Allen ISD 2009

Mathematics 11th Grade Historical Perspective 2003, 2004, 2006, & 2009

TAKS Student Expectations Obj. 1 The student will describe functional relationships in a variety of ways.

A.1 Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. A.1.A The student describes independent and dependent quantities in functional relationships.

Spring 2003 Spring 2004 Spring 2006 Spring 2009 55. A department store had a 20%-off sale on all clothing items.

Which statement best represents the functional relationship between the sale price of an article of clothing and the original price? A The original price is dependent on the sale price. B* The sale price is dependent on the original price. C The sale price and the original price are independent of each other. D The relationship cannot be determined.

13 An ice-cream vendor made a table showing the relationship between the daily high temperature and the number of ice-cream cones sold per day. What is the dependent quantity in this relationship? A The daily high temperature B* The number of ice-cream cones sold per day C All of the data in the table D Cannot be determined

11 During a sale at a shoe store, all shoes were 25% off the original price. Which statement best describes the functional relationship between the sale price of a pair of shoes and the original price? A The sale price is dependent on the original price. B The original price is dependent on the sale price. C The sale price and the original price are independent of each other. D The sale price is dependent on the number of pairs of shoes purchased.

A.1.B [gather and record data and] use data sets to determine functional relationships between quantities; 28 An equation can be used to find the total cost of buying square-foot floor tiles to cover an area of floor. Using the table below, find the equation that best represents y, the total cost, as a function of x, the number of square feet to be covered.

45 The table shows the number of slices of pepperoni placed on each size of pizza at Pepe’s Pizza Shop.

Let r represent the radius of the pizza and let n represent the number of slices of pepperoni. Identify the equation that best represents the relationship between the radius and the number of slices of pepperoni.

A r = 2n + 1 B n = 2r + 1 C r = n2

+ 1 D* n = r2

+ 1

31 Which equation best describes the relationship between x and y shown in the table below?

40 Casey conducted an experiment and recorded the data in the table shown below.

Which equation best describes these data?

F y = x G y = 2x − 1 H y = x2

+ x − 1 J* y = (x − 1)2

+ 1

44. The function table shows the values of f(n) for given values of n.

Which function best describes the relationship between the quantities in the table?

Allen ISD 2009

A.1.C Describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations; 11 Eddie’s Towing Company charges $40 to hook a vehicle

to the tow truck and $1.70 for each mile the vehicle is towed. Which equation best represents the relationship between the number of miles towed, m, and the total charges, c?

A c = 40 + 1.70 B* c = 40 + 1.70m C c = 40m + 1.70m D c = 40m + 1.70

37 The profit earned on the sale of tool sets can be represented as the product of the number of tool sets sold and the difference between the selling price and the cost of making each set. The selling price of each tool set is $19.95, and the cost of making each set is $4.37. Which equation represents p, the profit, in terms of s, the number of tool sets sold? A* p = s(19.95 − 4.37) B p = s(19.95 + 4.37) C p = 19.95 + 4.37s D p = 19.95s − 4.37

60. The height in centimeters, h(x), of a human female of European ancestry can be estimated by multiplying the length of the tibia in centimeters, x, by 2.90 and then adding 61.53 to the product. Which of the following best represents this relationship? F h(x) = (2.90 + x)(61.53) G h(x) = 2.90(x + 61.53) H h(x) = 2.90x + 61.53

J h(x) = + 61.53

A.1.D Represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities 50 Which graph best represents all the pairs of numbers (x, y) such that x + y < −6?

20 Which graph best represents the inequality x + 2y < −14?

54 Which graph best represents the relationship shown in the table below?

3. Which graph best represents the relationship in the table below?

Allen ISD 2009

A1.E The student interprets and makes inferences from functional relationships 59 Gina did a research project on how age affects sleep

patterns. She concluded that as people age, they sleep fewer hours until a point in adulthood when the number of hours remains constant. Gina also found that after the age of 70 the amount of time spent sleeping increases slightly. Which graph best shows the results of Gina’s research?

3. Karen jogs at a steady pace up a hill in her neighborhood. She then runs down the hill, and her speed increases. Which graph best describes this situation?

59 According to the data shown below, which would be the best prediction of the number of passengers at the International Jetport for the year 2008?

31 The function below shows a relationship between x and y. y = 7x + 3 If the value of x increases by 1, what happens to the value of y? A The value of y increases by 3. C The value of y increases by 10. B The value of y increases by 7. D The value of y increases by 21 .

Obj. 2 The student will demonstrate an understanding of the properties and attributes of functions. A.b.2 Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: A.2.A identify [and sketch] the general forms of linear ( y = x) and quadratic ( y = x2) parent functions;

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

57 Which equation is the parent function of a quadratic equation?

10 Which equation is the parent function of the graph shown below?

Allen ISD 2009

A.2.B Identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. 27 What is the domain of the function shown on the graph?

12 Mr. Maxwell asked his students to identify the domain represented by the function graphed below.

A.2.C Interpret situations in terms of given graphs [or create situations that fit given graphs]. 37 At the Dallas-Fort Worth International Airport, a DC-10, at 4500 feet, is descending toward the east runway a a rate of 150 feet per minute, and a 727, at 600 feet, is

climbing at a rate of 75 feet per minute. Which graph shows when the two planes will be at the same altitude?

47 The graph below shows the decrease in the value of a personal computer over a period of 60 months.

Which is a reasonable conclusion about the value of this personal computer during the time shown on he graph? A Its value at 18 months was twice its value at 36 months. B Its value at 36 months was half its value at 54 months. C It depreciated $200 every 12 months. D* It depreciated $400 every 18 months.

47 Two car-rental companies are advertising special rates for a midsize car. Wendell’s Motor Rentals is advertising a rate of $35 a day plus $0.20 per mile traveled, tax included. Marina’s Car Rentals is advertising a rate of $25 a day plus $0.40 per mile traveled, tax included. Which graph correctly compares the cost of renting a midsize car for one day from each company?

Allen ISD 2009

A.2.D [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.

60 The energy output from a chemical reaction is dependent on the amount of chemicals used. The table shows this relationship.

