# 11th Grade TAKS - Released Tests - by Objective

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11th Grade TAKS - Released Tests - by Objective
1 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
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 A.B1 (A) Correct Answer - B April 2006 #13

Correct Answer - B A π B V C r D
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? A π B V C r D A.B1 (A) Correct Answer - B Fall 2005 #35

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. A.B1 (A) Correct Answer - H October 2005 #36

A department store had a 20%-off sale on all clothing items
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. A.B1 (A) Correct Answer - B April 2004 #55

A(b)(1) Foundations for functions
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. (B) The student [gathers and records data, or] uses data sets, to determine functional (systematic) relationships between quantities.

Correct Answer - G F y = 2x + 1 G y = 2x3 + 1 H y = 2x2 – 3
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 A.B1 (B) Correct Answer - G July 2006 #56

Correct Answer - J F y = x G y = 2x – 1 H y = x2 + x – 1
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 A.B1 (B) Correct Answer - J April 2006 #40

Correct Answer - H F {(-1, -1), (1, 1), (2, 2), (3, 3), (4, 4)}
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)} A.B1 (B) Correct Answer - H February 2006 #44

Which of the following equations best represents the relationship in the set of data shown below?
A.B1 (B) Correct Answer - D February 2006 #57

Correct Answer - G F h = 8.2 + 3.75t G h = 1.12 + 7.82t
The table below shows h, the approximate height of an Ameri-Willow tree after t years. Which equation best fits these data? A.B1 (B) F h = t G h = t H h = t2 J h = t Correct Answer - G Fall 2005 #10

Which of the following graphs does not represent y as a function of x?
A.B1 (B) Correct Answer - C October 2005 #19

Correct Answer - D A y = 3x B x = 3y C x = 3y2 D y = 3x2
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 A.B1 (B) 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 A.B1 (B) 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 A.B1 (B) Correct Answer - G Spring 2003 #28

Correct Answer - D A r = 2n + 1 B n = 2r + 1 C r = n2 + 1 D n = r2 + 1
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 A.B1 (B) Correct Answer - D Spring 2003 #45

A(b)(1) Foundations for functions
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. (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 = t H p = 200t + 7.5 J p = 200t + 7.5t A.B1 (C) Correct Answer - G July 2006 #14

Mitesh is m years old, and his brother Hiren is h years old
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. A.B1 (C) Correct Answer - B July 2006 #37

Correct Answer - A A p = s(19.95 – 4.37) B p = s(19.95 + 4.37)
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 \$ 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( ) C p = s D p = 19.95s – 4.37 A.B1 (C) 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 A.B1 (C) 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 A.B1 (C) 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 = m B c = m C c = m D c = m A.B1 (C) Correct Answer - D October 2005 #49

Correct Answer - A A y = ¾x B y = -¾x C y = x – ¾ D y = x + ¾
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 A.B1 (C) Correct Answer - A April 2004 #1

Correct Answer - A A s = 240,000 – 2000d B s = 240,000 + 2000d
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, d C s = 240,000d – 2000d D s = 240,000d d A.B1 (C) Correct Answer - A July 2004 #1

The Texas Pecan Company ships pecans in wooden boxes
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 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 = – 2.5p J m = p A.B1 (C) 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 = B c = m C c = 40m m D c = 40m A.B1 (C) Correct Answer - B Spring 2003 #11

A(b)(1) Foundations for functions
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. (D) The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

Correct Answer - C A y = x2 + x + 5 B y = x2 + 5 C y = -x2 + 5
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 A.B1 (D) Correct Answer - C July 2006 #17

Which graph best represents the relationship shown in the table below?
A.B1 (D) Correct Answer - G April 2006 #54

Correct Answer - F Which equation best represents the graph below?
A.B1 (D) Correct Answer - F February 2006 #40

Which graph best represents the equation y = 2x2 + 1?
A.B1 (D) Correct Answer - D Fall 2005 #57

Which inequality does the graph shown below best represent?
A.B1 (D) Correct Answer - B October 2005 #9

Which graph best represents the inequality x + 2y ≤ –14?
A.B1 (D) Correct Answer - H April 2004 #20

Correct Answer - F The graph is the solution for which inequality?
A.B1 (D) Correct Answer - F July 2004 #54

Which graph best represents all the pairs of numbers (x, y) such that x + y < –6?
A.B1 (D) Correct Answer - G Spring 2003 #50

A(b)(1) Foundations for functions
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. (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 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 Correct Answer C A.B1 (E) July 2006 #25

Correct Answer - C A 70.1 million B 68.5 million C 74.8 million
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 A.B1 (E) Correct Answer - C April 2006 #59

The total cost, c, of leasing a car can be expressed by the equation c = m, 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. A.B1 (E) Correct Answer - G February 2006 #12

The payroll clerk at an appliance store calculates each salesclerk’s weekly salary using the function f(x) = x, 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 A.B1 (E) Correct Answer - G Fall 2005 #14

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.B1 (E) 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
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? A.B1 (E) Correct Answer - D April 2004 #3

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. A.B1 (E) Correct Answer - B July 2004 #29

Gina did a research project on how age affects sleep patterns
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? A.B1 (E) 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
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.

