11 th Grade TAKS - Released Tests - by Objective

11th Grade TAKS - Released Tests - by Objective

Objective1 Functional relationships

2 Properties and attributes of functions

3 Linear functions

4 Linear equations and inequalities

5 Quadratic and other nonlinear functions

6 Geometric relationships and spatial reasoning

7 Two- and three-dimensional representations of geometric relationships and shapes

8 Concepts and uses of measurement and similarity

9 Percents, proportional relationships, probability, and statistics in application problems

10 Mathematical processes and tools used in problem solving

Objective 1:The student will describe

functional relationships in a variety of ways.

A(b)(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) The student describes independent and dependent quantities in functional relationships.

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

Correct Answer - B April 2006 #13

The volume of a sphere can be found by using the function V = πr3, where V represents the volume and r represents the radius. What is the dependent quantity in this function?

Correct Answer - B Fall 2005 #35

A π

B V

C r

D4

3

4

3

A community-service organization is selling $10 tickets to a fund-raiser for the local children’s hospital. The money raised from ticket sales will be donated to the children’s hospital. Which best describes the dependent quantity in this situation?

F The number of tickets sold is dependent on the amount of the donation.

G The price of each ticket is dependent on the number of tickets sold.

H The amount of the donation is dependent on the number of tickets sold.

J The price of each ticket is dependent on the amount of the donation.

Correct Answer - H October 2005 #36

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.



(B) The student [gathers and records data, or] uses data sets, to determine functional (systematic) relationships between quantities.

The table below shows the relationship between x and y. Which function best represents the relationship between the quantities in the table?

F y = 2x + 1

G y = 2x3 + 1

H y = 2x2 – 3

J y = 2x2 + 4x + 1

Correct Answer - G July 2006 #56

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

Correct Answer - J April 2006 #40

Which of the following sets does not represent a function?

F {(-1, -1), (1, 1), (2, 2), (3, 3), (4, 4)}

G {(-1, 0), (0, 2), (1, 4), (2, 6), (3, 8)}

H {(-1, 2), (1, 1), (1, -1), (2, 1), (4, 2)}

J {(-2, 4), (-1, 1), (1, 1), (2, 4), (3, 9)}

Correct Answer - H February 2006 #44

Which of the following equations best represents the relationship in the set of data shown below?

Correct Answer - D February 2006 #57

The table below shows h, the approximate height of an Ameri-Willow tree after t years. Which equation best fits these data?

F h = 8.2 + 3.75t G h = 1.12 + 7.82t

H h = 7.5 + 0.65t2 J h = -1.24 + 9.75t

Correct Answer - G Fall 2005 #10

Which of the following graphs does not represent y as a function of x?

Correct Answer - C October 2005 #19

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

A y = 3x

B x = 3y

C x = 3y2

D y = 3x2

Correct Answer - D April 2004 #31

A consumer group measured an automobile’s acceleration by using the data shown below. Which equation best represents the relationship between d, the automobile’s distance from the starting line, and t, the time?

A d = 10.5t2

B d = 10.5t3

C d = 5.25t

D d = 5.25t2

Correct Answer - D July 2004 #13

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.

F x = 0.35y

G y = 0.35x

H x = 2.86y

J y = 2.86x

Correct Answer - G Spring 2003 #28

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

Correct Answer - D Spring 2003 #45


(C) The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations.

The initial pressure inside a closed container is 200 pounds per square inch (psi). As the temperature inside the container increases, the pressure increases. If the pressure increases 7.5 psi for each degree Fahrenheit of increased temperature, which equation best represents p, the pressure inside the container after the temperature has increased t degrees?F p = 7.5t

G p = 200 + 7.5t

H p = 200t + 7.5

J p = 200t + 7.5tCorrect Answer - G July 2006 #14

Mitesh is m years old, and his brother Hiren is h years old. Which statement best describes the inequality m ≥ h + 3?

A Mitesh is at least 3 times as old as Hiren.

B Mitesh is at least 3 years older than Hiren.

C Hiren is more than 3 years older than Mitesh.

D Hiren is more than 3 times as old as Mitesh.

Correct Answer - B July 2006 #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

Correct Answer - A April 2006 #37

The wheels on Lee’s bike each have a circumference of approximately 7 feet. Which of the following equations could be used to determine y, the total distance traveled in feet for each wheel as a function of x, the number of wheel revolutions?

Correct Answer - H

February 2006 #48

The runners on a cross-country team need to buy bottles of water for their next meet. Each runner will buy at least four bottles, and the coach will buy six extra bottles. Which inequality best describes the total number of bottles, b, the runners and coach will buy in terms of n, the number of runners on the team?

A b < 4n + 6

B b ≥ 6n + 4

C b ≥ 4n + 6

D b < 6n + 4

Correct Answer - C Fall 2005 #19

Luxury Limousine charges a fee of $50 per hour to rent a limousine plus $0.15 per mile driven. Which equation can be used to determine c, the total cost to rent a limousine for 3 hours, if m represents the number of miles the limousine is driven?

A c = 50 + 0.15m

B c = 50 + 0.45m

C c = 150 + 0.45m

D c = 150 + 0.15m

Correct Answer - D October 2005 #49

An artist studies human proportions in order to make realistic drawings. He observes that a person’s kneeling height, y, is ¾ of the person’s standing height, x. Which equation best represents this relationship?

A y = ¾x

B y = -¾x

C y = x – ¾

D y = x + ¾


At the beginning of the school year, teachers had 240,000 sheets of copier paper to use. If about 2000 sheets of paper are used each day during a school year, which equation best describes s, the number of sheets that are left after d days of school?

A s = 240,000 – 2000d

B s = 240,000 + 2000d

C s = 240,000d – 2000d

D s = 240,000d + 2000d

Correct Answer - A July 2004 #1

The Texas Pecan Company ships pecans in wooden boxes. An empty wooden box has a mass of 2.5 kilograms. The pecans have an average mass of 0.015 kilograms each. Which equation expresses m, the total mass of a box of pecans, in terms of p, the number of pecans in the box?

F m = 0.015p + 2.5

G m = 0.015p – 2.5

H m = 0.015 – 2.5p

J m = 0.015 + 2.5p

Correct Answer - F July 2004 #46

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

Correct Answer - B Spring 2003 #11


(D) The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

Which quadratic equation best represents the parabola shown below?

A y = x2 + x + 5

B y = x2 + 5

C y = -x2 + 5

D y = -x2 + x + 5

Correct Answer - C July 2006 #17

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

Correct Answer - G April 2006 #54

Which equation best represents the graph below?

Correct Answer - F February 2006 #40

Which graph best represents the equation y = 2x2 + 1?

Correct Answer - D Fall 2005 #57

Which inequality does the graph shown below best represent?

Correct Answer - B October 2005 #9

Which graph best represents the inequality x + 2y ≤ –14?

Correct Answer - H April 2004 #20

The graph is the solution for which inequality?


Which graph best represents all the pairs of numbers (x, y) such that x + y < –6?



(E) The student interprets and makes inferences from functional relationships.

The graph below shows the number of light bulbs in thousands that the Electric Lightbulb Company sold from 1998 to 2001. If the trend shown on the graph continues, in what year can the Electric Lightbulb Company first expect to sell more than 1.3 million light bulbs?

A 2010

B 2008

C 2009

D 2011

July 2006 #25

Correct Answer

C

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?

A 70.1 million

B 68.5 million

C 74.8 million

D 78.0 million

Correct Answer - C April 2006 #59

The total cost, c, of leasing a car can be expressed by the equation c = 1800 + 185m, where m is the number of months the car is leased. Which statement is true based on the information given?

F The car must be leased for at least 60 months.G The total cost of leasing this car for 1 year is

more than $4000.H The total cost of leasing this car for 2 years is

$4020.J The cost of leasing this car is greater than the

cost of buying one.

Correct Answer - G February 2006 #12

The payroll clerk at an appliance store calculates each salesclerk’s weekly salary using the function f(x) = 75 + 0.10x, where x is each salesclerk’s total weekly sales. The best interpretation of this situation is that each salesclerk is paid –F $75 plus a 10% commission on the total weekly

sales of all the salesclerks

G $75 plus a 10% commission on his or her weekly sales

H $75 plus a 10% commission on the total weekly profit for the store

J the same amount regardless of his or her total weekly sales


The owner of a candle store purchases his candles from a local distributor. The graph below shows the relationship between n, the number of candles ordered, and c, the total cost of the candle order. Which conclusion can be drawn about this relationship?

A An order of 50 candles will cost less than $20.

B An order of 100 candles will cost more than $60.

C An order of 150 candles will cost less than $70.

D An order of 200 candles will cost more than $90.Correct Answer - D October 2005 #11

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?


The net profit, p, that a company makes from the production of widgets is represented by the equation p = 2.5n – 25,000, where n is the number of widgets the company sells. Which is the best interpretation of this information?

A The company has made a profit of $25,000.

B The company needs to sell more than 10,000 widgets before it makes a profit.

C The company’s profit needs to be more than $25,000.

D The company has sold more than 10,000 of its widgets.


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? Correct Answer - A Spring 2003 #59

Objective 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.

(A) The student identifies [and sketches] the general forms of linear (y = x) and quadratic (y = x2) parent functions.

Which equation is the parent function of a quadratic equation?


A y = √x

B y = x

C y = │x│

D y = x2

The graph below represents which type of parent function?

F Exponential

G Absolute value

H Linear

J Quadratic

Correct Answer - H July 2006 #36

Which of the following does not describe the graph of the parent function of a quadratic equation?

A The graph that has its vertex at the origin.

B The graph is a parabola that opens upward.

C The graph has the x-axis as its line of symmetry.

D The graph has a minimum value at (0, 0).


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


F y = | x |

G y = x

H y = x2

J y = √x

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

A Exponential

B Absolute value

C Linear

D Quadratic



(B) For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Mr. Maxwell asked his students to identify the domain represented by the function graphed below. Which of the following student responses is correct?

F -5 ≤ x < 6

G -6 ≤ x ≤ 2

H -5 ≤ x ≤ -2

J Not here

Correct Answer - F April 2006 #12

The graph of the function y = √25 – x is shown on the coordinate grid below. What is the domain of the function?

F x ≤ 5

G x ≥ -5

H -5 ≤ x ≤ 5

J 0 ≤ x ≤ 5


Which inequality best represents the domain of the function shown on the graph?

F -3 ≤ x ≤ 6

G -3 < x < 6

H -1 < x < 5

J -1 ≤ x ≤ 5

Correct Answer - G October 2005 #30

What is the domain of the function shown on the graph?

A -3 ≤ x ≤ 3

B -3 < x < 3

C -5 < x ≤ 4

D -5 ≤ x < 4


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

A y ≤ 3

B y ≤ 2

C y ≥ 3

D y ≥ 2



(C) The student interprets situations in terms of given graphs [or creates situations that fit given graphs].

The graph below shows the relationship between temperature and the density of water. Which of the following statements best describes this relationship?F The density of water increases as temperature increases between 4°C and 10°C.

G The density of water decreases as temperature increases between 0°C and 4°C.

H The density of water decreases as temperature increases between 4°C and 10°C.

J The density of water remains constant as temperature increases. Correct Answer - H July 2006 #8

The water level in a creek was at a maximum height after a heavy rain. The water level in the creek receded at a constant rate for several hours until it leveled off to its regular height. Which of the following graphs best represents this information?