A.3 Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to:

A.3.A Use symbols to represent unknowns and variables. 56 A sporting-goods store sold a total of 80 backpacks at the

beginning of a new school year. Each backpack sold for either $35 or $50, not including tax. If x represents the number of $35 backpacks the store sold, which expression represents the total amount of money in dollars from the sales of the two kinds of backpacks, not including tax? F 35x + 50(x − 80) G 50x + 35(80 − x) H* 35x + 50(80 �−x) J 50x + 35(x − 80)

23 During the second week of summer vacation, Reuben practiced his guitar for 10 minutes less than twice the amount of time he practiced the first week. If he practiced m minutes the first week, which of the following expressions represents the number of minutes that Reuben practiced during the second week? A 2 − 10m C 2m − 10 B 10 − 2m D 10m − 2

Allen ISD 2009

A.3.B Look for patterns and represent generalizations algebraically. 54 The figures below show a pattern of dark tiles and white

tiles that can be described by a relationship between 2 variables.

Which rule relates d, the number of dark tiles, to w, the number of white tiles?

F d = 2w H d = 2w − 2

G* w = d − 1

11 Let a represent the average speed in miles per hour a car traveled on a trip. Let f(t) represent the distance in miles the car had traveled t hours after the beginning of the trip. The function f(t) is best represented by —

A t 2 + a B at 2

C t + a D* at

54 The table below shows the value of a term in a given position in a sequence of numbers that follows a pattern.

Which expression best represents the value of the nth term?

A.4 Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: A.4.A Find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. 21 Solve the equation 2a − 6 + 5a = 3a + 10 for a. Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

48 The graph below shows the amount of force needed to stretch a certain spring to various distances.

A.4.B Use the commutative, associative, and distributive properties to simplify algebraic expressions. 25 Which expression is equivalent to (5n − 2)3n − (5n − 2)(n − 1)? A n − 1 C 10n2 − 13n + 2 B 3n2 − 3n D* 10n2 + n − 2

41. Which expression is equivalent to

32

(3x − 15y) + (9y − 11x)?

A* −9x − y C 10x − 4y B 11x − 21y D −9x − 26y

39 Which of the following expressions is equivalent to the expression −5x(2x + 7y) + 7xy − 4x(y + 3)? A −10x2+ 7y + 3xy + 3 C −10x2− 32xy −12x B −10x2 + 38xy + 12x D −10x2− 38xy + 12x

Allen ISD 2009

A.4.C Connect equation notation with function notation , such as y = x + 1 and f(x) = x + 1 New TEKS for 2006, 2009

TEK was not implemented in 2003

TEK was not implemented in 2004

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Obj. 3 The student will demonstrate an understanding of linear functions. A.5 Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: A.5.A Determine whether or not given situations can be represented by linear functions.

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A.5.C Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. 16 The algebraic form of a linear function is d = 1/4 l, where d is the distance in miles and l is the number of laps. Which of the following choices identifies the same linear function? F* For every 4 laps on the track, an athlete runs 1 mile. G For every lap on the track, an athlete runs 1/8 mile.

28 Which equation best represents the line graphed below?

F 7x + 4y = 35 H 4x + 7y = −35 G 4x − 7y = 35 J 7x − 4y = − 35

Allen ISD 2009

A.6 Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear function in real-world and mathematical situations. The student is expected to:

A.6.A Develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations. 57 What is the slope of the line identified by 2y = −3(x − 2)?

13 What are the slope and y-intercept of the equation of the line graphed below?

7 Scientists developed the linear model below to show the relationship between altitude, or elevation above sea level (0 feet), and air temperature.

According to the model, what would be the air temperature at an altitude of 0 feet? A 16°F B 45°F C 59°F D 77°F 52 What is the slope of the linear equation 101x + 53y = 12?

Allen ISD 2009

A.6.B Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. 43 What are the slope and y-intercept of a line that contains the point (5, −1) and has the same y-intercept as x − 3y = 6?

A.6.C Investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b. 29 Given the function y = 3.54x − 54.68, which statement best describes the effect of increasing the y-intercept by 33.14? A* The new line is parallel to the original. B The new line has a greater rate of change. C The x-intercept increases. D The y-intercept decreases.

17 The graph of a line is shown below.

26 The graph of a linear function is shown below.

18 The function y = −3x − 8 is graphed below.

In the function above, the slope will be multiplied by −2, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function?

Allen ISD 2009

A6.D Graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. 44 Which equation represents the line that passes through the

points (−1, 4) and (3, 2)?

A.6.E Determine the intercepts of the graphs of linear functions and zeros of linear functions from graph, tables, and algebraic representations. 53 What is the y-intercept of the function graphed below?

8 What are the coordinates of the x-intercept of the equation −3y = 8 − 2x?

49 Find the x- and y-intercepts of −4x + 7y = −28. A x-intercept: (−4, 0) y-intercept: (0, 7) B* x-intercept: (7, 0) y-intercept: (0, −4) C x-intercept: (0, 7) y-intercept: (−4, 0) D x-intercept: (0, −4) y-intercept: (7, 0)

A.6.F Interpret and predict the effects of changing slope and y-intercept in applied situations.

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A.6.G Relate direct variation to liner functions and solve problems involving proportional change.

45 Matt is a speed skater. His coach recorded the following data during a timed practice period.

If Matt continues to skate at the rate shown in the table, what is the approximate distance in meters he will skate in 25 seconds? A 250 m C 150 m B 175 m D* 278 m

28 If y is directly proportional to x and y = 12 when x = 16, what is the value of x when y = 5?

20 Two quantities, x and y, are in a relationship in which y varies directly with x. The graph of this function contains the point (−16, 28). Which of the following represents this relationship?

Allen ISD 2009

Obj. 4 The student will formulate and use linear equations and inequalities. A.7 Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of method to solve them, and analyzes the solutions in terms of the situation. The student is expected to: A.7.A Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. 56 On Wednesdays an athlete’s schedule allows no more than 75 minutes for morning training. One round of a strength routine, s, requires 8 minutes. One round of an endurance routine, e, requires 12 minutes. Which of these best represents the time available for the athlete to spend on strength and endurance routines on Wednesdays? F 20(s + e) > 75 G 8s = 75 − 12e H* 8s + 12e < 75 J 12e < 75 + 8s

45 Denise can assemble a chair in 0.75 hour and a table in 0.4 hour. Which inequality best represents the number of chairs, c, and the number of tables, t, that Denise can assemble in one day if she works a maximum of 8 hours? A (0.75 + 0.4)(c + t) ≤ 8 C 0.75c + 0.4t ≤ 8 B 0.75c + 0.4t ≥ 8 D (0.75 + c) + (0.4 + t) ≥ 8

A.7.B 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. 35 Anna makes hand-painted plates. Her overhead costs are $750 per week, and she pays an additional $10 per plate in material costs. If Anna sells the plates for $25 each, how many plates does she have to sell each week before she can make a profit?

