses can hold combined is equal to the amount of water that the large glasses can hold combined. There are 16 small glasses. How many large glasses are there?F 5 H 10G 8 J 16

59 Three points A, B, and C are plotted in the coordinate plane shown. Which are the coordinates of a fourth point D that would form the vertices of a parallelogram together with the other 3 points?

A B

C

y

xO

A (–4, 2)B (–4, 1)C (–5, 2)D (–3, 3)

60 Simplify (x + x + x)(x + x).F 5xG 6xH 5x2

J 6x2


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Benchmark Test 2


best answer.

1 The surface area S of a sphere is given by the formula S = 4πr2, where r is the radius of the sphere. Which symbol represents an independent variable?A S C π

B 4 D r

2 Michael is watching computers being packed away at a manufacturing plant. He notices that in every shipment, D = 2L + 3, where D is the number of desktops and L is the number of laptops. Which statement best describes the relationship between D and L in words?F The number of desktops is 3 more than

the number of laptops.G The number of laptops is twice the

number of desktops plus 3.H The number of desktops is more than

twice the number of laptops.J The number of desktops is 3 more than

twice the number of laptops.

3 Walter tries to solve the equation 4x – 5 = 7 + 2x. His steps are shown below. Which is the fi rst step that contains an error?

Step Result

1 4x – 5 = 7 + 2x

2 4x = 12 + 2x

3 6x = 124 x = 2

A Step 1 B Step 2 C Step 3D Step 4

4 The chart shows the volume of water let out by a water tank that supplies 2 identical water fountains in a high school in El Paso. At which of the times listed were both water fountains running?

Qu

arts

of

Wat

er

2

3

1

0

4

5

6

7

Time (A.M.)

9:00 9:10

F 9:01 A.M. H 9:11 A.M.G 9:05 A.M. J 9:16 A.M.

5 Claudia rolled a marble down an inclined plane. The table shows the distance d that the marble traveled during the nth second. Which equation best represents the relationship between n and d?

Second (n) Distance (d)1 2 cm2 6 cm3 10 cm4 14 cm

A d = n + 1 C d = 4n – 2B d = 2n D d = 4n + 2

6 What is the slope of line �?F –2 y

xO

G 1 _ 2

H 1J 2



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7 Paula uses wooden planks to make a patio deck for her home in Galveston. Each plank is 12 feet long, 6 inches wide, and about 1.25 inches thick. She places 19 of them side by side with a half-inch gap between them as shown in the fi gure. How wide is the patio deck?

0.5 in.

6 in.

A 114 in. C 123 in.B 117 in. D 123.5 in.

8 The two right triangles shown are similar to each other. Which is the correct value for x?

40

16

10

x

F 20 H 30G 25 J 32

9 How does the graph of y = 4x2 compare to the graph of y = 3x2?A The graph of y = 4x2 is wider.B The graph of y = 4x2 is narrower.C The graph of y = 4x2 is shifted up from

the graph of y = 3x2.D The graph of y = 4x2 is shifted down

from the graph of y = 3x2.

10 Factor the quadratic 3x2 - 18x + 24.F 3(x – 2)(x – 4) G 3(x – 2)(x + 4)H 3(x + 2)(x – 4)J 3(x + 2)(x + 4)

11 Use the Quadratic Formula to fi nd the larger of the two roots of the quadratic equation 7x2 - 5x - 3 = 0. Which choice represents this root rounded to the nearest hundredth?A –0.39B 1.10C 2.21D 15.44

12 Which point, together with point P, defi nes a line that is perpendicular to line m?

y

xO

m

A

P

B

D

C

F point AG point BH point CJ point D


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13 At a certain company in Abilene, employees earn a salary of $y. This can be represented by the equation y = 30,000 + 1000x, where x is the number of years the employee has worked at the company. What is the effect of increasing the y-intercept of this equation by 5000? A The starting salary becomes $5,000.B The starting salary becomes $35,000.C The raise each year becomes $5,000.D The raise each year becomes $6,000.