Lisa stayed to talk to her friends for about 5 minutes after school. Then she started to walk home. Halfway home she realized that she had forgotten her math book, so she ran back to school in half the time that she had already spent walking. Lisa took about 2 minutes to get her book and then walked home. She got home approximately 35 minutes after school was over. Which graph best represents this scenario?

Correct Answer

J

October 2005 #34

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 the 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


Amy is choosing between two local Internet providers, Simple.com and Call.com. The graph shows the relationship between the total cost per month of each Internet provider and the hours spent on-line. According to the graph, which of these statements is true?

F Simple.com would cost less than Call.com if Amy used the Internet more than 5 hours a month.

G Call.com would cost less than Simple.com if Amy used the Internet less than 5 hours a month.

H Simple.com would cost less than Call.com if Amy used the Internet for exactly 5 hours a month.

J Call.com would cost less than Simple.com if Amy used the Internet more than 5 hours a month.

Correct Answer - J July 2004 #32

At the Dallas-Forth Worth International Airport, a DC-10, at 4500 feet, is descending toward the east runway at 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?

Correct Answer

A

Spring 2003 #37


(D) In solving problems, the student [collects and] organizes data, [makes and] interprets scatterplots, and models, predicts, and makes decisions and critical judgments.

In a recent survey conducted at a mall, 18 people between the ages of 10 and 35 were asked how many sit-ups they do for exercise on a weekly basis. What is the relationship between a person’s age and the number of sit-ups done on a weekly basis?F The younger a person is, the moresit-ups the person does weekly.

G The older a person is, the moresit-ups the person does weekly.

H There is a constant correlationbetween the age of a personand the number of sit-ups done weekly.

J There is no correlation betweena person’s age and the numberof sit-ups done weekly.

Correct Answer - J Fall 2005 #48

The energy output from a chemical reaction is dependent on the amount of chemicals used. The table shows this relationship. What is a reasonable amount of energy output from the reaction of 32 moles of the chemical?

F 77 joules

G 92 joules

H 110 joules

J 128 joules

Correct Answer - J Spring 2003 #60

A(b)(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.

(A) The student uses symbols to represent unknowns and variables.

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)


Brian was 1 out of 25 students who took a practice college entrance exam. No two students scored the same on the exam. If x represents the number of students who scored higher than Brian, which expression represents the number of students who scored lower than Brian?

F 24 – x

G x – 24

H 25 – x

J x – 25


A physicist determines the kinetic energy of a moving particle by multiplying one-half the particle’s mass, m, by the square of the particle’s velocity, v. The kinetic energy is best represented by –

Correct Answer - A February 2006 #53

An appliance store put one kind of refrigerator and one kind of freezer on sale. The total sales of these two appliances were $8000. The refrigerator was on sale for $750, and the freezer was on sale for $325. If f represents the number of freezers sold, which expression can be used to determine the number of refrigerators sold during this sale?

Correct Answer - A

Fall 2005 #33

A certain fan operates at a rate of 30 rotations per second at high speed. When the fan is turned off, the rate of rotation decreases at a constant rate of 6 rotations per second. If t represents the time in seconds after the fan has been turned off, which expression can be used to determine the number of seconds for the fan to come to a complete stop?


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 t2 + a

B at2

C t + a

D at


The land area of Texas is about 50,000 square miles smaller than twice the land area of California. It x represents the land area of California, which expression can be used to determine the land area of Texas?


A(b)(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.

(B) Given situations, the student looks for patterns and represents generalizations algebraically.

The blocks below are arranged in sequence to show a pattern. Which expression can be used to determine the number of blocks at Stage n?

Correct Answer - J February 2006 #28

F √n

G (n – 1) + 1

H 2n

J n2

Below are congruent isosceles triangles arranged in a sequence to obtain a geometric pattern. Which expression can be used to find the perimeter of a composite figure made up of t triangles arranged in this pattern?

F 12t

G 2t + 10

H 5t + 2

J 12t – 5

Correct Answer - G

Fall 2005 #56

The figures below show a pattern of dark tiles and white tiles that can be described by a relationship between 2 variables. Which rule related d, the number of dark tiles, to w, the number of white tiles?

F d = 2w H d = 2w – 2

G w = d – 1 J w = ½d + 1


A(b)(4) 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.

(A) The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations.

The graph below shows the amount of force needed to stretch a certain spring to various distances. Which of the following best represents the difference between the amount of force in pounds needed to stretch the spring to 10 inches and the amount needed to stretch it to 4 inches?

F 6

G 14

H 30

J 70

Correct Answer

HApril 2006 #48

A function is described by the equation y = 2x2 – 5x – 3, in which y is dependent on x. If a value for the independent variable is selected from the set {-4, -1, 0, 2, 5}, which of the following is a corresponding dependent value?

A 9

B -6

C -5

D 0


Which of the following is equivalent to2x – 3y ≥ 9?


Look at the two polynomials modeled below using algebra tiles. Which expression describes the sum of the two polynomials in terms of x?

F 3x2 + 12x – 10

G 3x4 + 12x2 – 2

H 3x2 + 12x + 2

J 2x4 + 35x2 – 24

Correct Answer - H Fall 2005 #58

If (-3.5, y) is a solution to the equation 2x – 5y = 10, what is the value of y?

F -3.4

G 13.75

H -0.6

J -3.75

Correct Answer - F October 2005 #28

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.

Correct Answer - 4 Spring 2003 #21

A(b)(4) 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.

(B) The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.

Simplify the polynomial below.

–3x(7x – 4) + 6x – (13 – 24x2)

F 3x2 + 18x – 13

G -24x2 – 15x – 17

H -24x2 + 10x – 17

J 3x2 + 18x + 13


Simplify the algebraic expression

F 5a2b – 2ab2

G 31a2b – 28ab2

H a2b + 3ab2

J 15a2b + 18ab2


Which expression is equivalent to⅔(3x – 15y) + (9y – 11x)?

A -9x – y

B 11x – 21y

C 10x – 4y

D -9x – 26y


Simplify the algebraic expression5(x – 2) + 2(3x2 – 12x + 12).

A -x + 10

B -13x + 14

C 6x2 – 7x + 10

D 6x2 – 19x + 14


Which expression is equivalent to(5n – 2)3n – (5n – 2)(n – 1)?

A n – 1

B 3n2 – 3n

C 10n2 – 13n + 2

D 10n2 + n – 2


Objective 3:The student will demonstrate an

understanding of linear functions.

A(c)(1) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(A) The student determines whether or not given situations can be represented by linear functions.

Chanté bought a package of 36 tickets for carnival rides. Each ride requires 4 tickets per person. Which linear function, if any, represents the relationship between x, the number of carnival rides Chanté went on, and y, the number of tickets remaining?

February 2006 #46

F y = 4x – 36

G y = 4(x – 36)

H y = 36 – 4x

J No linear function exists.

Correct Answer - H

Identify the situation that best represents the amount f(n) in the function f(n) = 75 + 80n.

Fall 2005 #2

F Alton paid $75 each for n gifts and spent $80 on himself.

G Bonita spent $75 on registration fees and $80 each for n credit hours last summer.

H Carlton deposited $75 per month for n months and an extra $80 in the summer.

J Dylan worked for 75 hours at n dollars per hour and earned $80 in tips.

Correct Answer - G

A(c)(1) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(C) The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions.

Which table identifies points on the line defined by the equation y – 5x = –9?

February 2006 #3Correct Answer - C

Which equation best represents the line on the graph?

July 2004 #40

F 3x – 2y = -4

G 3x + 2y = -6

H 3x – 2y = 6

J 2x – 3y = -6

Correct Answer - H

The algebraic form of a linear function is , where d is the distance in miles

and l is the number of laps.Which of the following choices identifies the same linear function?

Spring 2003 #16Correct Answer - F

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.

A(c)(2) Linear functions. The student understands the meaning of the slope and intercepts of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

(A) The student develops the concepts of slope as rate of change and determines slopes from graphs, tables, and algebraic representations.

What is the rate of change of the function y = -7?

April 2006 #52

F 7

G -7

H 0

J Undefined

Correct Answer - H

What is the apparent slope of the line graphed below?

July 2006 #15Correct Answer - D

What is the slope of the function –6x – 2y = 8?

February 2006 #52

F ⅓

G -3

H -4

J 3

Correct Answer - G

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

April 2004 #13Correct Answer - D

Find the slope of the line identified by the equation 4x + 5y = 20.

July 2004 #26

F 4

G 5/4

H -4/5

J -4

Correct Answer - H

What is the slope of the line identified by 2y = -3(x – 2)?

Spring 2003 #57

A -3

B -3/2

C 2/3

D 2

Correct Answer - B


(B) The student interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.

The graph below shows the number of pies and the number of cakes that the students in the art club need to sell at the school bake sale in order to raise $150. Which of the following represents the maximum number of cakes the art club could sell to raise exactly $150?

July 2006 #58

F 40

G 25

H 50

J 30

Correct Answer - J

The graph below shows the number of caramel apples and the number of popcorn balls that the students in the math club need to sell at their bake sale to raise $200. Which of the following numbers represents the maximum number of caramel-apple sales needed to raise exactly $200.

October 2005 #53

A 50

B 40

C 25

D 20

Correct Answer

B

What are the slope and y-intercept of a line that contains the point (5, -1) and has same y-intercept as x – 3y = 6?

Spring 2003 #43Correct Answer - C


(C) The student investigates, describes, and predicts the effects of changes in m and b on the graph of y = mx + b.

The graph of a linear function is shown below. If the line is translated 2 units down, which equation will best describe the new line?

April 2006 #26Correct Answer - G

If the slope of the equation is changed to and the y-intercept is changed to (0, -4), which statement best describes this situation?

July 2006 #33

A The new line is perpendicular to the original line.

B The new line is parallel to the original line.

C The new line and the original line have the same y-intercept.

D The new line and the original line have the same x-intercept.

Correct Answer - D

How does the graph of y = 3x + 2 compare to the graph of y = 4x + 2?

Fall 2005 #18

F The slope of y = 3x + 2 is less steep.G The slope of y = 3x + 2

is steeper.H The graph of y = 3x + 2

has a greater y-intercept.J The graph of y = 3x + 2

has a smaller y-intercept.

Correct Answer - F

If the slope of the function y = -3.5x + 12.8 is changed to 1.5, which of the following best describes the graph of the new function?

October 2005 #31

A The graph of the new function intercepts the y-axis at the same point as the original function.

B The graph of the new function intercepts the x-axis at the same point as the original function.

C The graph of the new function has a negative slope.

D The graph of the new function has a positive x-intercept.

Correct Answer - A

The graph of a line is shown below. If the slope of this line is multiplied by -1 and the y-intercept decreases by 2 units, which linear equation represents these changes?

April 2004 #17

A y = -2x + 1

B y = -x + 1

C y = -x – 1

D y = -½x – 1

Correct Answer - A

The line represented by the equation y = (3/2)x + 3 is graphed below. Which of the following best describes the effect on the graph when the slope is doubled?

July 2004 #43

A The y-intercept increases.

B The y-intercept decreases.

C The x-intercept increases.

D The x-intercept decreases.

Correct Answer - C

Given the function y = 3.54x – 54.68, which statement best describes the effect of increasing the y-intercept by 33.14?

Spring 2003 #29

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.

Correct Answer - A


(D) The student graphs and writes equations of lines given characteristics, such as two points, a point and a slope, or a slope and y-intercept.