A 20 C* 50 B 30 D 75

60 Ms. Barton determined that the total cost of her wedding, c, could be represented by the equation c = 75n + 1500, where n is the number of people attending the wedding. If Ms. Barton’s wedding cost $8625, how many people attended the wedding? F 135 H 115 G* 95 J 75

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

59 The graph of −x + 5y = 9 is shown below.

Which point represents a solution to this equation? A (0, 1) B (2, 1) C (1, 2) D (−7, 0)

A.7.C Interpret and determine the reasonableness of solutions to liner equations and inequalities. 23 Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polish at $2 each. She spent less than $12, not including tax. Use the grid below to graph the inequality 4x + 2y < 12.

Which point represents a reasonable number of lipsticks and bottles of nail polish that Valerie purchased? A (1, 5) B (2, 3) C* (1, 3) D (2, 2)

48 The amount of an employee’s weekly pay, p, including a bonus, can be represented by the inequality 6.00h + 100 < p < 6.50h + 125, where h represents the number of hours worked by the employee. If an employee worked 25 hours, which of the following is a reasonable amount for that week’s pay? F $118.75 G $250.00 H* $272.50 J $290.25

55 Lisa wants to make a long-distance telephone call to her friend. She does not want to spend more than $5.00 on the telephone call. If there is a $0.50 connection fee and a charge of $0.11 per minute, which best represents the number of minutes that Lisa can talk to her friend?

13 Ms. Rodríguez plans to order from 20 to 26 books for her class. The prices of the books she plans to order range from $4.95 to $12.95 each. If the publisher charges a shipping fee of $0.50 per book ordered, which of the following is not a reasonable price for the books, including shipping? A $145 B $245 C $345 D $445

Allen ISD 2009

A.8 (A.8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: A.8.A Analyze situations and formulate systems of linear equations in two unknowns to solve problems. 3 At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk? A t + m = 2.10 C t + m = 2.10 2t + 2m = 5.15 3t + 2m = 5.15 B t + m = 2.10 D* t + m = 2.10 3t + 3m = 5.15 2t + 3m = 5.15

40 a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

F m + n = 8 H* m + n = 54 m = 3n + 54 m = 3n + 8 G m + n = 8 J m + n = 54 m = 3n − 54 m = 3n − 8 53 The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store? A 2e − u = 220 C 2e − 2u = 440 e − u = −175 e − u = −175 B 2e − u = 220 D* e − 2u = −220 e + u = 175 e − u = 175

1 The student council at Jefferson High School sold a total of 220 brownies and cookies during its fund-raiser. Each brownie sold for $0.75, and each cookie sold for $0.50. The student council made $136.50 from the sales of brownies and cookies. Which system of linear equations can be used to find b, the number of brownies sold, and c, the number of cookies sold? A b + c = 220 B b + c = 136.50

0.50b + 0.75c = 136.50 0.75b + 0.50c = 220

C b + c = 136.50 D* b + c = 220 0.50b + 0.75c = 220 0.75b + 0.50c = 136.50

5 A restaurant sold a total of 418 large and small hamburgers during one day. Total hamburger sales were $1077. Large hamburgers sold for $3, and small hamburgers sold for $1.50. Which system of linear equations can be used to find l, the number of large hamburgers sold, and s, the number of small hamburgers sold? A l + s = 1077 C 1.50l + 3s = 418 3l + 1.50s = 418 l + s = 1077 B l + s = 418 D l + s = 418 3l + 1.50s = 1077 1.50l + 3s = 1077

A.8.B The student solves systems of linear equations using [concrete] models, graphs, tables, and algebraic methods. 46 At a firefighters’ pancake breakfast, the firefighters served 345 people and raised $1395. If the cost of a, an adult’s ticket to the pancake breakfast, was $5 and the cost of c, a child’s ticket, was $3, what was the number of adult tickets sold? F 165 G* 180 H 279 J 345

32 The graph of a system of linear equations is shown below.

Which of the following is the solution to this system of linear equations? F (0, 4) H (0, −3) G (8, 1) J* (10, 2)

25 A city bus collected $780 in fares on one day. The price of a regular fare was $0.80, and the price of a discount fare was $0.40. If a total of 1200 people paid the fares on this bus, how many people paid the regular fare? A 1000 B 1950 C 600 D 750

A.8.C Interpret and determine the reasonableness of situations to systems of liner equations.

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Allen ISD 2009

Obj. 5 The student will demonstrate an understanding of quadratic and other nonlinear functions. A.9 Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters

of quadratic functions. The student is expected to: A.9.B Investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c. 49 Which shows the functions correctly listed in order from widest to narrowest graph?

59 Which equation will produce the widest parabola when graphed? A y = 2x2

B y = −6x2

C y = −0.6x2

D* y = 0.2x2

14 Barbara graphs a family of equations of the form y = ax2 + 1. How does each new graph compare to the previous graph as Barbara increases the value of a from ½ to 1 to 1 ½ and finally to 2? F Each new graph is above the previous graph. G Each new graph is wider than the previous graph. H Each new graph is narrower than the previous graph. J Each new graph is to the right of the previous graph.

A.9.C Investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c 4 What is the effect on the graph of the equation y = x2 + 1 when it is changed to y = x 2 + 5? F The slope of the graph changes. G The curve translates in the positive x direction. H* The graph is congruent, and the vertex of the graph moves up the y-axis. J The graph narrows.

7 The graph of a function of the form y = ax2 + c is shown below.

60 The illustration below shows a 3-dimensional view of a screw.

Allen ISD 2009

A.9.D Analyze graphs of quadratic functions and draw conclusions.

4 The graph below shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground.

How much time elapses while the baseball is 80 meters or more above the ground? F 1 sec H 7 sec G 9 sec J* 6 sec

43 Which of the following is the vertex of the graph of the equation y = −x2 + 2x + 3?

4 If the graph of y = 19x2 + 31 is translated up 15 units, which of the following equations will best describe the resulting graph? F y = 34x2 + 31 H y = 19x2 + 46 G y = 34x 2+ 46 J y = 19x2 + 16 58 The graph below represents the relationship between the density of water and the temperature of water.

According to the graph, which of the following intervals best represents the temperature at which the density of water is greater than 999.9 kilograms per cubic meter? F Less than 1°C H Between 4°C and 8°C G Between 0°C and 4°C J Between 1°C and 7°C

A.10 Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. A.10.A Solve quadratic using [concrete] models, tables, graphs, and algebraic methods. 47 What is the solution set for the equation 4(3x − 2)2= 36?