14 Which choice best describes the relationship between the graphs of y = 10x and y = 0.1x?F One graph is the 90° counterclockwise

rotation of the other.G One graph is the refl ection of the other

graph in the x-axis.H One graph is perpendicular to the other

graph.J One graph is the refl ection of the other

in the line y = x.

15 Which equation is consistent with the table below?

x 1 4 9 11y 101 404 909 1111

A y = x(100 + x) C y = x + 0 + xB y = x2+ x D y = 101x

16 Juan, Lucas, and Gayla live in San Antonio. Gayla lives exactly halfway between Juan and Lucas. On a map, the coordinates of Juan and Lucas’ homes are (-10, 8) and (8, -10), respectively. What are the coordinates of Gayla’s home?F (–9, 9) H (–1, –1) G (–2, –2) J (–1, 1)

17 What is the value of x, given the triangle shown below?A 5

5

30˚

60˚

x

B 6C 5 √

__

3 D 10

18 The table shows the number of calories per serving for four different brands of yogurt. Which brand has not yet been added to the bar chart?

Brand CaloriesA 160B 190C 150D 180

140

170Cal

ori

es

200

Brand

F Brand A H Brand CG Brand B J Brand D



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19 Which could NOT be used as the net of a cube?

A B C D

A fi gure AB fi gure BC fi gure CD fi gure D

20 Terrill uses a paint roller to paint the walls of a restaurant in Austin. The roller is a cylinder with a height of 9 inches and a base radius of 1 inch. About how much of a wall is covered by paint after a single revolution of the paint roller?F 9 in.2

G 18 in.2

H 28.27 in.2

J 56.55 in.2

21 The fi gure shows fi ve checkered squares of increasing side lengths. Which answer is a reasonable conjecture about this pattern?

A There is an even number of white squares in each square.

B There is an odd number of black squares in each square.

C There is an odd number of black squares when the side length is even.

D There is an odd number of white squares when the side length is odd.

22 Which graph shows a linear function?

BA

D

Cy

xO

F graph AG graph BH graph CJ graph D

23 Line � passes through the point (3, 0) and intersects the y-axis at the point (0, –6). If the equation of line � is y = mx + b, what is b?A –6B 0C 2D 3

24 Janelle sold cookies shaped like the state of Texas in order to raise $50 for a fundraiser. She determined that her profi t p, in dollars, is represented by the equation p = 2c – 10, where c is the number of cookies she sells. If n represents the solution of this equation for c when p = 0, what does n represent?F the number of cookies she bakedG the number of cookies she must sell to

break evenH the number of cookies she must sell to

make a profi tJ the number of cookies she must sell in

order to meet her goal of raising $50


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25 If Joshua places his money in Account A, the value of his account will be 100 + 10t after t years. If he places his money in Account B, the value of his account will be 100 + 2t2 after t years. For how many years must Joshua be willing to invest his money before it becomes more valuable to use Account B instead of Account A? (Fractional parts of years are not allowed in this problem.)


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26 The fi gure shows a regular hexagon. What is the area of this hexagon?

2 m

B C

DA

F E

A 2 m2

B 3 m2

C 2 √

__

3 m2

D 3 √

__

3 m2

27 To be consistent with the pattern, what image should be placed where the question mark is found in the tiling shown below?

?

F H

G J

28 Which point is inside the circle, outside the triangle, and on the border of the rectangle?

y

xO

A (–5, 2) C (–3, 2)B (–4, 3) D (–1, 3)



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29 What is the equation of the line that passes through the points at (–3, –4) and (–5, –4)?F y = –4 H y = x – 1G y = –4x J y = 2x + 2

30 There are 32 ounces of milk in a carton. A recipe for Pan de Campo (Cowboy Bread) calls for 3 ounces of milk per roll. Let m represent the amount of milk left in the carton after r rolls are baked. Which equation correctly relates m and r?A m = 3r C m = 32 – 3rB m = 32 – r D m = 32 + 3r