Which graph best represents the line that has a slope of -5/6 and contains the point (4, -3)?

April 2006 #4Correct Answer - J

Which equation describes the line passing through the points (3, 0) and (0, 4)?

February 2006 #26

F y = 3x + 4

G x = 4y + 3

H 3x + 4y = 12

J 4x + 3y = 12

Correct Answer - J

Which graph best represents the line that has intercepts at (5, 0) and (0, -4)?

Fall 2005 #5Correct Answer - B

What is the equation of the line that passes through the points (-4, 1) and (4, -6)?

October 2005 #24Correct Answer - F

Which equation represents the line that passes through the points (-1, 4) and (3, 2)?

April 2004 #44Correct Answer - F

Which function represents the line that contains the point (2, 12) and has a slope of -3?

July 2004 #42

F f(x) = -3x + 6

G f(x) = -3x + 18

H f(x) = -3x + 34

J f(x) = -3x + 38

Correct Answer - G


(E) The student determines the intercepts of linear functions from graphs, tables, and algebraic representations.

Find the x- and y-intercepts of -4x + 7y = -28.

April 2006 #49

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)

Correct Answer - B

What are the coordinates of the x-intercept of the function graphed below?

July 2006 #20

F (4, 0)

G (-3, 0)

H (0, 4)

J (0, -3)

Correct Answer - F

What is the y-intercept of the linear function described by the data below?

Fall 2005 #20

F (0, 1)

G (1.25, 0)

H (0, -1)

J (0, -1.25)

Correct Answer - F

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

April 2004 #8

F (-2, 0)

G (0, -8/3)

H (2/3, 0)

J (4, 0)

Correct Answer - J

What are the coordinates of the y-intercept of the line represented by the equation 4x + 2y = 10?

July 2004 #3

A (0, 2)

B (0, 5/2)

C (0, 5)

D (0, 10)

Correct Answer - C

What is the y-intercept of the function graphed below?

Spring 2003 #53

A -24

B -21

C -18

D -9

Correct Answer - C


(F) The student interprets and predicts the effects of changing slope and y-intercept in applied situations.

Kirk repairs computers. He charges an hourly rate plus a base fee for his services. The table below shows the relationship between h, the number of hours of labor, and c, the total cost for Kirk’s services. If Kirk decides to keep his base fee the same but increase his hourly rate by $2, what will be the total cost for 8 hours of work?

Fall 2005 #27October 2005 #37

A $112

B $141

C $143

D $157

Correct Answer - D


(G) The student relates direct variation to linear functions and solves problems involving proportional change.

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

April 2006 #28Correct Answer - H

If y varies directly with x and y is 14 when x is 6, which of the following represents this situation?

July 2006 #42Correct Answer - G

If y varies directly with x and y is 42 when x is 4, what is the constant of variation expressed in decimal form?


February 2006 #21Correct Answer – 10.5

At Vicky’s Grocery Store the cost of a bag of ice varies directly with the weight of the ice. If a 7-pound bag of ice costs $0.86, which of the following best represents the cost of a 20-pound bag of ice?

October 2005 #60

F $1.63

G $2.86

H $3.01

J $2.46

Correct Answer - J

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?

April 2004 #45

A 250 m

B 175 m

C 150 m

D 278 m

Correct Answer - D

Objective 4:

The student will formulate and use linear equations and inequalities.

A(c)(3) Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A) The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems.

A salesclerk earns $250 per week plus a commission of 1/5 of her total sales. If her sales total x dollars, which equation can be used to determine her total weekly earnings?


An oyster provides approximately 17 calories, and a shrimp provides approximately 26 calories. Jay wants to consume no more than 300 calories eating oysters and shrimp. Which inequality best represents the number of oysters, x, and the number of shrimp, y, that Jay can eat and stay within this limit?

F (17 + 26)(x + y) > 300

G (17 + x) + (26 + y) > 300

H (17 + 26)(x + y) ≤ 300

J 17x + 26y ≤ 300


The table below shows the relationship between I, the current in milliamperes (mA) through a filament, and t, the filament’s temperature in degrees Celsius. Which equation best represents the relationship between the quantities in the table?


William completed x math homework problems after eating dinner. Had he completed 6 more math problems, William would have finished ⅔ of his math homework. If y represents the total number of math homework problems, which equation best represents the relationship between x and y?

A x + 6 = ⅔y

B x = ⅔y + 6

C x = ⅔(y + 6)

D ⅔x + 6 = y

Correct Answer - A October 2005 #29

Andy drove y miles to work in 0.5 hour. He drove an average of 60 miles per hour on the freeway and an average of 30 miles per hour the rest of the way. If x is the number of hours Andy drove on the freeway, which equation can be used to find y?

A 30x + 60(0.5 – x) = y

B 60x + 30(0.5 – x) = y

C 30x + 60(x – 0.5) = y

D 60x + 30(x – 0.5) = y


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

Correct Answer - H Spring 2003 #56


(B) The student investigates methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities.

The equation F = C + 32 represents the relationship between F, the temperature in degrees Fahrenheit, and C, the temperature in degrees Celsius. If the temperature is 104°F, what is the temperature in degrees Celsius?


Correct Answer - 40 April 2006 #21

If (5⅓, y) is a solution to the equation 5x – 4y – 20 = 0, what is the value of y?


Use the grid to graph y ≥ ¾x – 2. Which coordinate point represents a solution of this inequality?

A (4, 0)

B (-3, -5)

C (7, 2)

D (-2, 3)


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

G 95

H 115

J 75


Us the graph of y = ⅔x + 1 to solve the equation for x when y = -3.

F x = -6

G x = -1

H x = 1

J x = 3


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

B 30

C 50

D 75

Correct Answer - C Spring 2003 #35


(C) For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities.

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?


Ms. Collins’s car traveled between 25 and 29 miles per gallon of gasoline on a recent road trip. If the road trip was 614 miles, which could be the number of gallons of gasoline that Ms. Collins used during this road trip?

A 23 gal

B 29 gal

C 21 gal

D 25 gal


Hoaung went to a doughnut shop where jelly-filled doughnuts cost $0.50 including tax and glazed doughnuts cost $0.30 including tax. If Hoaung has $2 to spend and wants to purchase at least one of each of these two kinds of doughnuts, which of the following does not represent a reasonable combination of doughnuts that he could purchase?

A 2 jelly-filled doughnuts and 2 glazed doughnuts

B 2 jelly-filled doughnuts and 3 glazed doughnuts

C 3 jelly-filled doughnuts and 2 glazed doughnuts

D 1 jelly-filled doughnut and 5 glazed doughnuts

Correct Answer - C February 2006 #39

Victor purchased motor oil for $2 a bottle and car wax for $4 a bottle. The inequality 2x + 4y < 16 can be used to determine the number of bottles of motor oil, x, and the number of bottles of car wax, y, Victor purchased for less than $16, not including tax. Which of the following ordered pairs best represents a reasonable combination of bottles of motor oil and car wax that Victor could have purchased?

A (4, 2)

B (2, 3)

C (5, 2)

D (3, 2)


The Future Teachers of America club sold cookies for $0.25 each and cupcakes for $0.50 each to raise money to attend the state convention. If the club raised $24.75 from selling cookies and cupcakes during lunchtime, which of the following is a reasonable combination of the number of cupcakes and cookies that were sold?

A 24 cookies and 51 cupcakes

B 50 cookies and 25 cupcakes

C 51 cookies and 24 cupcakes

D 35 cookies and 30 cupcakes


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


A waitress at a restaurant calculated her daily pay, p, using the equation p = 0.15f + 17.60, where f is the total amount of food purchased by customers. If the waitress sold between $600.00 and $720.00 in food, then the amount of her daily pay should be between —

F $40.00 and $48.00

G $57.60 and $65.60

H $90.00 and $108.00

J $107.60 and $125.60


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)


A(c)(4) 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.

(A) The student analyzes situations and formulates systems of linear equations to solve problems.

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 = 2200.50b + 0.75c = 136.50

B b + c = 136.500.75b + 0.50c = 220

C b + c = 136.500.50b + 0.75c = 220

D b + c = 2200.75b + 0.50c = 136.50


An investor has a total of 45 one-ounce ingots, made of either gold or silver, worth $7636.50. The value of a gold ingot is $280.00, and the value of a silver ingot is $4.25. Which system of equations can be used to find g, the number of gold ingots, and s, the number of silver ingots?

A g – s = 45280.00g + 4.25s = 7636.50

B g + s = 45280.00g + 4.25s = 7636.50

C g + s = 454.25g + 280.00s = 7636.50

D g – s = 7636.50280.00g + 4.25s = 45


A school district held a meeting for all its physical education teachers. The number of women attending was 5 more than twice the number of men attending. A total of 53 teachers attended the meeting. Which system of equations could be used to find w, the number of women, and m, the number of men, at this meeting?

A m = 2w + 5w + m = 53

B 2w + m = 5w + m = 53

C w = m + 5w + m = 53

D w = 2m + 5w + m = 53


An isosceles triangle has legs that are each x inches long and a base that is y inches long. The perimeter of this triangle is 38 inches. The base is 8 inches shorter than the length of a leg. Which system of linear equations can be used to find the length of each of the 3 sides?

F 2x + y = 38y = x – 8

G 2x + 2y = 38y = x – 8

H 2x + y = 38x = y – 8

J 2x + 2y = 38x = y – 8

Correct Answer - F Fall 2005 #16

Lon caught 24 trout and bass while on a fishing trip. The total weight of his catch was 137 pounds. The average weight of a trout was 2.5 pounds, and the average weight of a bass was 8 pounds. Which system of equations can be used to find t, the number of trout, and b, the number of bass, that Lon caught?

A t = 24 + b2.5t + 8b = 137

B t + b = 242.5t + 8b = 137

C t + b = 1372.5t + 8b = 24

D t = 137 + b2.5t + 8b = 24


At 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 = 8m = 3n + 54

G m + n = 8m = 3n − 54

H m + n = 54m = 3n + 8

J m + n = 54m = 3n − 8


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 = 220e – u = -175

B 2e – u = 220e + u = 175

C 2e – 2u = 440e – u = -175

D e – 2u = -220e – u = 175


At Candy’s Sweet Shop, Sarah made c pounds of chocolate-covered raisins, which sell for $1.50 a pound, and y pounds of yogurt-covered raisins, which sell for $1.20 a pound. Sarah wants to make 40 pounds of a mixture of the two kinds of raisins that sells for $1.35 a pound. Which system of equations can be used to findthe number of pounds of eachkind of raisin needed toproduce the mixture?

A c + y = 401.50c + 1.20y = 1.35(40)

B c + y = 40150c + 120y = 1.35(40)

C c + y = 401.20c + 1.50y = 1.35(40)

D c + y = 40120c + 150y = 1.35(40)


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 = 2.102t + 2m = 5.15

B t + m = 2.103t + 3m = 5.15

C t + m = 2.103t + 2m = 5.15

D t + m = 2.102t + 3m = 5.15



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

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)

G (8, 1)

H (0, -3)

J (10, 2)


A large cheese pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?


Correct Answer - 2 July 2006 #21

Look at the system of linear equations graphed on the coordinate grid below. Which of the following is closest to the solution to this system of linear equations?

Correct Answer - B February 2006 #9

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of shirts would the cost be the same?