Correct Answer - D A y = √x B y = x C y = │x│ D y = x2
Which equation is the parent function of a quadratic equation? A y = √x B y = x C y = │x│ D y = x2 A.B2 (A) Correct Answer - D April 2006 #57

Correct Answer - H F Exponential G Absolute value H Linear J Quadratic
The graph below represents which type of parent function? F Exponential G Absolute value H Linear J Quadratic A.B2 (A) 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). A.B2 (A) Correct Answer - C Fall 2005 #23

Correct Answer - H F y = | x | G y = x H y = x2 J y = √x
Which equation is the parent function of the graph represented below? F y = | x | G y = x H y = x2 J y = √x A.B2 (A) Correct Answer - H April 2004 #34

Which type of parent function is represented by the function graphed below?
A Exponential B Absolute value C Linear D Quadratic A.B2 (A) Correct Answer - D July 2004 #15

A(b)(2) Foundations for functions
A(b)(2) Foundations for functions. The student uses the properties and attributes of functions. (B) For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Correct Answer - F F -5 ≤ x < 6 G -6 ≤ x ≤ 2 H -5 ≤ x ≤ -2
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 A.B2 (B) Correct Answer - F April 2006 #12

Correct Answer - H F x ≤ 5 G x ≥ -5 H -5 ≤ x ≤ 5 J 0 ≤ x ≤ 5
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 A.B2 (B) Correct Answer - H February 2006 #50

Correct Answer - G F -3 ≤ x ≤ 6 G -3 < x < 6 H -1 < 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 A.B2 (B) 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 A.B2 (B) Correct Answer - B April 2004 #27

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 A.B2 (B) Correct Answer - D July 2004 #35

A(b)(2) Foundations for functions
A(b)(2) Foundations for functions. The student uses the properties and attributes of functions. (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. A.B2 (C) 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 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? A.B2 (C) Correct Answer - F February 2006 #4

Lisa stayed to talk to her friends for about 5 minutes after school
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 A.B2 (C) 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 A.B2 (C) Correct Answer - D April 2004 #47

Amy is choosing between two local Internet providers, Simple
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. A.B2 (C) 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 A.B2 (C) Spring 2003 #37

A(b)(2) Foundations for functions
A(b)(2) Foundations for functions. The student uses the properties and attributes of functions. (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 more sit-ups the person does weekly. G The older a person is, the more sit-ups the person does weekly. H There is a constant correlation between the age of a person and the number of sit-ups done weekly. J There is no correlation between a person’s age and the number of sit-ups done weekly. A.B2 (D) Correct Answer - J Fall 2005 #48

Correct Answer - J F 77 joules G 92 joules H 110 joules J 128 joules
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 A.B2 (D) Correct Answer - J Spring 2003 #60

A(b)(3) Foundations for functions
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.

Correct Answer - H F 35x + 50(x – 80) G 50x + 35(80 – x)
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) A.B3 (A) Correct Answer - H April 2006 #56

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.B3 (A) Correct Answer - F July 2006 #26

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 – A.B3 (A) 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 \$ 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 A.B3 (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? A.B3 (A) Correct Answer - H October 2005 #42

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 A.B3 (A) Correct Answer - D April 2004 #11

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.B3 (A) Correct Answer - J July 2004 #10

A(b)(3) Foundations for functions
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
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? F √n G (n – 1) + 1 H 2n J n2 A.B3 (B) Correct Answer - J February 2006 #28

Correct Answer - G F 12t G 2t + 10 H 5t + 2 J 12t – 5
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 A.B3 (B) Correct Answer - G Fall 2005 #56

Correct Answer - G F d = 2w H d = 2w – 2 G w = d – 1 J w = ½d + 1
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? A.B3 (B) F d = 2w H d = 2w – 2 G w = d – 1 J w = ½d + 1 Correct Answer - G Spring 2003 #54

A(b)(4) Foundations for functions
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 A.B4 (A) Correct Answer H April 2006 #48

Correct Answer - C A 9 B -6 C -5 D 0
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 A.B4 (A) Correct Answer - C July 2006 #5

Which of the following is equivalent to 2x – 3y ≥ 9?
A.B4 (A) Correct Answer - G February 2006 #18

Correct Answer - H F 3x2 + 12x – 10 G 3x4 + 12x2 – 2 H 3x2 + 12x + 2
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 A.B4 (A) Correct Answer - H Fall 2005 #58

Correct Answer - F F -3.4 G 13.75 H -0.6 J -3.75
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 A.B4 (A) 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. A.B4 (A) Correct Answer - 4 Spring 2003 #21

A(b)(4) Foundations for functions
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.