31 Circle A has radius 2 units. Circle B has radius 8 units. Equilateral triangles are inscribed in both circles. What is the ratio of the area of the larger equilateral triangle to the area of the smaller triangle?F 2:1 H 8:1 G 4:1 J 16:1

32 Let a, b, and c represent the side lengths of three different cubes. Which choice lists all the possible heights of structures built by stacking exactly 2 of the 3 cubes?A a, b, c B a + b + cC a + b, b + c, a + cD 2a, 2b, 2c

33 What is the x-intercept of the line represented by the equation 2x – 9y = 18?F –2 H 9 G 2 J 16

34 How can one obtain the graph of y = x2 + 1 from the graph of y = x2 - 1?A Shift the graph of y = x2 - 1 down by

2 units.B Shift the graph of y = x2 - 1 up by

2 units.C Refl ect the graph of y = x2 - 1 in the

x-axis.D Refl ect the graph of y = x2 - 1 in the

y-axis.

35 The fi gure below shows the beginning of a sequence of polygons. What equation relates the number of sides s to the nth polygon in the sequence?

F s = 3 + 2nG s = 3 + 5nH s = 5 + nJ s = 5 + 2n

36 The wheel of a large unicycle has a diameter that is 1.2 times the diameter of the wheel of a small unicycle. If the large unicycle travels 48 feet after 8 revolutions, how far does the small unicycle travel after 8 revolutions?A 24 ftB 36 ftC 40 ftD 42 ft


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37 Marcus and Vassia play a game to decide whether to go to a concert by the Dallas Jazz Orchestra or the Dallas Symphony Orchestra. They take a bag that contains 10 cards, each with a single number written on it. The cards have different numbers. Marcus closes his eyes and picks a card randomly. Vassia then closes her eyes and picks another card randomly. What is the probability that the number on Vassia’s card is higher than the number on Marcus’ card?F 0.1G 0.5H 0.9J The answer depends on what Marcus

drew.

38 Which of the following situations CANNOT be modeled by a linear function?A the height of an elevator rising at a

constant speedB the shape of a ramp that rises with

constant slopeC the conversion formula that shows the

number of meters equivalent to a given number of feet

D the shape made by the steps of a staircase

39 A circle in a playground in Round Rock has an area of 36 square meters. What is the area of a 108° sector of this circle?F 9 m2

G 10.8 m2

H 12 m2

J 14.4 m2

40 The table below shows the number of hours 4 different employees worked at a clothing store in Abilene during the course of a week. Based on the data, on which day did people work collectively the greatest number of hours?

Worker M Tu W Th FA 4 5 4 4 3B 3 3 2 3 3C 8 6 8 8 8D 5 4 5 6 4

A MondayB TuesdayC WednesdayD Thursday

41 In the fi gure below, identify congruent groups of shapes and count how many shapes are in each group. How many shapes are in the largest group of congruent shapes?

F 2 H 5G 4 J 7

42 Let f(x) = ax2 + bx + c. It turns out

that -b + √

________

b2 - 4ac __ 2a = 31. What is f(31)?

A 0 B 1C 31D 961



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43 Samantha uses the function h(t) = 32t - 16t2 to model the height in feet of a ball bouncing on the ground, where a height of 0 represents being on the ground. For what values of t is this function meaningful?F t = 0 or 2G 0 < t < 2H 0 ≤ t ≤ 2J all real numbers

44 Suppose x and y satisfy the two equations x – y = 5 and 3x – 6y = 6. Which is the value of x?A 2B 4C 6D 8

45 Martin has to drive from Houston to Dallas. The two cities are about 230 miles apart. Martin gets 24 miles per gallon and starts off with 7 gallons of gasoline. Martin does not realize that his tank is not full when he starts his trip and ends up running out of gas. How many miles away from Dallas is he when he runs out of gas?F 30 mi G 62 miH 115 miJ 168 mi

46 A number cube is rolled 30 times. How many times would you expect the number 6 to be rolled?A 5B 6C 8D 10

47 The fi gure shows a corner view of a cube with a smaller cube one eighth the area of the larger cube removed. Which point represents the center of the cube?