A 6

B 12

C 81

D 159


The equations of two lines are 6x − y = 4 and y = 4x + 2. What is the value of x in the solution for this system of equations?

A x = 14

B x = 3

C x = 1

D x = 6


The graph of the equation y = (5/3)x – 3 is given below. Graph y = x + 1 on the grid. What is the solution to this system of equations?

A (0, 1)

B (5, 6)

C (6, 7)

D No solution


Which of the following is the solution for this system of linear equations?


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



(C) For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations.

Maricella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?

F 10

G 4

H 3

J 9


Mrs. Travis wants to have a clown deliver balloons to her secretary’s office. Clowns R Fun charges $1.25 per balloon and $6 for delivery. Singing Balloons charges $1.95 per balloon and $2 for delivery. What is the minimum number of balloons Mrs. Travis needs to purchase in order for Clowns R Fun to have a lower price than Singing Balloons?

A 5

B 6

C 11

D 12


A certain video rental store rents video games for $4.99 and movie videos for $2.99. One day the store rented a total of 35 video games and movie videos. If the total rental income for this day was $144.65, not including tax, which of the following statements is a reasonable conclusion?

F There were more video games than movie videos rented on this day

G There were more movie videos than video games rented on this day.

H The total rental income for movie videos on this day was $99.80, not including tax.

J The total rental income for video games on this day was $74.85, not including tax.Correct Answer - F October 2005 #12

Objective 5:

The student will demonstrate an understanding of quadratic and other

nonlinear functions.

A(d)(1) Quadratic and other nonlinear functions. The student understands that the graph 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.

(B) The student investigates, describes, and predicts the effects of changes in a on the graph of y = ax2.

How does the graph of differ from the graphof ?


The graphs below represent functions of the form y = ax2. In which of the following graphs does a have the smallest value?


Which of the following functions of the form y = ax2 produces the widest graph and opens upward?


The formula for the volume of a cylinder with a height of 5 units can be represented as y = 5πx2, where x represents the radius. If the cylinder’s height is tripled, what is the effect on the graph of y as a function of x?

F The graph is translated up.

G The graph remains the same.

H The graph becomes narrower.

J The graph becomes wider.


How does the graph of y = 7x2 differ from the graph of ?

A The vertex of the graph of y = 7x2 is 7 units higher.

B The vertex of the graph of y = 7x2 is 7 units lower.

C The graph of y = 7x2 is wider.

D The graph of y = 7x2 is narrower.


Which equation will produce the widest parabola when graphed?

A y = 2x2

B y = -6x2

C y = -0.6x2

D y = 0.2x2


Which statement describes what happens to the graph of y = ax2 when the value of a is changed from 1 to 6?

A The graph translates 6 units up.

B The graph translates 6 units to the right.

C The graph narrows.

D The graph widens.


Which shows the functions correctly listed in order from widest to narrowest graph?



(C) The student investigates, describes, and predicts the effects of changes in c on the graph of y = x2 + c.

The graph of a function of the form y = ax2 + c is shown below. If the graph is translated only up or down to include the ordered pair (6, 7), which of the following equations best represents the resulting graph?


The graph of the equation y = 0.4x2 – 2 is shown below. If the graph is translated 3 units up, what will be the equation of the resulting graph?

A y = 0.4x2 + 1

B y = 0.7x2 – 2

C y = 0.4x2 + 5

D y = 3.4x2 – 2


The grid below shows parabolas A and B of the form y = ax2 + c. How are parabolas A and B related?

F Parabola A is narrowerthan parabola B.

G Parabola A is widerthan parabola B.

H All the points onparabola A are 7 unitsbelow thecorresponding pointson parabola B.

J All the points onparabola A are 7 unitsabove the corresponding points on parabola B.

Correct Answer - J February 2006 #36

Which quadratic function has a vertex below the origin and opens upward?

A y = -x2 + 3

B y = -x2 – 1

C y = x2 + 5

D y = x2 – 2


If the graph of the equation y = x2 + 1 is translated 3 units down, what will be the equation of the new graph?

F y = (x – 3)2 + 1

G y = x2 – 2

H y = x2 + 4

J y = -3x2 + 1


How does the graph of y = x2 – 1 differ from the graph of y = x2 + 7?

A The graph of y = x2 – 1 is 8 units to the left of the graph of y = x2 + 7.

B The graph of y = x2 – 1 is 8 units to the right of the graph of y = x2 + 7.

C The graph of y = x2 – 1 is 8 units above the graph of y = x2 + 7.

D The graph of y = x2 – 1 is 8 units below the graph of y = x2 + 7.


The graph of y = 11x2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c?

A c > 0

B c < 0

C c = 0

D c = 11


What is the effect on the graph of the equation y = x2 + 1 when it is changed to y = x2 + 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.



(D) For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.

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

A (0, 3)

B (-1, 0)

C (1, 4)

D (3, 0)


Look at the equations shown below.

Which of the following statements is true for the graph of all the equations given?

A The graphs are congruent and open downward.

B The graphs open upward and are symmetrical about the y-axis.

C The graphs are congruent and are listed from narrowest to widest.

D The graphs open downward and are symmetrical about the y-axis.


B The ball reached a maximum height of about 13 feet after traveling a horizontal distance of approximately 14 yards.

C The ball was thrown from a height of approximately 6 feet above the ground and traveled a horizontal distance of approximately 20 yards before it reached its maximum height.

D The ball was thrown from a height of approximately 7 feet above the ground and traveled a horizontal distance of approximately 10 yards before it reached its maximum height.

The graph represents the relationship between the height of a ball and the distance it traveled after the ball was thrown. What conclusion can be drawn from the graph about this relationship?

A The ball reached a maximum height of about 16 feet after traveling a horizontal distance of approximately 33 yards.


A The ball reached a maximum height of about 16 feet after traveling a horizontal distance of approximately 33 yards.

B The ball reached a maximum height of about 13 feet after traveling a horizontal distance of approximately 14 yards.

C The ball was thrown from a height of approximately 6 feet above the ground and traveled a horizontal distance of approximately 20 yards before it reached its maximum height.

D The ball was thrown from a height of approximately 7 feet above the ground and traveled a horizontal distance of approximately 10 yards before it reached its maximum height.

The graph shows the relationship between a 1-ton car’s kinetic energy, K, and its velocity, v. If the kinetic energy of the car is proportional to the square of its velocity, then its kinetic energy when traveling at 60 miles per hour is about –

A 320 kilojoules

B 480 kilojoules

C 720 kilojoules

D 1280 kilojoules


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

G 9 sec

H 7 sec

J 6 sec


A(d)(2) 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) The student solves quadratic equations using [concrete] models, tables, graphs, and algebraic methods.

The graph of the function y = x2 + 2x – 3 is shown below. What are the y-intercept and x-intercepts of the function?

F (0, -3, (0, 1), (-3, 0)

G (0, -3), (1, 0), (-3, 0)

H (-3, 0), (1, 0), (-3, 1)

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


What is the solution set for the equation 4x2 + 11x – 10 = 7?

F {-3, 0.25}

G {-3.47, 0.72}

H {3, -0.25}

J {-3.85, 1.1}


What are he zeros of the following function?

A -4 and 6

B -3 and 2

C 4 and -6

D -2 and 3


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?

F 5°C

G 7°C

H 10°C

J 12°C


Nancy threw a ball upward from the roof of a 50-foot-high building at an initial velocity of 40 feet per second. The table shows the relationship between the time elapsed and the ball’s height above the ground. If the height of the ball is a quadratic function of time, between what times did the ball reach a height of 70 feet?

F Between 0 seconds and 0.5 second

G Between 1 second and 1.5 seconds

H Between 0.5 second and 1 second and between 1.5 seconds and 2 seconds

J Between 1 second and 1.5 seconds and between 1.5 seconds and 2 seconds


What is the solution set for the equation 4(3x – 2)2 = 36?


A(d)(2) 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.

(B) The student relates the solutions of quadratic equations to the roots of their functions.

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

F (6½, 0) and (4½, 6)

G (4½, 6) and (2½, 0)

H (2½, 0) and (6½, 0)

J (0, 2½) and (0, 6½)


Which of the following polynomial equations best represents this graph?

A (x + 6)(x – 2) = y

B (x – 2)(x – 16) = y

C (x – 6)(x + 2) = y

D (x + 2)(x + 16) = y


Part of the graph of a quadratic equation is shown below. If the line of symmetry for this quadratic equation is x = 1.25, between which two integers will the other part of the graph intersect the x-axis?

A -4 and -3

B -3 and -2

C -2 and -1

D -1 and 0


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


What are the x-intercepts of the graph of the equation y = x2 + x – 12?

A 4 and 3

B -4 and 3

C -4 and -3

D 4 and -3


A(d)(3) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

(A) The student uses [patterns to generate] the laws of exponents and applies them in problem-solving situations.

What is the simplified form of ?


The mass of Earth is close to 5.97 × 1024 kilograms, and the mass of Venus is close to 4.87 × 1024 kilograms. What is the combined mass of both planets?

A 1.08 × 1025 kg

B 2.91 × 1049 kg

C 1.08 × 1048 kg

D 1.10 × 1024 kg


Jupiter has an equatorial diameter of about 8.9 × 104 miles, which is about 11.2 times as great as Earth’s equatorial diameter. According to this information, what is Earth’s approximate equatorial diameter in scientific notation?

F 2.3 × 103 mi

G 9.97 × 105 mi

H 7.95 × 103 mi

J 2.01 × 102 mi


Which expression best represents (3a2b3c)(-3ab)(-2a3bc3)?

F 18a6b5c4

G -18a6b3c3

H 18a6b9c4

J -8a6b5c4


Which expression describes the area in square units of a rectangle that has a length of 10x3y4 units and a width of 5x2y units?

F 2x5y4

G 15x5y5

H 50x5y4

J 50x5y5

Correct Answer - J October 2005 #4

The area of a rectangle is 144j9k15 square units. If the width of the rectangle is 8j

4k5 units, what is the rectangle’s length?

F 1152 j13k20 units

G 152j13k20 units

H 136j5k10 units

J 18j5k10 units


Which polynomial best represents the area of the regular hexagon shown below?[Area = ½(apothem)(perimeter)]

F 5x + 6

G 2x2 + 3x

H 4x2 + 12x

J 4x + 12


Which expression best represents the simplification of (3m-2n4)(-4m6n-7)?

Correct Answer - F Spring 2003 #48

Objective 6:

The student will demonstrate an understanding of geometric

relationships and spatial reasoning.

G(b)(4) Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

(A) The student selects an appropriate representation ([concrete,] pictorial, graphical, verbal, or symbolic) in order to solve problems.

Look at the cube shown below. Which equation best represents the area of the shaded rectangle located diagonally in the cube?


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


The polygon RSTU is shown below. Which expression represents the area of this polygon?

F 4n2

G 4n

H 2n

J n2


Shown below is ∆LMN, an isosceles triangle. Which equation can be used to find the measure of the vertex angle of this isosceles triangle?


Mitch drew lines l, k, and t. Lines l and k were parallel to each other. Mitch measured 2 alternate interior angles. He labeled theangles 1 and 2. Whichof the following showsangles 1 and 2correctly labeled?

Correct Answer - B February 2006 #55 Fall 2005 #50

Which expression best represents the area of a circle with a radius of (1/3)a units?


In ∆ABC, m BAC = (6x + 3)° andm ABC = (3x – 6)°. Which equation can be used to find m BCA?