37 The completion of a certain chemical reaction is expressed by the equation y = 250 − 5x − x2, where y is the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius at which the reaction occurs. If the reaction is complete in 200 seconds, what is the temperature at which the reaction occurs? A* 5°C B 7°C C 10°C D 12°C

43 What is the solution set for the equation 2x2 − 16x − 96 = 0? A { 4, 12} C {−4, −12} B {−4, 12} D {4, −12}

Allen ISD 2009

A.10.B 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. 15 What are the x-intercepts of the graph of the equation y = x2 + x − 12? A x = 4, x = 3 C x = −4, x = −3 B* x = −4, x = 3 D x = 4, x = −3

42 Which ordered pair represents one of the roots of the function f(x) = 2x2 + 3x − 20?

18 Which points best represent the roots of the graphed quadratic equation shown below?

A.11 Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to: A.11.A Use [patterns to generate] the laws of exponents and apply them in problem-solving situations.

24 The length of a rectangle is 4r 2s5t3 units, and the rectangle’s area is 20r5s7t4 square units. If r ≠ 0, s ≠ 0, and t ≠ 0, which of the following best describes the width of the rectangle? F 5r3s2t units H 16r3s2t units G 5r7s12t7 units J 24r7s12t7 units

Allen ISD 2009

Obj. 6 The student will demonstrate an understanding of geometric relationships and spatial reasoning. G.4 Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: G.4.A Select and appropriate representation([concrete], pictorial, graphical, verbal, or symbolic) in order to solve problems.

51 Find the equation that can be used to determine the total area of the composite figure shown below.

7 Doris had a circular garden with a radius of 30 feet. She used all of the fencing from the circular garden to enclose a square garden. The length of each side of Doris’s square garden was approximately — A* 47 feet B 94 feet C 120 feet D 188 feet

19 Look at the cube shown below.

33 Look at the figure shown below.

Which expression does not represent the area of the figure? A bc − ef B* af + ad − de C de + af + ad D af + cd

22 The diagram below shows a circle inscribed in an isosceles right triangle.

Which equation best represents the area, A, of the shaded region?

51 Which expression represents the perimeter of the triangle below?

Allen ISD 2009

G.5. Geometric Patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: G.5.A Use numeric and geometric patterns to develop algebraic expressions representing geometric properties. 34 The figure below shows the first 3 stages of a fractal.

How many circles will the nth stage of this fractal contain? F 2n G 2n

H 2n − 1 J* 2n − 1

5. Use the table to determine the expression that best represents the number of diagonals of any convex

polygon having n sides.

6 The table below shows the number of line segments that can be drawn between a given number of points.

Which expression can be used to determine the number of line segments that can be drawn between n points?

G.5.B

Use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. This TEK was under G.c.1.A before TEKS Revisions of 2005

2 On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island formed by the intersections of four streets shown below.

What are the measures of the three angles of the garden? F 90°, 65°, 25° H 90°, 60°, 30° G* 90°, 50°, 40° J 130°, 40°, 10°

What is the measure of ∠BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value

38 The figure below shows a conical cup containing water. The water depth can be represented by x, and the area of the water surface can be represented by A. As the water depth changes, the area of the water surface changes, as shown in the table below.

Which equation best represents the relationship between the area of the water surface and the water depth?

37 The table below shows how many triangles are formed when all the diagonals are drawn from one vertex in different regular polygons.

Based on the table, which of the following statements is true? A All the triangles formed in each regular polygon are congruent. B All the triangles formed in each regular polygon are isosceles. C The number of triangles formed in any regular polygon is 2 less than the number of sides in the polygon. D The number of triangles formed in any regular polygon is half the number of sides in the polygon.

Allen ISD 2009

G.5.C Use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations.

8 The first 4 stages of a certain fractal are shown below.

In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain? F 243 G 54 H* 81 J 27

40 Chan drew the following design.

He then used the design to create the pattern below.

What type of transformation did Chan use to create his pattern? F Dilation G Reflection H Rotation J Translation

Allen ISD 2009

G.5.D 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. 20 A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden. F 12 ft G* 17 ft H 21 ft J 24 ft

30 Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet. He sees a cornfield at an angle of depression of 30°.

What is Mr. Ryan’s approximate horizontal distance from the cornfield at this point? F 1200 ft G 3394 ft H* 4157 ft J 4800 ft

12 A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground.

About how high off the ground is the kite? F 110 ft H* 156 ft G 127 ft J 311 ft 19 Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be? A 13.4 in. C 8.5 in. B* 10.4 in. D 5.2 in 46 The lengths of the bases of an isosceles trapezoid are shown below.

If the perimeter of this trapezoid is 32 units, what is its area? F* 44 square units H 88 square units G 110 square units J 55 square units

15 Mr. Schultz has a garden shaped like an equilateral triangle that measures 11 feet on each side. He has placed a watering hose that extends from the faucet located at a vertex to the opposite side, as shown below.

Which is closest to the length of the hose in the garden? A 7.8 ft B* 9.5 ft C 6.4 ft D 5.5 ft

29. A rhombus is shown below.

If the height, h, intersects the base at its midpoint, which of these is closest to the height of the rhombus? A 0.9 inch B 0.7 inch C 1.4 inches D 1.7 inches

Allen ISD 2009

G.10 Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems. The student is expected to: G.10.A Use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane. 27 Figure MNPQ is shown on the coordinate plane.

10 Which pair of the following polygons is congruent?

F Polygon A and Polygon C G Polygon B and Polygon D H Polygon A and Polygon B J* Polygon B and Polygon C

36 Parallelogram WBMP is shown on the grid below.

If WBMP is reflected across the line y = −x and then translated 4 units down to become parallelogram W*B*M*P*, what will be the coordinates of M*? F (−6, −7) G* (6, −1) H (6, 7) J (6, 3)

33 ∆ABC has vertices A (−2, 5), B (−2, 2), and C (−5, 2). If ∆ABC is reflected across the line y = x, which of the following will be the coordinates of A2?

A (−2, −5) B (5, −2) C (2, 5) D (−5, 2)

Allen ISD 2009

Obj. 7 The student will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes. G.6 Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related tow dimensional representations and uses these representations to solve problems.

The student is expected to: G.6.B Use nets to represent [and construct] three-dimensional geometric figures. 1 The net below shows the surface of a 3-dimensional figure.

Which 3-dimensional figure does this net represent?

38 Which of the following is a true statement about the net of the cube shown?

31 Which net best represents the triangular prism shown below?

36 Which of the following nets forms a triangular pyramid?

G.6.C Use orthographic and isometric views of three-dimensional geometric figures to represent [and construct] three-dimensional geometric figures and solve problems. 44 What is the volume of a 3-dimensional object with the dimensions shown in the 3 views below?