CA

BD


48 Two congruent squares with a side length of 3 units overlap in such a way that the corner of one of them sits on the exact center of the other, as shown in the fi gure. What is the area of the shaded region?

118˚

A 2 sq. unitsB 2.25 sq. unitsC 2.5 sq. unitsD 3 sq. units


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49 A square prism has side lengths a, a, and a2. What is its volume?F a2

G a3

H a4

J a6

50 City offi cials want to determine the income level that half the population earns less than and half the population earns more than. They collect the income levels of all the working people in the town. Which measure should they use to fi nd their answer?A meanB medianC modeD range

51 George’s balloon is launched from a height of 50 feet and rises at a rate of 7 feet per minute. Linda’s balloon is launched from a height of 20 feet and rises at a rate of 9 feet per minute. In both cases, t represents time after launch in minutes and altitude is measured in feet. Which equation can be used to determine the number of minutes after launch when the balloons are at the same altitude?F 50 + 7t = 20 + 9tG 50 – 7t = 20 – 9tH 50 + 9t = 20 + 7tJ 50t + 7 = 20t + 9

52 Dimita must solve the following problem for homework: For each integer A, how many rectangles with integer side lengths have an area of A square units? Which of the following questions represents a simpler problem that Dimita would necessarily be able to solve if she could solve the original problem?A How many triangles with integer side

lengths have an area of 6 square units?B How many rectangles with integer side

lengths have an area of 6 square units?C How many rectangles with integer side

lengths have a perimeter of 6 units?D How many triangles with integer side

lengths have a perimeter of 6 units?

53 The 4 points A, B, C, and D lie on the graph of a quadratic function. Which of the following is a root of the quadratic function?

y

xO

DA

B

C

F point A H point CG point B J point D

54 Nikia paints a cube. Faces that do not share a common edge are painted the same color, and faces that do share a common edge are painted different colors. How many different colors are on the cube that Nikia painted?A 2 C 4B 3 D 5



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55 A drawer in a hardware store in downtown Waco contains 300 nails that come in two sizes. There are 3 times as many short nails as long nails. Which of the following linear equations can be used to determine n, the number of long nails?F 300 = 3nG 300 = 4nH 300 = 5nJ 300 = 6n

56 A right triangle has integer side lengths. Which choice gives the length of the third side if two of the side lengths are 33 and 65?A 32B 56C 73D 98

57 The variables x and y are related by the linear equation 4x + y = 17. Which answer choice lists the missing entries in the table from top to bottom?

x y–3 ?–1 ?2 ?4 ?

F 1, 9, 17, 25G 1, 9, 21, 29H 29, 21, 9, 1J 29, 21, 13, 5

58 The sum of all the edge lengths of a cube is 9 centimeters. If the cube is stretched in one direction by a factor of 2, what is the sum of all the edge lengths of the resulting square prism?A 9 cmB 10 cmC 11 cmD 12 cm

59 All the points shown in the fi gure below have coordinates that are integers. Which point is on the line that passes through P and the midpoint between Q and R?

y

xOD

A

B CR

Q

P


60 Simplify 1 _ a (a + 1)(a + a).

A a + 1

B 2a + 2

C a + 1 _ a

D 2 a + 1

_ a


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Benchmark Test 3


best answer.

1 The distance d that a rocket-powered car travels in feet for the fi rst few seconds is given by the equation d = 64t2, where t is time in seconds. Which statement best represents the functional relationship between the variables d and t?A The distance d is dependent on the

time t.B The time t is dependent on the

distance d.C The distance d and time t are

independent of each other.D The relationship cannot be determined.