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


In isosceles triangle WXY, the interior angle W measures 100°. The measures of all three interior angles of triangle WXY are —

F 100°, 100°, and 160°

G 100°, 100°, and 100°

H 100°, 60°, and 20°

J 100°, 40°, and 40°


If A and B are complementary angles and m A is x, which equation can be used to find y, m B?

F y = 90 + x

G y = 90 – x

H y = 180 – x

J y = x + 180


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

Correct Answer - A Spring 2003 #51

G(c)(1) Geometric patterns. The student identifies, analyzes, and describes patterns that emerge from two- and three-dimensional geometric figures.

(A) The student uses 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.

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?


Look at the figures and the table below. How many triangles will the nth stage contain?


The pattern below represents the areas of several squares.

1, 9, 25, 49, ...This pattern was formed by changing the length of the sides of the squares. How does each new length compare to the previous length?

F Each new length is 2 units greater.

G Each new length is 2½ units greater.

H Each new length is 4 units greater.

J Each new length is 8 units greater.


The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon with n sides?

Correct Answer

D

February 2006 #13

Parallelogram MPQR is shown below. What are the lengths of diagonals MQ and RP?

A MQ = 10 and RP = 14

B MQ = 7 and RP = 5

C MQ = 14 and RP = 10

D MQ = 2 and RP = 3


According to the table, which expression best represents the numberof white triangles atany stage, n, in thisgeometric pattern?

A (n – 1)n – 1

B (2n – 1)2

C 3n – 1

D n2


Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides.


In the figure shown below, BC is parallel to ED, and AE is perpendicular to ED. The measure of ABC is 130°. What is the measure of BAE in degrees?


Correct Answer - 140 April 2004 #21

On the map below, First Ave and Second Ave 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°

G 90°, 50°, 40°

H 90°, 60°, 30°

J 130°, 40°, 10°


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 – 1Correct Answer - J Spring 2003 #34


(B) The student uses the properties of transformations and their compositions to make connections between mathematics and the real world in applications such as tessellations or fractals.

The first 4 stages of a certain fractal are shown. 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


The figure below shows the positions of a surveying crew measuring the distance to a tree across the river. Which of the following best represents the measure of angle TAP?

A 58°

B 69°

C 90°

D 122°


The regular octagon below shows selected positions on a combination lock. The dial of the lock is turned 90° clockwise and then 45° counterclockwise. Which pair of points can describe the starting and ending points of a marker on the dial of this lock?

A T to U

B S to V

C W to V

D Z to W

Correct Answer - A July 2006 #31Fall 2005 #25

The figure below shows Aaron’s recent hiking course, which started at point L, went to point M and then point P, and then returned to point L. What is the measure of angle LMP formed by Aaron’s hiking course?

A 101°

B 79°

C 54°

D 43°


A student begins drawing a fractal by dividing each side of an equilateral triangle into 3 segments. The student then replaces the middle segments with 2 equal segments to form the sides of smaller equilateral triangles. If the student repeats this process on the 12 sides of the second figure, how many sides will the next figure have?

F 24

G 36

H 48

J 60


A city council wants to build train tracks through the city’s business district. A city planner shows the council a map for the proposed train track. State Avenue is parallel to Madison Avenue. Market Street is parallel to Washington Street. What is the measure of HGL?

A 63°

B 29°

C 34°

D 56°


Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration. Step 1: Divide the square into a 3-by-3 grid of squares Step 2: Shade only the center square of this 3-by-3 gridWhat fraction of the 1-unit-by-1-unit square is shaded after the second iteration?



(C) The student identifies and applies patterns from right triangles to solve problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

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 isclosest to the length of the hosein the garden?

A 7.8 ft

B 9.5 ft

C 6.4 ft

D 5.5 ft


In the figure, MN = 10 cm. Which is the closest to the length of TN?

A 7 cm

B 6 cm

C 17 cm

D 14 cm


A diagonal walkway through a park is 18 meters long. If the park is a square, how long is one of its sides to the nearest tenth of a meter?

A 9.0 m

B 12.7 m

C 18.0 m

D 25.5 m


If the perimeter of the equilateral triangle shown below is 37 centimeters, what is the approximate area of the triangle?

F 132 cm2

G 54 cm2

H 33 cm2

J 66 cm2


In ∆PKN, PN = 14 inches, m N = 30°, and m K = 90°. Which is closest to the perimeter of ∆PKN?

F 42 in.

G 33 in.

H 31 in.

J 28 in.


In the figure below, circle M and circle R intersect at point P. Which is closest to the length of LT?

F 14 units

G 11 units

H 18 units

J 16 units


The area of this regular polygon is 72 in2. Find the approximate length of one side of this polygon.

A 12.9 in.

B 15.8 in.

C 22.3 in.

D 24.0 in.

Correct Answer - A Fall 2005 #39

∆TCL is shown below. If TL = 12 inches, what is the area of ∆TCL?


In the figure shown below, ∆MPQ ~ ∆PQR, MR = 45 units, and RQ = 15 units. What is the length of PR?


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

G 127 ft

H 156 ft

J 311 ft


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.

B 10.4 in.

C 8.5 in.

D 5.2 in.


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 units2

G 110 units2

H 88 units2

J 55 units2


Find the area of triangle RST.

A 16 ft2

B 32 ft2

C 24 ft2

D 40 ft2


∆WXY is a right triangle. Find the length of WY.


In the figure below, what is the length of ML in cm?


Correct Answer - 117 July 2004 #21

The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out?

F 1.7 ft

G 18 ft

H 10.4 ft

J 6 ft


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


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


G(e)(3) Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(A) The student uses congruence transformations to make conjectures and justify properties of geometric figures.

F (-6, -7)

G (6, -1)

H (6, 7)

J (6, 3)


Parallelogram WBMP is shown on the grid below. If WBMP is reflected across the line y = -x and thentranslated 4 units downto become parallelogramW’B’M’P’, what will bethe coordinates of M’?

The graph shows quadrilateral TUVW, KN, and KL. At what coordinate point should vertex M be placed to make quadrilateralKLMN congruent toquadrilateral TUVW?

A (6, -4)

B (4, -5)

C (5, -5)

D (6, -5)


Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a singlereflection of the otheracross the x-axis?


A ∆KLM ∆PNM

B ∆KRM ∆PQM

C ∆KRM ∆PNM

D ∆KLM ∆KRM

Look at the triangle graphed on the coordinate grid below. Which coordinates are the vertices of a triangle congruent to this figure?

Correct Answer - A Fall 2005 #11

A (3, -1), (2, -3), (6, -3)

B (-3, 3), (1, 1), (-2, 1)

C (-4, -1), (0, -1), (-4, -3)

D (3, 1), (2, 3), (-3, 6)

∆MNP is shown below. If ∆MNP is translated so that point N(-3, 4) is mapped to point N’(-1, 1), which ordered pair best represents either point M’ or point P’?

A M’(-2, -6)

B P’(3, 8)

C P’(4, -7)

D M’(-7, -3)


Which pair of the following polygons is congruent?

F A and C

G B and D

H A and B

J B and C


Which coordinates are the vertices of a triangle congruent to ∆MNP?

F (-11,13), (-9,16), (-4,16)

G (-8,5), (-5,2), (-1,4)

H (-20,4), (-17,7), (-12,5)

J (-15,14), (-18,17), (-17,22)


Figure MNPQ is shown on the coordinate plane. Which transformation creates an image with a vertex at the origin?A Rotate figure MNPQ

90° around M

B Reflect figure MNPQ across the line x = 1

C Reflect figure MNPQ across the line y = 2.5

D Translate figure MNPQ to the left 6 and down 5


Objective 7:

The student will demonstrate an understanding of two- and three-dimensional representations of

geometric relationships and shapes.

G(d)(1) Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems.

(B) The student uses nets to represent [and construct] three-dimensional objects.

Which net best represents the triangular prism shown below?


Which net best represents the hexagonal prism shown below?


The net below can be folded to form a cube. Which cube could be formed from this net?

Correct Answer - H Fall 2005 #6October 2005 #26

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

F Faces R and S are parallel.

G Faces R and U are parallel.

H Faces S and U are perpendicular.

J Faces T and U are perpendicular.


The net shows the surface of a 3-dimensional figure. Which 3-dimensional figure does this net represent?


G(d)(1) Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems.

(C) The student uses top, front, side, and corner views of three-dimensional objects to create accurate and complete representations and solve problems.

The diagram below shows the top view of a structure built with identical cubes, as well as the number of cubes in each column. Which 3-dimensional view best represents the same structure?


The illustration shows a 3-dimensional view of a screw. Which of the following best represents a front, a side, or a top view of this screw?


The drawing shows the top view of a structure built with cubes as well as the number of cubes in each column of the structure. Which 3-dimensional view represents the same structure?


The figure shown is a cube with a corner sliced off. Which of the following sets of 2-dimensional drawings shows the top, front, and right views of the figure?


The 3-dimensional figure represents a structure that Corina built with 9 cubes. Which of the following best represents the top view of Corina’s 9-cube structure?

Correct Answer - D February 2006 #49Fall 2005 #49

The Transamerica Pyramid is a building in San Francisco, California, that resembles a square pyramid. The diagram shows a front and side view of the building. If the back view of the building is similar to the front view and the side views are similar to each other, which best represents the top view?


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


The front, side, and top views of a solid built with cubes are shown. How many cubes are needed to construct this solid?

A 6

B 8

C 12

D 16


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


G(d)(2) 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.

(A) The student uses one- and two-dimensional coordinate systems to represent points, lines, line segments, and figures.

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


Which ordered pairs form the vertices of an isosceles trapezoid?

A (1, 2), (3, -1),(-3, -4), and (-4, -1)

B (1, 2), (3, -1),(-4, -1), and (-2, 2)

C (-1, 3), (3, -1),(-2, 2), and (-4, -1)

D (-1, 3), (-4, -1),(-2, 2), and (3, 0)


Parallelogram GHJK is shown. Which of the following represents the x-value of point J?

F y – x

G x + y

H a + x

J x – a


If a line contains the points (1, -1) and (3, 3), which of the following points also lies on this line?

A (4, 2)

B (2, 4)

C (2, 1)

D (1, 2)

Correct Answer - C Fall 2005 #01 October 2005 #2

The coordinates of the vertices of a triangle are (-3, -4), (9, 0), and (1, 8). The best descriptions of this triangle is –

F a right isosceles triangle

G a right scalene triangle

H an isosceles triangle

J an equilateral triangle


A hexagon is graphed on the coordinate grid. Which two coordinate points lie on the same line of symmetry on this hexagon?

F (-3, -1) and (0, 3)

G (-1, 3) and (-1, -1)

H (0, 3) and (0, -1)

J (-4, 1) and (1, 1)


If quadrilateral STUV is rotated 180° around the origin, in which quadrant will point S appear?

A Quadrant I

B Quadrant II

C Quadrant III

D Quadrant IV


If the vertices of a polygon are (-2, 3), (2, 3), (3, 0), (0, -3), and (-3, 0), which graph best represents the polygon?

Correct Answer

JJuly 2004 #60

Which of the following is the correct name for figure ABCD, with vertices A(4, 6), B(8, 7), C(7, 3), D(3, 2)?

F Rectangle

G Rhombus

H Trapezoid

J Square



(B) The student uses slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and [special segments of] triangles and other polygons.

Which graph best represents a line that is parallel to the graph ofthe equation ?