F 120 cu ft G* 440 cu ft H 512 cu ft J 960 cu ft

15 Which of the following best represents the front view of the solid shown below?

14 The diagram below shows the top view of a structure built with identical cubes, as well as the number of cubes in each column of the structure.

Which 3-dimensional view best represents the same structure?

50 The front and right-side views of a figure made of identical cubes are shown below.

Which 3-dimensional figure is best represented by the two views above?

Allen ISD 2009

G.7 Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to:

G.7.A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. 58 Which of the following is the correct name for figure ABCD, with vertices A (4, 6), B (8, 7), C (7, 3), and D (3, 2)?

50 A hexagon is graphed on the coordinate grid.

9 Which of the following relationships could not be used to determine the length of DR, as shown below?

A DF + FQ + QR = DR B DQ + QR = DR C* DQ + FR = DR D DF + FR = DR

2 Which point on the number line below is farthest away from

F Point Q G Point R H Point S J Point T

Allen ISD 2009

G.7.B Use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and [special segments of] triangles and other polygons. 6 Which graph best represents a line parallel to the line with the equation y = 3x + 4?

16 Which of the following best describes the graph of the equations below?

2y = 3x + 2 4y = 6x + 1 F The lines have the same y-intercept. G The lines have the same x-intercept. H The lines are perpendicular. J* The lines are parallel. 57 Line q is shown below.

Which equation best represents a line parallel to line q?

15 Rectangle PQRS is shown on the grid below.

Which equation best represents a line that is parallel to

Allen ISD 2009

G.7.C Derive and use formulas involving length, slope, and midpoint. 19 A coordinate grid is placed over a map. City A is located at (−3, 2), and City B is located at (4, 8). If City C is at the midpoint between City A and City B, which is closest to the distance in coordinate units from City A to City C?

56 Rectangle MNPQ has diagonals that intersect at point X.

12 Circle Q has a diameter Point W is located at (3, −2), and point Y is located at (5, −6). Which of the following ordered pairs represents point Q, the center of the circle? F (8, −8) G (4, −4) H (−1.5, 1.5) J (3, −6)

G.9 Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. The student is expected to: G.9.D Analyze the characteristics of polyhedral and other three-dimensional figures and their component parts based on explorations and [concrete] models. 14 How many faces, edges, and vertices does a square pyramid have? F 4 faces, 6 edges, and 4 vertices G 5 faces, 6 edges, and 6 vertices H* 5 faces, 8 edges, and 5 vertices J 6 faces, 12 edges, and 8 vertices

24 Which two 3-dimensional figures have the same number of faces? F* A triangular prism and a square pyramid G A triangular prism and a rectangular prism H A triangular pyramid and a square pyramid J A triangular pyramid and a rectangular prism

10 How many faces, edges, and vertices does the solid shown below have?

46 For a regular pentagonal prism, what is the ratio of the number of vertices to the number of edges? F 2:3 G 3:2 H 3:5 J 5:3

55 How many vertices does the polyhedron below have?

F 3 G 5 H 8 J Not here

Allen ISD 2009

Obj. 8 The student will demonstrate an understanding of the concepts and uses of measurement and similarity.

G.8 Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to:

G.8.A Find areas of regular polygons, circles, and composite figures. 9 Use the ruler on the Mathematics Chart to measure the dimensions of the composite figure to the nearest tenth of a centimeter. Which best represents the approximate area of this composite figure?

A 34.7 cm 2 C* 44.6 cm 2

B 38.8 cm 2 D 54.5 cm 2

43 What is the area of the unshaded part of the rectangle below?

35 The figure below shows a CD in its rectangular storage case.

35 The figure below shows circle P and circle Q. are each 3 units long.

What is the area of the shaded region in terms π? A 36π B 72π C 12π D 78π

G.8.B Find areas of sectors and arc lengths of circles using proportional reasoning.

52 A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.

22 A diagram of a power/volume control knob on a stereo is shown below.

When the stereo is turned on and the knob is turned to a volume level of 5, the knob is rotated 100° from its off position. What is the approximate arc length of the path traveled by the knob’s rotation from the off position to a volume level of 5? F 545 mm H 22 mm G 157 mm J* 44 mm

41 The diagram below represents a sector of a circle.

Which of the following is closest to the length of if the central angle is 75° and the radius of the circle is 36 inches? A 23.6 in. B 47.1 in. C 179.1 in. D 89.5 in.

Allen ISD 2009

(G.8.C) [Derive,] extend, and use the Pythagorean Theorem. 41 The total area of trapezoid FGHJ is 52 square inches.

25 Kim walked diagonally across a rectangular field that measured 100 feet by 240 feet.

51 About how many feet of fencing are needed to enclose a rectangular garden with a 30-foot-long side and a 40-foot-long diagonal? A* 113 ft B 133 ft C 140 ft D 160 ft

16 Triangle XYZ is shown below.

What is the length of

Allen ISD 2009

(G.8.D) Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations. 42 Oatmeal is packaged in a cylindrical container with the dimensions shown in the drawing.

Find the approximate volume of this oatmeal container. F 471 cm3

G 566 cm3

H* 1413 cm3

J 5655 cm3

20 Jackie made a rectangular prism to hold her earrings. The net of the rectangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the rectangular prism to the nearest ¼ inch.

27 Henry built a wooden storage shed in the shape of a rectangular prism for his tools. The figure below shows the dimensions of the storage shed.

If Henry plans to paint only the top, front, left, and right sides of his shed, which is closest to the surface area that will be painted? A* 121 ft2 C 154 ft2

B 181 ft2 D 91 ft2

26 The drawing below shows the net of a rectangular prism. Use the ruler on the Mathematics Chart to measure the dimensions of the net to the nearest tenth of a centimeter.

If the net is folded to form the rectangular prism, which of the following is closest to the prism’s volume? F 17.3 cm3

G 5.8 cm3

H 4.8 cm3

J 10.8 cm3

(G.11) Similarity and the geometry of shape. The student applies to concepts of similarity to justify properties of figures and solve problems. The student is expected to: (G.11.A) Use and extend similarity properties and transformations to explore and justify conjectures about geometric figures. 32 A triangle with vertices (1, 2), (5, 2), and (3, �2) is shown below.

Which triangle below is similar to the figure above?