2 Howard wants to make a geometric design using construction paper. He fi gures out that the number of blue sheets he needs to use is 8 more than 4 times the number of yellow sheets. Let B be the number of blue sheets and Y be the number of yellow sheets. Which mathematical equation shows this relationship between B and Y ?F Y = 4B + 8G Y = 8B + 4H B = 4Y + 8J B = 8Y + 4

3 Mr. Ahrenson wrote a book on the history of Texas. He determined that the cost c in dollars to self-publish n copies of his book is represented by the equation c = 1.25n + 520. If Mr. Ahrenson spent $832.50 to self-publish his book, how many copies did he make?A 150 C 520B 250 D 666

4 The chart below shows the progress of 3 teams labeled A, B, and C in a 7-kilometer race around the city of Austin. Based on the chart, for approximately how many minutes was team B in the lead?

Dis

tan

ce (

km)

23

10

45

76

Time (min) 0 9 18

AB

C

27

F 0 min H 4 minG 2.5 min J 6 min

5 Martha examined the following sequence of numbers: 1, 2, 5, 14, 41, etc. Suppose that n is a number in this sequence. In terms of n, what formula could be used to obtain the next number in the sequence after n?A n + 1 C 2n + 1B 2n D 3n – 1

6 The variables x and y are related by the linear equation y = mx + b. Some values of x and y are shown in the table. What is m?

x –10 4 18 28y 0 7 14 19

F 0 H 1

G 1 _ 2 J 2



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7 The two squares shown below share the same center. What is the approximate length of x?

6 cm

3 cm

x

A 0.88 cmB 1 cmC 1.5 cmD 1.76 cm

8 What is the value of x in the diagram below?

x 2021

F 400 _ 29

G 420 _ 29

H 441 _ 29

J 16

9 How does the graph of y = 8x2 compare to the graph of y = 32x2?A The graph of y = 8x2 is wider than the

graph of y = 32x2.B The graph of y = 8x2 is narrower than

the graph of y = 32x2.C The graph of y = 8x2 is shifted up from

the graph of y = 32x2.D The graph of y = 8x2 is shifted down

from the graph of y = 32x2.

10 The area of a rectangle is given by the function f(x) = x2 + 7x + 12. What is f (7)?F 98G 100H 110J 132

11 Lucia wants to solve a quadratic equation by completing the square. She manipulates her equation into the following form: x2 - 6x = 16. What should she add to both sides of this equation so that the left side becomes the square of a binomial?A 3 B 6C 9D 36

12 The triangle shown below has vertices at(–4, –1), (1, –3) and (3, 5). What is the equation of the line that contains the median of the triangle to vertex A?

O

B

A

C

x

y

F y = –1

G y = 1 _ 3 x + 1 _ 3

H y = 44 _ 35 x + 141

_ 35

J y = 3x + 11


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13 What can be done to the line shown below so that it becomes horizontal?

x

y

O

m

A Decrease its y-intercept by 1.B Decrease its y-intercept by 0.5.C Decrease its slope by 0.5.D Multiply its slope by –1.

14 Which choice best describes the relationship between the graphs of y = 4x

and y = - 1

_ 4 x?

F One graph is the 45° counterclockwise rotation of the other graph.

G One graph is the refl ection of the other graph in the x-axis.

H One graph is perpendicular to the other graph.

J One graph is the refl ection of the other graph in the line y = x.

15 Which equation is consistent with the table below?

x y1 –12 –43 –94 –16

A y = –xB y = –x2

C y = (–x)2

D y = x – 2x2

16 Quadrilateral ABCD is a diagram of a kite that Ricardo likes to fl y. It is formed by attaching two 30-60-90 right triangles together along their hypotenuses as shown in the diagram below. What is the value of x, the length of

___ AM ?

60°20 in.

B D

C

A

M

x

F 20 in. H 20 √

__

3 in.G 30 in. J 40 in.

17 The histogram below shows the frequency of scores on a chemistry test in Ms. Matthew’s class. How many students are there in the class?