∆RST is a right triangle. If the equation of the line containing ST is , which of the following best represents the equation of the line containing RT?


A right triangle has two vertices with coordinates (0, 3) and (4, 1). Which coordinate could be a third vertex of this right triangle?

A (2, 2)

B (4, 4)

C (6, 5)

D (8, -1)


Which two lines are parallel?

F 6x – 2y = -8 and 3x+ y = -4

G 3x – y = -1 and 9x – 3y = -6

H 12x – 4y = -4 and x – 3y = -9

J 9x – 3y = -6 and 5x + 15y = 15


Line l1 has an x-intercept at (3, 0) and a y-intercept at (0, 6). The x-intercept for line l2 is (4, 0). If lines l1 and l2 are perpendicular, what is the y-intercept of line l2?

A (0, -8)

B (0, -2)

C (0, 2)

D (0, 8)


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

2y =3x + 24y = 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.


Line q is shown. Which equation best represents a line parallel to line q?


Which two lines are parallel?

F 2x + 5y = 6 and 5x + 2y = 10

G 3x + 4y = 12 and 6x + 8y = 12

H 2x + 5y = 6 and -2x + 5y = 14

J 3x + 4y = 12 and 6x – 8y = 20


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

y = 4 – 2x

4y = 2x + 1

F The lines have the same x-intercept.

G The lines have the same y-intercept.

H The lines intersect to form right triangles.

J The lines are parallel to each other.


Which graph best represents a line parallel to the line with the equation y = 3x + 4?

Correct Answer - J Spring 2003 #6

Which graph best represents the line passing through the point (0, 4) and perpendicular to y = –½x?



(C) The student [develops and] uses formulas, including distance and midpoint.

AB is a diameter of the circle shown below. Which is closest to the length of the radius of the circle?

A 3.1 units

B 4.3 units

C 6.1 units

D 12.2 units


What is the approximate distance between points (-7, 2) and (11, -5)?

A 18.36 units

B 19.31 units

C 18.25 units

D 8.06 units


The midpoint of the diagonals of rectangle PTQW is (-0.5, 1). The coordinates of P are (-3.5, 6). What are the coordinates of Q?

A (-2, 3.5)

B (-6.5, 11)

C (-1.5, 2.5)

D (2.5, -4)

Correct Answer

D July 2006 #57

The midpoint of AB is M. If the coordinates of M are (½, -2) and the coordinates of B are (6, 1), what are the coordinates of A?

A (-5, -5)

B (2, -10)

C (-3¼, -1½)

D (-5, 5)


Find the midpoint of the line segment with endpoints (4, -6.25) and (-15, 12.25).

A (-5.5, 3)

B (-9.5, 9.25)

C (-11, 6)

D (-19, 18.5)

Correct Answer - A Fall 2005 #59October 2005 #16

Rectangle MNPQ has diagonals that intersect at point X. What are the coordinates of point X?


What is the approximate length of MN when the coordinates of its endpoints are (-4, 5) and (-6, 9)?

F 2.4 units

G 4.5 units

H 10.8 units

J 17.2 units


AB is the diameter of circle C. If the endpoints of the diameter are (3, -4) and (7, 2), what are the coordinates of the center of circle C?

F (2, -1)

G (4, -2)

H (5, -1)

J (10, -2)


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 betweenCity A and City B,which is closest to thedistance in coordinateunits from City Ato City C?

A 4.61 units

B 6.52 units

C 9.22 units

D 21.25 units


G(e)(2) Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

(D) The student analyzes the characteristics of three-dimensional figures and their component parts.

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

F 4 faces, 10 edges, and 17 vertices

G 9 faces, 10 edges, and 8 vertices

H 10 faces, 16 edges, and 9 vertices

J 9 faces, 16 edges, and 9 vertices


Which of the following 3-dimensional figures is made from a set of points in space that are equidistant from a fixed point?

A Cylinder

B Sphere

C Cube

D Tetrahedron


Which set of figures can be used to construct a representation of the surface area of the triangular prism shown below?


Which of the following describes a solid with 1 base and no vertices?

F Cone

G Sphere

H Cylinder

J Hemisphere


Which set of figures can be used to construct a representation of the surface area of the solid shown?


Which of these 3-dimensional figures has the following characteristics: 12 faces, 8 vertices, and 18 edges?


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 pyramid


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


Objective 8:

The student will demonstrate an understanding of the concepts and uses

of measurement and similarity.

G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to find area, perimeter, and volume in problem situations.

(A) The student finds area of regular polygons and composite figures.

The figure shows a CD in its rectangular storage case. Which is closest to the area of the storage case not occupied by the CD?

A 55 cm2

B 46 cm2

C 51 cm2

D 60 cm2


The drama department at McHenry High School has built a stage floor in the shape of a regular octagon. The length of each side of the octagon is 4 yards. CD is the apothem. What is the approximate area of the stage floor?

F 57.9 yd2

G 76.8 yd2

H 115.9 yd2

J 154.5 yd2


Linda has divided her garden into 3 parts as shown. What is the area of her garden?

A 1005 ft2

B 1230 ft2

C 1350 ft2

D 1470 ft2


The figure shows a triangle on top of a rectangle. If the area of the triangle is 83 square feet, which of the following best represent the area of the rectangle?

A 405 ft.2

B 239 ft.2

C 322 ft.2

D 166 ft.2


The figure shows the dimensions of a section of Mr. Green’s garden that he will use for planting flowers. What is the area of Mr. Green’s garden that he will use for planting flowers?

F 42 ft2

G 30 ft2

H 39 ft2

J 24 ft2


What is the area of the unshaded part of the rectangle blow?

A 19,000 ft2

B 45,000 ft2

C 28,000 ft2

D 26,000 ft2

Correct Answer - D

April 2004 #43

A circle with a diameter of 10 centimeters is to be cut out from a square piece of paper that measures 10 centimeters on each side, as shown below. Which is closest to the amount of paper that will be left over after the circle is cut out?

F 9 cm2

G 21 cm2

H 25 cm2

J 69 cm2



(B) The student finds area of sectors and arc lengths of circles using proportional reasoning.

F 545 mm

G 157 mm

H 22 mm

J 44 mm


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

When the door handle is pushed down to open the door, it makes a 45° angle with its former position. What is the approximate arc length of the path traveled by the outside end of the door handle when the handle is pushed down?A 34.56 in.

B 11.88 in.

C 4.32 in.

D 2.16 in.

Correct Answer - C July 2006 #45Fall 2005 #15

A building-trades class built a circular spinner for the school carnival. The spinner has a diameter of 48 inches and is divided into 12 congruent sectors. What is the approximate area of each of the sectors on this spinner?

F 603 in.2

G 151 in.2

H 25 in.2

J 13 in.2


What is the approximate length of arc PQ?

A 13 cm

B 98 cm

C 94 cm

D 7 cm


A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. What is the approximate length of the arc of the section containing peas?

F 3 in.

G 21 in.

H 16 in.

J 5 in.


The shaded area in the circle below represents the section of a park used by the chamber of commerce for a fund-raising event. What is the approximate area of the section of the park used for the fund-raiser?

A 339 square feet

B 1,357 square feet

C 4,071 square feet

D 12,214 square feet



(C) The student [develops, extends and] uses the Pythagorean Theorem.

∆WXY is isosceles. WY is 10 centimeters long. Find the length of XZ.

F 5 cm

G 10 cm

H 12 cm

J 13 cm

Correct Answer - H April 2006 #2Fall 2005 #3

Which of the following sets of numbers represents the side lengths in units of a right triangle?

A 5, 3.2, 4.1

B 3.6, 6, 4.8

C 4.5, 8, 6.7

D 8.5, 5.2, 10


Mr. Krueger attended an event at the Good Time Sports Arena. The arena is in the shape of a circle with a radius of 200 feet. He parked his car in the lot at point S, which is 250 feet away from the entrance at point F. Mr. Krueger left the arena through the exit at point D and walked a straight-line path tohis parked car. About how far awaywas his parked car from the exitat point D?

F 200 ft

G 403 ft

H 492 ft

J 650 ft


The figure shows three right triangles joined at their right-angle vertices to form a triangular pyramid. Which of the following is closest to the length of XZ?

F 7 inches

G 20 inches

H 12 inches

J 9 inches


Kim walked diagonally across a rectangular field that measured 100 feet by 240 feet. Which expression could be used to determine how far Kim walked?


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


The map shows 2 different routes Ms. Bentsen can take to drive to the airport from her house. How many miles could Ms. Bentsen save by traveling on Airport Road instead of Mountain Highway and Oak Road to get to the airport?

A 20 mi

B 30 mi

C 35 mi

D 60 mi


What is the area of the square in the figure?A 5.2 square units

B 6.7 square units

C 27 square units

D 45 square units


The total area of trapezoid FGHJ is 52 square inches. What is the approximate length of FJ?

A 8.0 in.

B 8.5 in.

C 11.0 in.

D 11.5 in.



(D) The student finds surface area and volumes of prisms, pyramids, spheres, cones, and cylinders in problem situations.

Henry built a wooden storage shed in the shape of a rectangular prism for his tools. 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

B 181 ft2

C 154 ft2

D 91 ft2


Mrs. Wong has a bookcase shaped like an isosceles trapezoid. The height of the bookcase isapproximately 150 centimeters. Theother dimensions are shown. Whichof the following is closest to thesurface area of the top, left, andright rectangular sides ofMrs. Wong’s bookcase?

A 11,000 cm2

B 22,000 cm2

C 36,000 cm2

D 9,000 cm2


A cube-shaped piece of playground equipment has a cylindrical portion removed, as shown in the diagram. The diameter of the opening is 5 feet. What is the approximate volume of the remaining portion of the cube?

F 255 ft3

G 122 ft3

H 98 ft3

J 28 ft3


Mr. Martinez bought a solid-glass globe with a stand. If the diameterof the globe is7 centimeters, which isclosest to the volumeof glass in the globe?

A 51 cm3

B 180 cm3

C 154 cm3

D 101 cm3


A company plans to design a new version of its Millennium Doll that will be larger than the old version. The figure below shows the dimensions of the box for the old version of the doll. If all the dimensions of the box are increased by 2 inches for the new doll, what will be the total surface area of the new box?

F 496 in.2

G 696 in.2

H 992 in.2

J 1920 in.2


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


G(f)(1) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

(A) The student uses similarity properties and transformations to [explore and] justify conjectures about geometric figures.

A parallelogram is graphed on the grid. Which set of coordinates identifies the vertices of a similar figure?

Correct Answer

H

February 2006 #30

F (-2, -1), (-4, -1), (-3, -6), (-5, -6)

G (0, -2), (0, -5), (8, 1), (8, -2)

H (1, 2), (1, 6), (9, 6), (9, 10)

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


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

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

Which statement best describes why pentagon PQRST is similar to pentagon VWXYZ?


A The ratio of the length of PTto YZ equals the ratio of thelength of RS to WV.

B Both pentagons have corresponding right angles.

C Pentagon VWXYZ is theresult of a translation ofpentagon PQRST.

D The ratio of thecorresponding sides of pentagons PQRST and VWXYZ is 2:1.


Use theinformation ineach diagramto find the pair ofsimilar polygons.


(B) The student uses ratios to solve problems involving similar figures.

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

B 87.5 square units

C 21.875 square units

D 61.25 square units


In 2002, people in Laredo, Texas, erected the tallestflagpole in the United States. It can be seen frommiles away. According to the information shownin the drawing, what is the approximate heightof the flagpole?(The drawing is not drawn to scale.)