6 Which set of dimensions corresponds to a rectangular prism similar to the one shown below?

F 2 units by 3 units by 4 units G 4 units by 2 units by 8 units H 2 units by 1 unit by 6 units J* 4 units by 3 units by 6 units

30 The figure below shows a square pyramid with a base length of 32 inches and a slant height of 34 inches.

Which of the following square pyramids is similar to the square pyramid above?

Allen ISD 2009

G.11.B Use rations to solve problems involving similar figures. 39 In El Paso, Texas, the streets named Hercules Avenue, Hondo Pass Drive, and Trans Mountain Road are parallel. They all intersect Dyer Street and U.S. Route 54, as shown on the map below

.

23 A rectangle has a length of 4 feet and a perimeter of 14 feet. What is the perimeter of a similar rectangle with a width of 9 feet? A 36 ft B* 42 ft C 108 ft D 126 ft

51 In the figures below, ∆HKM ∼ ∆RTV, and the area of ∆HKM is equal to 10 square units.

What is the area of ∆RTV? A* 30.625 square units C 21.875 square units B 87.5 square units D 61.25 square units

8 Quadrilateral UVWX is shown below.

If ∆UYX and ⊗VZW are similar, which of the following is closest to the area of ∆VZW? F 61 cm2 G 38 cm2 H 30 cm2 J 9 cm2

G.11.C [Develop,] apply, and justify triangle similarity relationships, such as right triangle ratios, [trigonometric ratios,] and Pythagorean triples using a variety of methods. 13 Use the information in each diagram to find the pair of similar polygons.

Allen ISD 2009

G.11.D (Describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems. 33 A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to ½ their original size, what will be the new volume of the rectangular solid? A* 3 dm3

B 4 dm3

C 6 dm3

D 12 dm3

26 If the surface area of a cube is increased by a factor of 4, what is the change in the length of the sides of the cube?

F* The length is 2 times the original length. G The length is 4 times the original length. H The length is 6 times the original length. J The length is 8 times the original length.

3 Mr. Kelly’s company manufactures a cylindrical soup can that has a diameter of 6 inches and a volume of 226 cubic inches. If the diameter stays the same and the height is doubled, what will happen to the can’s volume? A It will remain the same. B* It will double. C It will triple. D It will quadruple.

53 The rectangle below has a perimeter of 18 feet with a length of 6 feet.

A new rectangle is formed by decreasing the width of the original rectangle by 1 foot and keeping the length the same. How will the perimeter of the new rectangle compare with the perimeter of the original rectangle? A The perimeter of the new rectangle will be 3 feet shorter than the perimeter of the original rectangle. B The perimeter of the new rectangle will be 2 feet shorter than the perimeter of the original rectangle. C The perimeter of the new rectangle will be 1 foot shorter than the perimeter of the original rectangle. D The perimeter of the new rectangle will be foot shorter than the perimeter of the original rectangle.

Obj. 9 The student demonstrates an understanding of percents, proportional relationships, probability, and statistics in application problems. 8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:

8.3 B Estimate and find solutions to application problems involving percents and other proportional relationships, such as similarity and rates. 18 Olivero is choosing between two brands of AAA batteries for his graphing calculator A package of three Brand M batteries costs $5.50, and a package of three Brand P batteries costs $3.85. What percent of the cost of Brand M batteries did Olivero save by buying a package of Brand P batteries? F 17% G* 30% H 43% J 70%

35 wo race cars travel at constant speeds in the same direction around a track. The faster car travels 186 miles per hour and completes 50 laps each time the slower car completes 47.6 laps. Which is a reasonable estimate of the slower driver’s speed?

A Between 180 mph and 185 mph B* Between 175 mph and 180 mph C Between 145 mph and 150 mph D Between 135 mph and 140 mph 38 Amber is making a patchwork quilt using 3 different types of fabric. Each type of fabric is cut into rectangles. The first fabric is cut into pieces measuring 3 inches by 5 inches. The dimensions of the rectangles of the second type of fabric are 125% those of the first type, and the dimensions of the third type of fabric are 125% those of the second. What are the approximate dimensions of the third type of fabric? A 3.75 in. by 6.25 in C 5.50 in. by 7.50 in.. B* 4.69 in. by 7.81 in D 4.25 in. by 6.25 in

42 The energy of a certain particle is 3.86 joules. If this particle loses 0.105 joule of energy every 30 seconds, what will its energy be after 8 minutes? F* 2.18 joules G 1.68 joules H 3.02 joules J 2.29 joules

48 Nisha can solve a set of 5 math problems in 12 minutes. At this rate, how long will it take her to solve 20 sets of 7 math problems? F 58 minutes G 5 hours 16 minutes H 48 minutes J 5 hours 36 minutes

Allen ISD 2009

8.11 Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: 8.11 A Find the probabilities of dependent and independent events.

2 In a high school auditorium, 1 junior and 2 sophomores are seated randomly together in a row. What is the probability that the 2 sophomores are seated next to each other?

14 Jamal has a game with 2 groups of tiles. The first group of 26 tiles is labeled with all the letters of the alphabet. The second group of 10 tiles is numbered 0 through 9. If Jamal draws 1 letter tile and 1 number tile at random, what is the probability that he will draw a letter in his name and an odd number?

32 At an ice-cream shop, customers can order a sundae with 1 type of ice cream, 1 type of sauce, and 1 type of topping. The types of ice cream, sauces, and toppings offered are shown below.

If each type of ice cream, sauce, and topping is equally likely to be selected, what is the probability that a customer will order a sundae with vanilla ice cream, caramel sauce, and walnuts?

8.11 B Use theoretical probabilities and experimental results to make predictions and decisions 26 The student council at Monroe High School is planning a schoolwide trip. A local roller-skating rink will provide a discounted rate if at least 250 of the school’s 2340 students sign up for the trip. The student council surveyed a random sample of students and asked which of the following activities the students would prefer as a school trip.

34 The Hawthorne Mustangs have won 4 games and lost 6 games this season. Based on these results, which is the best prediction of the number of games the Mustangs must play in order to win 6 games? F 8 G 9 H 12 J* 15

57 Francis, Leon, and Shelby are running for president of their school’s student council. A random survey of 60 students was taken to determine whom they planned to vote for in the election. The results are shown in the table below.