41–50

2

3

1

0

4

Freq

uen

cy

5

6

Score51–6

061–7

071–8

081–9

0

91–100

A 6 C 40B 19 D 100

18 What is the distance between the points at (–3, 9) and (1, 3)?

F √

___

10 H 2 √

___

10 G √

___

13 J 2 √

___

13



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19 The net shown below consists of a square surrounded by congruent isosceles triangles. Which is the approximate volume of the solid that this net represents?

10 ft 13 ft

A 363.6 ft3 C 433.3 ft3

B 400 ft3 D 1300 ft3

20 A triangular prism has a base that is a right triangle with legs measuring 5 meters and 12 meters. The height of the prism is 2 meters. What is the area of the largest lateral face of this prism?F 24 m2 H 30 m2

G 26 m2 J 34 m2

21 John has been studying the kinds of triangles he can make by joining two congruent right triangles, like the one shown in the fi gure below. Which of the following statements is true about such triangles?

A All such triangles are equilateral.B All such triangles are isosceles.C All such triangles are obtuse.D All such triangles are right.

22 What does the graph of a linear equation look like?F a pointG a straight lineH a curved lineJ a circle

23 Line � has slope - 2 _ 3 . Points P(–3, 3) and

Q(4, y) are on �. What is y?

O

P

Q

x

y

A - 5 _ 3

B - 8 _ 5

C - 3 _ 2

D - 4 _ 3

24 Kyle plays high school basketball in Dallas. He is in Boys Class 5A. During the most recent basketball season, he scored between 12 and 18 points (inclusive) every game. The season consisted of 11 games. Let T denote the total number of points Kyle scored the whole season. Which choice represents the best that can be said about the value of T with the given information?F T ≤ 66G T ≤ 198H 132 ≤ T ≤ 198J 132 ≤ T


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25 Let f(x) = 5x. Let g(x) = x + 8c, where c is a positive constant. Which of the following statements is true?A f (x) > g(x) for all x > 0B f (x) > g(x) for all x > cC f (x) > g(x) for all x > 2cD If c is large enough, f (x) < g(x)

for all x > 0.

26 What is the ratio of the area of a square with side length s to the area of an equilateral triangle with side length s?

F 16 _ 9 H 2 √

__

3

G √

__

3 J 4 √

__

3 _ 3

27 The fi gure below was made from repeated rotations of the rectangle shown on the right through 45°. What is the total perimeter of the fi gure?

12.5 ft

5m

A 240 m C 260 mB 250 m D 500 m

28 Which choice lists the prime numbers between 1 and 30, inclusive, that are no more than 2 units away from a perfect square?F 2, 3, 5, 11, 23G 2, 3, 5, 7, 11, 17, 23H 2, 3, 5, 7, 11, 13, 17, 23J 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

29 What is the equation of the line that has slope 6 and y-intercept –3?A y = –3x + 6 C y = 6x – 3B y = –3x – 3 D y = 6x + 6

30 In order to control inventory, a Kingwood company tries to make sure that the number of chairs it owns is always less than or equal to twice the number of employees, excluding the 250 chairs in the dining hall. Let c denote the number of chairs owned by the company and let p be the number of employees. Which statement refl ects the company’s endeavor?F c ≤ 2p – 250 H c ≤ 2p + 250G c ≤ 2p J c ≤ 2p + 500

31 Claire wants to cut the rectangle shown width-wise so that the resulting rectangles are similar to each other. What is the minimum distance, x, in order to accomplish this?

100

30

x


9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

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32 Let a, b, and c represent the side lengths of a rectangular prism. Assume that a < b < c. The prism is sliced along a plane parallel to the face of dimensions a × b. Which expression represents the total surface area of both pieces?A ab + ac + bcB 2ab + ac + bcC 2ab + 2ac + 2bcD 4ab + 2ac + 2bc

33 Line � passes through (3, 0) and has a slope of –5. What is the y-intercept of �?

y

xO

F –12 H 20G 15 J 25

34 The graph of a quadratic of the form y = x2 + c is shown in the coordinate plane below. How must c be modifi ed so that the graph of the resulting quadratic will pass through point P?

y

xO

P

A Reduce c by 6. C Reduce c by 2.B Reduce c by 4. D Double c.