A 308 feet

B 295 feet

C 205 feet

D 197 feet


Troy used chalk to outline a triangular plot of land in his backyard. The plot of land has a perimeter of 26 feet, with its longest side measuring 8 feet 10 inches. Troy wants to outline a second triangular plot of land similar to the first but with a perimeter of 42 feet. Which of these is closest to the measure of the longest side of the second triangular plot of land?

F 17 ft 2 in.

G 13 ft 1 in.

H 14 ft 3 in.

J 17 ft 11 in.


Brandon wants to reduce a figure that is 9 inches tall and 16 inches wide so that it will fit on a 9-inch-by-12-inch piece of paper. If he reduces the figure proportionally, what is the maximum size the reduced figure could measure?

Correct Answer - J Fall 2005 #38October 2005 #32

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


In ∆STR, QP and TR are parallel. If SQ = 6 units, QT = 24 units, and the perimeter of ∆SQP is 20 units, what is the perimeter of ∆STR?

A 80 units

B 100 units

C 320 units

D 500 units


In El Paso, Tx, the streets named Hercules Ave, Hondo Pass Dr, and Trans Mountain Rd are parallel. They all intersect Dyer St and U.S. Route 54, as shown on the map. If all of these streets are straight line segments, how long is Dyer St between Hercules Ave and Trans Mountain Rd?

A 8,450 ft

B 9,900 ft

C 13,200 ft

D 19,800 ft



(C) In a variety of ways, the student [develops,] applies, and justifies triangle similarity relationships, such as right triangle ratios, [trigonometric ratios,] and Pythagorean triples.

If XY = 8 feet and XZ = 17 feet, what is the area of ∆XYZ?

F 15 ft2

G 30 ft2

H 60 ft2

J 120 ft2


If ∆KLM ~ ∆RST, which is closest to the length of ST?

F 15.52 in.

G 9.81 in.

H 7.79 in.

J 12.04 in.


In the figure, ∆QNP ~ ∆PQH, and NM = 12.5 centimeters. What is the area of ∆PQN?

A 20.48 cm2

B 25.00 cm2

C 24.31 cm2

D 37.99 cm2



(D) The student describes the effect on perimeter, area, and volume when the length, width, or height of a three-dimensional solid is changed and applies this idea in solving problems

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.


F The volume will increase to less than 2 times the original volume.

G The volume will increase to between 2 and 3 times the original volume.H The volume will increase to between 3 and 4 times the original volume.J The volume will increase to between 4 and 5 times the original volume.

Mr. Norstam has just released a weather balloon with a diameter of about 3 feet. As the weather balloon rises, it will expand and eventually burst because of the changes in the atmospheric pressure. If the weather balloon rises and expands to 1.5 times its diameter before it bursts, what will be its change in volume?


What is the volume of a similar rectangular box with dimensions that are 3.5 times larger than the dimensions of the rectangular box shown below?F 5,880 in.3

G 17,836 in.3

H 20,580 in.3

J 1,680 in.3


The radius of a spherical beach ball is 24 centimeters. If another spherical beach ball has a radius 3 centimeters longer, about how much greater is its surface area, to the nearest square centimeter?

A 37 cm2

B 113 cm2

C 1,923 cm2

D 24,542 cm2

Correct Answer - C Fall 2005 #55October 2005 #18

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.


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


Objective 9:

The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics

in application problems.

(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations and solves problems. The student is expected to

(B) estimate and find solutions to application problems involving percents and proportional relationships, such as similarity and rates.

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


Mr. Jenkins designed a true-false science exam. The ratio of true answers to false answers is 5:3. Which is closest to the percentage of true answers on Mr. Jenkins’s science exam?

A 53%

B 60%

C 38%

D 63%


A salesman at a jewelry store earns a salary of $295 per week plus a commission of 15% of his weekly sales. If the salesman earned $936.30 in a week, what was the amount of his sales for the week?

A $4275.34

B $5947.07

C $2115.93

D $1371.75


The ratio of juniors to seniors enrolled in technology classes is 9 to 8. If the total number of juniors and seniors enrolled in these classes is 51, which of these best represents the percent of students enrolled in technology classes who are seniors?

A 27%

B 24%

C 53%

D 47%


An insurance company reimbursed members of the Alonzo family 80% of their medical expenses after the family paid the first $1000 of those expenses. If the family members received $160 from the insurance company, what were their total medical expenses?

A $960

B $1200

C $1128

D $1410


The athletic budget of $65,000 at Central East High School is allocated proportionally to male and female athletic teams according to the student population by gender. If there are 400 female and 475 male students enrolled at Central East High School, which of these is closest to the amount allocated to female athletics?

A $35,300

B $29,700

C $32,500

D $26,000


Two 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


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.

B 4.69 in. by 7.81 in.

C 5.50 in. by 7.50 in.

D 4.25 in. by 6.25 in.Correct Answer - B April 2004 #39

This year’s price for a certain car is 25% higher than last year’s price of $8800. What percent of this year’s price is last year’s price?

A 67%

B 75%

C 78%

D 80%


Mrs. Shelby earns $400 per week in salary plus an 8% commission on her total sales. How much must her total weekly sales be in order for her to earn exactly $650 per week?

A $2000

B $3125

C $5200

D $8125


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%


(8.11) Probability and statistics. The student applies the concepts of theoretical and experimental probability to make predications. The student is expected to

(A) find the probabilities of compound events (dependent and independent);

Winners from the math club’s fund-raiser randomly select a gift certificate from Box A and from Box B. The contents of each box are shown below. What is the probability that the first winner will randomly select a DVD certificate and an amusement park certificate?


The jar contains 24 solid-colored marbles of equal size. If Ray were to randomly select one marble from the jar, replace it, and then randomly select again, what is the probability that the firstmarble will be blue and thesecond will be white?


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?


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?


(8.11) Probability and statistics. The student applies the concepts of theoretical and experimental probability to make predications. The student is expected to

(B) use theoretical probabilities and experimental results to make predictions and decisions.

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


A basketball player made 12 free throws in his last 36 attempts. How many free throws would the basketball player be expected to make in 78 attempts?

F 20

G 26

H 52

J 234


A manufacturing company that makes semiconductors produced about 500 wafers of gallium nitride. The company found that 60 of the wafers contained defects and could not be used. Based on this information, which is the best prediction of the number of defective wafers produced when this company manufactures 8000 wafers?

A 133

B 500

C 960

D 367


The math club at Hawthorne High School surveyed 180 students and found that 36 of them have a March birthday. Based on this information, which is the best prediction of the number of students at Hawthorne High School who have a March birthday if there are 867 students enrolled?

F 289

G 173

H 72

J 24


A high school is changing its school colors. Melanie surveyed 50 students, and each student voted for one color combination. Some of the results are shown in the table below. According to the table, which is the best prediction of the number of students who will choose blue and gold if there are 1250 students enrolled at the high school?

F 350

G 900

H 486

J 98


Marcos has a spinner with 12 equal sections colored either blue or red. If the spinner lands on blue on 33 out of 50 spins, which is most likely the number of blue sections on the spinner?

F 4

G 6

H 8

J 10


The student council at Monroe High School is planning a school wide 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. Based on the data in the survey, how many students are likely to choose skating?

F 234

G 260

H 351

J 468


(8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to

(A) select the appropriate measure of central tendency to describe a set of data for a particular purpose;

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

B Median

C Mode

D Range


The table shows Cain’s 7 quiz scores for the first 9-week period. Each score is based on a 50-point scale. Which of the following gives the highest value for Cain’s quiz scores for the first 9-week period?

F Mode

G Mean

H Range

J Median


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

G Median

H Mode

J Range


(8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to

(C) construct circle graphs, bar graphs, and histograms, with and without technology.

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?


An orange-drink label reads “20% real fruit juice.” The other ingredients are water, sugar, and flavoring. Which section of the circlegraph best represents theamount of real fruit juicein the orange drink?

A W

B X

C Y

D Z


The senior class at Lambert High School raised $950 for a class trip. Nancy made a circle graph to represent the amount of money earned at each fund-raiser. Nancy forgot to indicate which fund-raiser corresponded to each sector. Which of the following fund-raisers could describe sector M?F Spirit ribbons earned $342.

G Homecoming photographs earned $161.50.

H The bake sale earned $237.50.

J School logo mugs earned $209.Correct Answer - H October 2005 #8

The manager of a sandwich shop is planning to make a circle graph showing the types of sandwiches sold in one day. The table 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°


(8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to

(B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

Amanda, Bonnie, Cindy, and Lindacompeted in a biathlon consistingof running and swimming events.The table shows the number ofseconds each of them took tocomplete the parts of thecompetition. The top rankings are awarded to the individuals with the fastest combined times. Based on the information 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

CorrectAnswer

B

April 2006 #5

A physical education class had 20 students. The table below shows the students’ grades and the number of days each student was absent. Which conclusion about the students in this class is true?

A Each student who earned a grade of A was absent fewer than 4 days.B Each student who was absent fewer than 4 days earned a grade of A.C Each student who was absent more than 2 days did not earn a grade of A.D Each student who did not earn a grade of A was absent more than 2 days.


A pharmaceutical company claimed that its product relieves acid indigestion more quickly than any other antacid. The company used the graph below to support its claim. According to the graph, which statement best describes the company’s product?

A Its product works faster than some brands but much slower than others.B Its product works many times faster than the other brands.C Its product works in about the same time as the other brands.D Its product works somewhat slower than the other brands shown. Correct Answer - C Fall 2005 #13

The table shows the monthlysales at a pizza parlor for a6-month period. Which isthe best inference that canbe made from the table?

A January had the lowest sales.

B The period with the greatest increase in monthly saleswas from May to June.

C Sales for July will be greater than $10,000.

D The sales will drop over the next 2-month period.


The table shows the cost of fertilizer, depending on the amount purchased.Which conclusion canbe made based on theinformation 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.


The table shows the yearly unemployment rates of a city over a 5-year period. Which conclusion can be made from the table?

A The unemployment rate continuously increased over these 5 years.B The unemployment rate for the sixth year is 4.1%.C Employers hired the most people in the third year.D The unemployment rate averaged more than 4% over these 5 years.


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.


Objective 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

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

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

B $1.50

C $3.00

D $13.50


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 theinformation given,which of the followingpoints best representsthe location where thenew Crispy SweetDoughnut Shop shouldopen?

F (9, 12)

G (5, 13)

H (6, 10)

J (8, 13)Correct Answer - F April 2006 #58

George saves 15% of his total gross weekly earnings from his 2 part-time jobs. He earns $6.15 per hour from one part-time job and $7.25 per hour from the other part-time job. George works a total of 40 hours between the two jobs each week. What additional information is needed to determine the amount of his earnings he saves each week?

A The number of days he works at each job

B The number of hours he works at each job

C The number of hours he works each day

D The number of hours he works each month


Karen, Simone, and Cameron contributed $64 altogether to pay their phone bill. Karen’s contribution was four dollars more than twice as much as Cameron’s. Karen’s contribution was three times as much as Simone’s. What was the amount of Cameron’s contribution?

F $36

G $16

H $12

J Not here


The Pruitts own a natural-foods store and purchase sacks containing 5 kilograms of flax seed for $30 each. The Pruitts then package the seed into 50-gram bags. The bags cost $0.06 each. If these bags of 50 grams of seed sell for $0.98 per bag, what is the profit on a 5-kilogram sack of flax seed?