Based on the data in the table, which of the following is the best prediction of the number of students who will vote for Leon if 2500 students vote? A 1208 B 292 C 916 D 550

Allen ISD 2009

8.12 Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: 8.12A Select the appropriate measure of central tendency of range to describe a set of data and justify the choice for a particular situation. 8 An automobile dealer is analyzing a frequency table identifying the number of vehicles of each color sold during the last 6 months. Which measure of data describes the most popular color of vehicle sold? F Mean H* Mode G Median J Range

23 Last Friday a used-car dealer had cars for sale for $600, $690, $695, $710, $725, $750, $850, $995, $995, $995, and $1495. Select the most effective measure to use to convince potential customers that the dealer’s prices are very low. A Mean C Mode B* Median D Range

8.12C 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.

5 The manager of a sandwich shop is planning to make a circle graph showing the types of sandwiches sold in one day. The table below summarizes these data.

What central angle should the manager use for the section representing the ham-and-cheese sandwich? A 270° B 75° C* 54° D 15°

53 The manager of the Sherbet Shoppe wants to construct a circle graph showing the popularity of the various sherbet flavors he offers. Here is the tally of the favorite flavors of his first 30 customers on Saturday.

In the circle graph, which proportion can be used to find the number of degrees in the sector for orange sherbet?

1 Ms. Ugalde has an 80-acre farm. • 38 acres are used for planting corn. • 18 acres are used for planting soybeans. • 10 acres are used for planting wheat. The remaining acres are used for planting oats. Which of the following graphs best represents these data?

Allen ISD 2009

8.13 Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to: 8.13 B Recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. 38 In a survey of 80 nutritionists, 8 said they eat tacos. Of the 8 who said they eat tacos, 2 said they eat Brand A tacos. If an advertisement for Brand A tacos states “25% of the nutritionists surveyed eat Brand A tacos,” which conclusion is valid based on the information given? F The ad is accurate because 2 out of 8 nutritionists is 25%. G The ad is accurate because nutritionists are food experts. H* The ad is inaccurate because only 2.5% of the surveyed nutritionists eat Brand A tacos. J The ad is inaccurate because the survey should include people who are not nutritionists.

49 The table below shows the cost of fertilizer, depending on the amount purchased.

Which conclusion can be made based on information in the table? A The cost of 10 pounds of fertilizer would be more than $4.00. B* The cost of 200 pounds of fertilizer would be less than $57.00. C The cost of fertilizer is always more than $0.35 per pound. D The cost of fertilizer is always less than $0.30 per pound.

5 Amanda, Bonnie, Cindy, and Linda competed in a biathlon consisting of running and swimming events. The table below shows the number of seconds each of them took to complete the parts of the competition.

The top rankings are awarded to the individuals with the fastest combined times. Based on the information given in the table, which event probably determined the outcome of the competition? A Running, because the times vary more B* Swimming, because the times vary more C Running, because the times are consistent D Swimming, because the times are consistent

9 A total of 1755 customers at an electronics store were asked to identify which item they planned to purchase in the next month. The table below shows the results of the survey.

According to the information above, which of the following statements is true?

A About of the customers planned to purchase a DVD player.

B About of the customers planned to purchase a television.

C About of the customers planned to purchase a laptop computer.

D More than of the customers planned to purchase either a computer or a DVD player.

Allen ISD 2009

Obj. 10 The student will demonstrate an understanding of the mathematical processes and tools used in problem solving. 8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The

student is expected to: 8.14 A Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical tools. 10 Galván’s Grocery Store sells 3 cans of soup for a total of $0.85. The total cost, c, of purchasing n cans of the soup can be found by — F multiplying n by c G* multiplying n by the cost of 1 can H dividing n by c J dividing c by the cost of 1 can 39 Maria has 4 more movie passes than Toni. Angela has half as

many passes as Maria. The three girls have a total of 21 movie passes. Which equation can be used to find how many movie passes Toni has?

41 Patti works as a waitress. She earns $4.50 per hour plus tips and serves an average of 6 customers per hour. If Patti earned $108 during an 8-hour shift, which amount best represents the average tip per customer? A $4.00 C $3.00 B* $1.50 D $13.50 58 The owners of Crispy Sweet Doughnut Shop want to open a shop centrally located to the police station, the high school, the fire station, and the factory.

Based on the information given, which of the following points best represents the location where the new Crispy Sweet Doughnut Shop should open? F* (9, 12) G (5, 13) H (6, 10) J (8, 13)

21 Kevin saves 20% of his total weekly earnings from his 2 part-time jobs. He earns $5.75 per hour at his first job and $6.55 per hour at his second job. Kevin works 20 hours this week at the first job and 10 hours this week at the second job. What is the amount that he will save this week? A $36.10 B $37.70 C $36.90 D $34.50 27 Michelle’s cellular-phone company offers a plan that allows 300 minutes of use for $29.95 per month and charges $0.19 for each additional minute. All prices include tax and fees. Michelle has budgeted $50 per month for calls on her cellular phone. What is the maximum number of minutes that she can use her cellular phone each month without spending more than $50? A 405 min B 105 min C 406 min D 106 min

Allen ISD 2009

8.14 B use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 17 As a waiter in a restaurant, Steven works 6-hour shifts. He earns $5 per hour and keeps 80% of his tip money. How much tip money does he need to receive per shift to earn a total of exactly $50 before taxes are deducted? A $16 B $20 C* $25 D $40

22 A wooden pole was broken during a windstorm. Before it broke, the total height of the pole above the ground was 25 feet. After it broke, the top of the pole touched the ground 15 feet from the base.

How tall was the part of the pole that was left standing? F* 8 ft G 10 ft H 17 ft J 20 ft

29 For each grading period Mr. Brown gives his students one project and two tests. The project counts as 20% of the students’ final grade, and the mean of the 2 test scores counts as the rest of their grade. In Mr. Brown’s class Anthony earned a grade of 87 on his first test and a grade of 96 on his second test. Which of the following is a reasonable minimum grade Anthony must score on his project in order to have a final grade of at least 90? A 66 C 87 B* 84 D 92 47 Four square pieces are cut from the corners of a square sheet of metal. As the size of the small squares increases, the remaining area decreases, as shown below.