35 Consider an arrangement of dots that consists of 3 rows of n dots, evenly spaced and aligned. The fi gure shows an example when n = 5. The table shows the answers for the fi rst few values of n. How many rectangles with horizontal and vertical sides can be made using 4 of the dots as its vertices?

n Numberof Rectangles

1 02 33 94 185 30

F n(n – 1)

_ 2

G n(n – 1)

H 3n(n – 1)

_ 2

J 3n(n – 1)

36 Carol and David are folding origami cranes for a celebration at the Taniguchi Oriental Garden in Austin. Carol can fold 12 origami cranes in 1 hour. Together, Carol and David can fold 11 origami cranes in 30 minutes. How long does it take David to fold a single origami crane?A 5 minB 6 minC 8 minD 10 min


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37 A number cube is rolled. What is the probability that the number rolled is either greater than 3, or even, but not both?

F 1 _ 6 H 1 _

3

G 1 _ 4 J 1 _

2

38 Which column could be represented by a linear function in x?

x A B C D1 –10 –2 1 12 –11 0 2 03 –12 2 4 14 –13 6 8 2

A column AB column BC column CD column D

39 A large wheel has a radius 3 times that of a small wheel. When the small wheel spins, it makes the large wheel spin. Assuming there is no slippage between the two wheels, how many times must the small wheel spin in order for point P to trace out an arc with a 300° central angle?

P

F 2G 2.5H 3J 3.5

40 Marjorie observed a small insect on the banks of Lake Livingston. She decided to follow it. She marked down 5 observations of the distance the insect traveled at 5 different times during her observations. She concluded that the insect would travel 6 miles in 4 hours. Is this a reasonable conclusion? Why or why not?

Dis

tan

ce (

mi)

23

10

45

76

89

Time (hr)1 2 3 4 5

A No, because her observations are not accurate enough.

B No, because she is extrapolating her data too far out.

C No, because she is not a qualifi ed entomologist.

D Yes, the data is sound and the prediction is highly likely to be true.

41 Two triangles in the plane are congruent to each other. Which of the following statements is NOT necessarily true?F They have the same area. G They have the same perimeter.H They have the same angles.J One is a translation of the other.

42 Which of the following is a root of the function f (x) = x2 + 2x - 15?A –5 C 5B 2 D 15



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43 The domain of the function f (x) = x2 + 1

is, by defi nition, the set {–2, –1, 0, 1, 2}. What is the range of this function?F {–5, –2, –1, 1, 2, 5} G {–4, –1, 0, 1, 4}H {1, 2, 5}J {0, 1, 4}

44 The lines y = 3x + 8 and y = –x + 6 are drawn in a coordinate plane. What is the y-coordinate of their point of intersection?A –0.5B 5.5C 6.5D 8.5

45 Giovanni owns 90 olive trees. He found that in 5 days, he could pick all the olives from 12.5 trees. Assume that people can pick olives at this same rate. Planning for next season, how many other people should Giovanni hire to help him if he needs to pick all 90 trees in 1 day?F 7G 12H 23J 35

46 Arlene, Ben, and Callie are schoolmates in Laredo and often play games together. To decide the order in which they play, they use a bag that contains the numbers 1, 2, and 3 written on identical cards. Without looking, Arlene, then Ben, and then Callie each pick out a card and do not put it back. They play in the order indicated by the number they picked. In 15 games, how many times would you expect that Ben went third?A 3B 4C 5D 10

47 A solid is obtained by taking the intersection of two solid cylinders of the same radius in such a way that their axes intersect at right angles. Which choice could represent top and front views of this object?F equilateral triangle, squareG circle, squareH circle, circleJ square, square