A $65

B $62

C $33

D $98


A cylindrical piece of pipe insulation is shown below. If the insulation is 0.5 inch thick, what is the approximate volume of insulation used?

F 231 in.3

G 74 in.3

H 41 in.3

J 33 in.3


Only 4 members of the student council attended a meeting, and they greeted one another with handshakes. Each member shook the hand of each of the other members only once, for a total of 6 handshakes. If all 8 student council members had been present and each member had shaken the hand of each of the other members only once, what would have been the total number of handshakes?

F 10

G 21

H 12

J 28


Mrs. Jones has a piece of carpet that is 12 feet long and 2 feet wide. She wants to cut off a section that is 3 feet long and 1 foot wide. She wants to cut up the remaining piece of carpet into 22 pieces that are 1 foot square. Why is this scenario impossible?

F A piece 3 feet long by 1 foot wide cannot be cutfrom the carpet.

G Some pieces of carpet would be left over.

H There is not enough carpet to cut all the pieces.

J The carpet cannot be cut into 1-square-footpieces.


Mike was driving his car at a constant speed of 50 miles per hour. Then he accelerated at a constant rate for 7 seconds. What additional information is needed to determine the speed of the car after 7 seconds?

A The speed of the car prior to acceleration

B The length of time Mike accelerated

C The speed limit

D The rate of acceleration


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


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?



(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

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

B 84

C 87

D 92


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. 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 units2 B 24 units2

C 49 units2 D 96 units2

The two bar graphs shown represent the populations and land areas of four states. Based on the information given in the bar graphs, which of these four states is the least densely populated?

A Indiana

B Louisiana

C Minnesota

D Wisconsin

Correct Answer - C February 2006 #27 Fall 2005 #36

Alfred has some nickels, dimes, and pennies in his pocket that add up to less than a dollar. Alfred has twice as many nickels as dimes and twice as many pennies as nickels. According to this information, what is the greatest possible total value of the coins that Alfred has in his pocket?

A $0.99

B $0.96

C $0.88

D $0.72


Neal has $5 to spend on lunch during a field trip. The restaurant where Neal will have lunch has many items for 99¢ plus tax. If he buys a soft drink for $0.89 plus tax, what is the maximum number of 99¢ items he can still purchase if the tax rate is 7.75%?


Correct Answer - 3 October 2005 #21

The nets of four rectangular prisms are shown. None of these prisms have tops. Which of the following statements is true?

F Figures 1 and 4 have equal volumes.G Figures 2 and 3 have equal lateral surface areas.H Figures 1 and 2 have equal lateral surface areas.J Figures 3 and 4 have equal volumes.


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


A square is shown below. How many of these squares can fit together without any gaps in order to make a similar figure with a perimeter of 24 inches?

A 36

B 32

C 24

D 20


Ms. Dinshaw and Ms. Burke rented a car for 3 days at a cost of $27.00 per day and $0.05 per mile driven. They shared the cost of the car equally. If Ms. Dinshaw paid $46.50, how many miles did they drive?

A 240 mi

B 390 mi

C 690 mi

D 3480 mi


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



(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.

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


Look at the solid sphere and the cylinder containing water shown in Figure 1. Figure 2 shows the sphere submerged in the water inside the cylinder. Which is closest to the height of the water level in Figure 2?

F 13 cm

G 17 cm

H 15 cm

J 11 cm


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


The circle graph below shows the different kinds of garbage collected in the year 2000 according to the Environmental Protection Agency. According to this information, which of the following combinations of items is closest to ⅔ of the garbage collected in the year 2000?

F Paper, food scraps, plastics, and other

G Paper, yard trimmings, food scraps, and metals

H Paper, yard trimmings, plastics, and glass

J Paper, food scraps, plastics, and wood


Taylor drove down the street to the recreation center. He passed a library, then a playground, and finally a hospital before arriving at the recreation center. The library is 1.7 kilometers from the hospital. The playground is 1.5 kilometers from the recreation center and 0.6 kilometer from the hospital. Which of the following best represents the distance from the library to the recreation center?

F 3.8 km

G 2.0 km

H 3.2 km

J 2.6 km


Thalia played a word game in which she had a minute to create 5- and 6-letter words from a given word. The given word was wonderful. Thalia scored 7 points for each 5-letter word she created and 15 points for each 6-letter word she created. Which of the following is not a possible value for the total points Thalia scored?

F 37

G 46

H 58

J 59


On a certain math problem, Cynthia mistakenly divided a number by 4 and then subtracted 24 and got 12 for her answer. After reading the problem again, she realized that she should have subtracted 24 before dividing by 4. What was the correct answer?

A -48

B -28

C 30

D 144

Correct Answer - C July 2006 #55Fall 2005 #51

A ship on the ocean left a dock, traveled 6 miles due north, and then traveled 4 miles due east. Which of the following describes the method for finding the straight-line distance from the ship to the dock?

A Use c = 6 and a = 4 in the equation c2 = a2 + b2 and then solve for bB Use a = 6 and b = 4 in the equation c2 = a2 + b2 and then solve for cC Use a = 6 and b = 4 in the equation c2 = a2 + b2, solve for c, and then find a + b + cD Use c = 6 and a = 4 in the equation c2 = a2 + b2, solve for b, and then find a + b + c


Jesse had a collection of baseball cards. He gave 10 cards to his little brother and equally divided the remaining cards among himself and 3 of his friends. He then had 15 cards. How many baseball cards did Jesse originally have in his collection?

F 20

G 50

H 70

J 100


Mr. Ortega photographed the students in the math club. He arranged the students into 4 parallel rows. Each row had 3 more people than the previous row. If the first 2 rows had a total of 9 people, how many people total were in the group?

F 30

G 27

H 24

J 21

Correct Answer - FFall 2005 #8

October 2005 #7

In ∆XYZ, XY < YZ, and XZ < XY. Which statement must be true?


The horizontal and vertical distances between each of the pegs on the geoboard shown below represent 1 unit. Which is closest to the area of the polygon modeled on the geoboard?

F 36 units2

G 29 units2

H 46 units2

J 24 units2


The radioactive isotope carbon-11 is used in medicine for brain-scan procedures. It decays, losing half its mass every 20 minutes. If a doctor checks on a patient two hours after the isotope has been administered and 0.10 microgram of it still remains, which is closest to the amount of isotope carbon-11 administered to the patient?

F 6 micrograms

G 3 micrograms

H 2 micrograms

J 1 microgram


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


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


Carol wants to solve the equation 3.8x + 2 = 7 − 0.5x by graphing. Which method can she use to find the solution for x?

A Graphing the line y = 3.8x + 2 + 7 − 0.5x and findingthe x-intercept

B Graphing the line y = 3.8x + 2 − 7 + 0.5x and findingthe y-intercept

C Graphing the lines y = 3.8x + 2 and y = 7 − 0.5x andfinding the x-coordinate of the intersection

D Graphing the lines y = 3.8x + 2 and y = 7 − 0.5x andfinding the average of the two x-intercepts


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


(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

The spreadsheet 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


A sports-drink company surveyed 600 athletes to find out if they liked Sports Drink G or Sports Drink P. The diagram shows the results of the survey. Which expression can be used to determine the number of athletes surveyed who did not like either Sports Drink G or Sports Drink P?

A (253 + 211)

B (253 + 79 + 211)

C 600 – (253 + 211)

D 600 – (253 + 79 + 211)


Kimberly and Pam ran a 1-mile race. If k represents the number of seconds Kimberly took to finish the race and p represents the number of seconds Pam took to finish the race, which of the following describes a situation in which Kimberly finished the race before Pam?

A k ≥ p

B k ≤ p

C k > p

D k < p


Look at the diagram below. Which of the following relationships must be true?


If x ◊ y = 2y – x + xy, what is the value of 7 ◊ 4?

F 38

G 28

H 29

J 43


As part of a classroom assignment, Kimberly was given this geoboard to model the slope of ⅔. If the peg in the lower left-hand corner represents the origin on a coordinate plane, where could Kimberly place a rubber band to represent the given slope?

F From peg V to peg W

G From peg V to peg X

H From peg V to peg Y

J From peg V to peg Z


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 ofthe 3 whole numbers


An architect determined the relationship between V, the volume of a sphere, and S, the surface area of the sphere. Which equation represents this relationship?


Nikolay made a fruit drink composed of 36% orange juice. The rest of the fruit drink was grape juice. If Nikolay drank x ounces of the fruit drink, which equation best represents y, the number of ounces of grape juice he drank?


An astronomer mathematically expressed the amount of space occupied by Earth. She reported Earth’s —

F radius

G volume

H surface area

J circumference


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


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 = x3

J y = -x


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?


(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to

(A) make conjectures from patterns or sets of examples and nonexamples;

The figure shows a partial view of Pascal’s triangle. If each square represents a missing number in Pascal’s triangle, which of the following could not be a missing number used to complete the partial view of Pascal’s triangle shown above?

A 24

B 15

C 35

D 10

Correct Answer - A February 2006 #31Fall 2005 #42

The years 707, 1001, and 2332 are examples of palindrome numbers. The year 2002 also represents a palindrome number. What is the nearest year before 2002 that also represents a palindrome number?


Correct Answer - 1991 Fall 2005 #21

Which generalization best describes the pattern shown in the figures below?

F Picking any figure from 2 through 4 and rotating it 90° clockwise will result in the adjacent figure to its right.

G Picking any figure from 2 through 5 and reflecting it across its vertical axis of symmetry will result in the adjacent figure to its left.

H Picking any figure from 2 through 4 and rotating it 90° counterclockwise will result in the adjacent figure to its right.

J Picking any figure from 2 through 5 and reflecting it across its horizontal axis of symmetry will result in the adjacent figure to its left. Correct Answer - H October 2005 #14

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


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)


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


Herman claimed that the square of a number is always greater than or equal to the number. Which of the following examples disproves Herman’s claim?

F A comparison of (-1.5)2 with -1.5

G A comparison of (-0.5)2 with -0.5

H A comparison of (0.5)2 with 0.5

J A comparison of (1.5)2 with 1.5


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.


(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to

(B) validate his/her conclusions using mathematical properties and relationships.

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


Line a intersects line b and line c, as shown. Which of the following angle relationships must be true?

A m 2 + m 6 + m 10 = 180°

B m 3 + m 6 + m 12 = 180°

C m 1 + m 6 + m 11 = 180°

D m 4 + m 6 + m 9 = 180°


Which of the following is a sufficient condition to show that a certain equation does not represent a linear function?

F The graph of the equation has a slope of zero.G The graph of the equation has the set of all real numbers as its domain.H The graph of the equation has an undefined slope.J The graph of the equation has exactly one y intercept.


Points M and N lie on circle P. If circle P has a radius r, which of the following statements cannot be true?

A MN > r

B MN > 2r

C MN = r

D MN = 2r


If JM is a base and LM is a side of isosceles trapezoid JKLM, then which statement must be true?

A JM and KL are parallel.B LM and JK are parallel.C JM and KL are perpendicular.D LM and JM are perpendicular.


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 besupplementary to another

J verifies itself because 90° is 20° more than 70°


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 rectanglehas been cut.

G A 10-inch-long rectangle cannot be cut from thecircular 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.


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11 th Grade TAKS - Released Tests - by Objective

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