If this pattern continues, what will be the difference between the first square’s shaded area and the fifth square’s shaded area? A 4 square units C 49 square units B 24 square units D* 96 square units

34 Carl was asked to solve the problem shown in the box below.

F Add the dimensions given in feet G Multiply each dimension given in feet by 2 inches H Convert 2 inches into 24 feet J Convert the dimensions of the box from feet to inches

Allen ISD 2009

8.14 C Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

7 On Friday Daniel wrote a check for $158. The following Monday he deposited $60 into his bank account. On Wednesday the bank informed him that he had overdrawn his account by $8. If Daniel made no other transactions between Friday and Wednesday, what was his balance before he wrote the check on Friday? A* $90 B $98 C $106 D $210

9 How many 2-inch cubes can be placed completely inside a box that is 8 inches long, 2 inches wide, and 6 inches tall? A 8 B* 12 C 24 D 48 28 Marsha brought cookies to school. She gave a third of her cookies to Ana. Ana then gave a fourth of her cookies to Cybil. Cybil gave half of her cookies to Betsy. If Betsy has 2 cookies, how many cookies did Marsha have in the beginning? F 18 G 24 H 36 J* 48

17 A biologist noticed that the population of ladybugs in a sample doubled every 3 days. If the initial population sample was 30 ladybugs, what was the population of ladybugs at the end of 9 days? A 90 B 270 C 120 D* 240

19 Wesley and Delia are playing a math game. Wesley gives Delia these steps to follow. Step 1 Multiply a number by 6 and then subtract 4. Step 2 Divide the result by 2. Step 3 Add 3 to the result from the second step. If Delia’s final answer is 19, what was the original number? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

38 In Figure 1 a cylinder with a diameter of 12 centimeters is filled with water to a height of 8 centimeters.

In Figure 2 a rock is submerged in the cylinder.

Which of the following is closest to the volume of the rock? F 139 cm3 G 418 cm 3 H 1674 cm3 J 1323 cm3

Allen ISD 2009

44 Look at the solid sphere and the cylinder containing water shown in Figure 1.

F 13 cm G 17 cm H 15 cm J 11 cm 50 Four friends took turns using the stationary bike at a health club. Huan used it three times as long as Melanie. Susie used it half as long as David, and David used it 15 minutes longer than Huan. The four friends used the stationary bike for a total of 2.5 hours. How long did Susie use the stationary bike? F 60 min G 45 min H* 30 min J 15 min

42 Dominique created a pattern using right triangles. She started the pattern with an isosceles right triangle, with each leg measuring 1 unit. The hypotenuse of each successive triangle follows a pattern, as shown in the diagram below.

If Dominique continues this pattern 5 more times, which of the following would be the measure of the final hypotenuse?

Allen ISD 2009

8.15 Underlying processes and mathematical tools. The student communicates about Grade8 mathematics through informal and mathematical language, representations, and models. The student is expected to: 8.15 A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 12 Allison has a cylindrical candle mold with the dimensions shown below.

If Allison has a rectangular block of wax that measures 12 centimeters by 10 centimeters by 20 centimeters, about how many candles can she make after melting the block of wax? F* 31 G 35 H 69 J 76 22 Which of these equations describes a relationship in which every real number x corresponds to a nonnegative real number? F y = x G* y = x2 H y = x 3 J y = −x

31 Jaime purchased a used car on sale for $3450. The original price of the used car was $4100. Which expression can be used to determine the percent of the original price that Jaime saved on the purchase of this car?

30 As part of a classroom assignment, Kimberly was given this geoboard to model the slope of 2/3.

32 Chase wanted to find 3 consecutive whole numbers that add up to 81. He wrote the equation (n − 1) + n + (n + 1) = 81. What does the variable n represent in the equation? F The least of the 3 whole numbers G* The middle of the 3 whole numbers H The greatest of the 3 whole numbers J The difference between the least and greatest of the 3 whole numbers

30 The spreadsheet below contains 20 cells. A cell in a spreadsheet can be identified first by the column letter and then by the row number. For example, the number 10 is found in Cell C4.

If the number in Cell A3 = B4 − 3(E2 + D4), which of the following must be the number in Cell E2? F −21 G −15 H −4 J* −12

55. Jalen needs to earn an average of $120 a week from his part-time job by the end of his 4th week. His first 3 weekly paychecks were for $95, $145, and $130. Which equation can Jalen use to find how much he must earn in the 4th week in order to meet his goal?

Allen ISD 2009

8.16 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. 8.16 A make conjectures from patterns or sets of examples and nonexamples 55 The graph shows the price of a share of Compuco stock at the close of each day during a 1-week period.

Based on the data in the graph, which conclusion is most accurate? A The closing price remained constant throughout the week. B The closing price increased at the beginning of the week and then leveled off at the end of the week. C* The closing price decreased at the beginning of the week and then increased at the end of the week. D The closing price each day was lower than the closing price on the previous day.

33 A leap year occurs when the number of a year is a multiple of 4. However, year numbers that are multiples of 100 are not leap years unless they are multiples of 400. Which is not an example of a leap year? A 2440 B 2400 C 2340 D* 2300 36 For a sports banquet Coach Mackey must use the rectangular tables in the school cafeteria. The diagram below shows the seating arrangements that Coach Mackey can use at 1 and 2 tables.

Which expression can be used to determine the number of people who can sit as a group if y tables are joined to form 1 long table? F 6y G 4(y + 1) H 3(y + 1) J* 2(2y + 1) 58 A pizza parlor surveyed 100 customers to determine their favorite pizza topping or combination of toppings. The results are shown below.

How many of the customers surveyed picked a combination of only 2 toppings as their favorite? F 5 G 7 H* 14 J 19

17 Each square design below is made up of rectangles of equal size. Each rectangle is twice as long as it is wide.

Within the same design, which of the following is possible? A A square with a side length of 68 made up of 36 rectangles B A square with a side length of 80 made up of 40 rectangles C A square with a side length of 76 made up of 32 rectangles D A square with a side length of 52 made up of 24 rectangles

Allen ISD 2009

8.16 B Validate his/her conclusions using mathematical properties and relationships. 52 Lisa has a circular piece of cardboard with a 10-inch diameter. She wants to cut a 10-inchby- 2-inch rectangle from the circle. She also wants to cut 10 square pieces that are 1 inch on each side. Which information makes this scenario impossible? F There will be no cardboard left after the rectangle has been cut. G* A 10-inch-long rectangle cannot be cut from the circular cardboard. H Squares cannot be cut from the circle. J There will not be enough cardboard to cut all the 1-inch-square pieces indicated.

18 Given: Two angles are supplementary. The measure of one angle is 20° more than the measure of the other angle. Conclusion: The measures of the angles are 70° and 90°. This conclusion — F* is contradicted by the first statement given G is verified by the first statement given H invalidates itself because a 90° angle cannot be supplementary to another J verifies itself because 90° is 20° more than 70°

24 If r + s = t and x = y, which of the following must be true? F r + s − x = y − t G r + s − t = x + y H r + s + t = x − y J* r + s + x = t + y

49 For any negative integers m, n, p, and q, which of the following is always true if mn < pq? A q > m B −mn > −pq C −n < −p D nq < mp