48 Jason has a map of Texas. He enlarges the map with a photocopier by 50%. If the area of Texas on the original map was 12 square inches, what is the area occupied by Texas on the enlarged map?A 18 in.2

B 24 in.2

C 27 in.2

D 36 in.2


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49 Lynnette makes 5 circles and labels them 1 through 5. The ratio of the radius of circle n + 1 to circle n is r. If the radius of circle 1 is 1 unit, what is the radius of circle 5?F r4 unitsG r5 unitsH 4r unitsJ 5r units

50 Leslie is reading a novel about the Alamo. She wants to estimate the number of words in the novel. The novel has 600 pages. She picks 10 pages at random and counts the number of words on each of these pages. What number should she compute from this data that she could then multiply by 600 to obtain the desired estimate?A meanB medianC modeD range

51 Marcus wants to build a tower in his backyard. He has $600 to spend on it. Each yard in height will cost him $50 in materials. At the top of the tower, he wants to place a platform that will cost $120 to build. Let y be the height of the tower in yards. Which inequality expresses the conditions under which Marcus must work?F 50y + 120 ≤ 600G 50y – 120 ≤ 600H 50y ≤ 600J 120y + 50 ≤ 600

52 Brad is given the following problem: Consider N congruent non-overlapping spheres. Call a point on a sphere “private” if every line segment from that point to a point on any other sphere passes through the interior of some sphere. To solve the total of all the private points, what would NOT be a good way to start?A Examine the simpler, similar problem

with circles in the plane.B Consider the case with N = 2.C Consider the case where the centers

are collinear.D Examine the simpler, similar problem

with cubes in place of spheres.

53 The three points A, B, and C all lie on the graph of a quadratic function. Which range of values is guaranteed to contain a root of the function?

y

xO

A

B C

F x < –3G 0 < x < 2H 2 < x < 5J 5 < x

54 How many different kinds of solids are there that have exactly 5 faces, and where each face is either a square or equilateral triangle? (For this problem, faces must separate the inside of the solid from the outside.)A 1 C 3B 2 D 4



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55 Brian and Hank are charged with the responsibility of mowing a 1200-square-yard grassy lawn in Wichita Falls. Once, to mow the entire lawn, Brian mowed for 3 hours and Hank mowed for 2 hours. Another time, Brian mowed for 4.5 hours and Hank mowed for just 1 hour. Assuming that Brian and Hank mow at their own constant rates b and h, respectively, what system of equations could be used to solve this situation?F 3b + h = 1200 4.5b + 2h = 1200G 3b + 2h = 1200 4.5b + h = 1200H 2b + 3h = 1200 4.5b + h = 1200J 3b + 2h = 1200 b + 4.5h = 1200

56 Which of the following could NOT be the side lengths of a right triangle?A 8, 15, 17B 15, 20, 25C 20, 21, 31D 25, 25 √

__

3 , 50

57 The variables x and y are related linearly as shown in the table below. Which choice gives this relationship algebraically?

x –2 –1 0 1 2y 0 5 10 15 20

F 5x – y = 0 G 5x – y + 5 = 0H 5x – y + 10 = 0J 5x + y + 10 = 0

58 A tetrahedron is a triangular pyramid with all 4 sides equilateral. If the side length of a tetrahedron is doubled, by what factor is its surface area multiplied?A 2B 4C 6D 8

59 Which choice lists three vertices of a triangle that contains the square shown in the coordinate plane below?

y

xO

F (–5, –2), (0, 3), (5, –2)G (–2, –4), (6, 0), (–2, 4)H (0, 4), (4, 0), (–100, –100)J (–5, 0), (5, 5), (0, –5)

60 Simplify (a + 2b + (5 – a – b) + (5 – b))(a + b).A 10(a + b) B a2 + 4ab + 2b2

C a2 + 4ab + 2b2 + 5a + 5bD a2 + 5ab + 4b2 + 5a - 5b


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