Correct Answer - F F 3x2 + 18x – 13 G -24x2 – 15x – 17
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 A.B4 (B) Correct Answer - F April 2006 #6

Correct Answer - F F 5a2b – 2ab2 G 31a2b – 28ab2 H a2b + 3ab2
Simplify the algebraic expression F 5a2b – 2ab2 G 31a2b – 28ab2 H a2b + 3ab2 J 15a2b + 18ab2 A.B4 (B) Correct Answer - F July 2006 #44

Which expression is equivalent to ⅔(3x – 15y) + (9y – 11x)?
A -9x – y B 11x – 21y C 10x – 4y D -9x – 26y A.B4 (B) Correct Answer - A April 2004 #41

Simplify the algebraic expression 5(x – 2) + 2(3x2 – 12x + 12).
A -x + 10 B -13x + 14 C 6x2 – 7x + 10 D 6x2 – 19x + 14 A.B4 (B) Correct Answer - D July 2004 #2

Correct Answer - D A n – 1 B 3n2 – 3n C 10n2 – 13n + 2 D 10n2 + n – 2
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 A.B4 (B) Correct Answer - D Spring 2003 #25

Objective 3: The student will demonstrate an understanding of linear functions.

A(c)(1) 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.

Correct Answer - H F y = 4x – 36 G y = 4(x – 36) H y = 36 – 4x
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? F y = 4x – 36 G y = 4(x – 36) H y = 36 – 4x J No linear function exists. A.C1 (A) Correct Answer - H February 2006 #46

Identify the situation that best represents the amount f(n) in the function f(n) = 75 + 80n.
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. A.C1 (A) Correct Answer - G Fall 2005 #2

A(c)(1) 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. (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?
A.C1 (C) Correct Answer - C February 2006 #3

Correct Answer - H F 3x – 2y = -4 G 3x + 2y = -6 H 3x – 2y = 6
Which equation best represents the line on the graph? F 3x – 2y = -4 G 3x + 2y = -6 H 3x – 2y = 6 J 2x – 3y = -6 A.C1 (C) Correct Answer - H July 2004 #40

The algebraic form of a linear function is
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? 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.C1 (C) Correct Answer - F Spring 2003 #16

A(c)(2) Linear functions
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.

Correct Answer - H What is the rate of change of the function y = -7?
J Undefined A.C2 (A) Correct Answer - H April 2006 #52

What is the apparent slope of the line graphed below?
A.C2 (A) Correct Answer - D July 2006 #15

Correct Answer - G What is the slope of the function –6x – 2y = 8? F ⅓
J 3 A.C2 (A) Correct Answer - G February 2006 #52

What are the slope and y-intercept of the equation of the line graphed below?
A.C2 (A) Correct Answer - D April 2004 #13

Find the slope of the line identified by the equation 4x + 5y = 20.
G 5/4 H -4/5 J -4 A.C2 (A) Correct Answer - H July 2004 #26

Correct Answer - B A -3 B -3/2 C 2/3 D 2
What is the slope of the line identified by 2y = -3(x – 2)? A -3 B -3/2 C 2/3 D 2 A.C2 (A) Correct Answer - B Spring 2003 #57

A(c)(2) Linear functions
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. (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? F 40 G 25 H 50 J 30 A.C2 (B) Correct Answer - J July 2006 #58

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. A 50 B 40 C 25 D 20 A.C2 (B) Correct Answer B October 2005 #53

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? A.C2 (B) Correct Answer - C Spring 2003 #43

A(c)(2) Linear functions
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. (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
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? A.C2 (C) Correct Answer - G April 2006 #26

If the slope of the equation is changed to and the y-intercept is changed to (0, -4), which statement best describes this situation? 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. A.C2 (C) Correct Answer - D July 2006 #33

How does the graph of y = 3x + 2 compare to the graph of y = 4x + 2?
F The slope of y = 3x 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. A.C2 (C) Correct Answer - F Fall 2005 #18

If the slope of the function y = -3. 5x + 12. 8 is changed to 1
If the slope of the function y = -3.5x is changed to 1.5, which of the following best describes the graph of the new function? 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. A.C2 (C) Correct Answer - A October 2005 #31

Correct Answer - A A y = -2x + 1 B y = -x + 1 C y = -x – 1
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? A y = -2x + 1 B y = -x + 1 C y = -x – 1 D y = -½x – 1 A.C2 (C) Correct Answer - A April 2004 #17

The line represented by the equation y = (3/2)x + 3 is graphed below
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? A The y-intercept increases. B The y-intercept decreases. C The x-intercept increases. D The x-intercept decreases. A.C2 (C) Correct Answer - C July 2004 #43

Given the function y = 3. 54x – 54
Given the function y = 3.54x – 54.68, which statement best describes the effect of increasing the y-intercept by 33.14? A The new line is parallel to the original. B The new line has a greater rate of change. C The x-intercept increases. D The y-intercept decreases. A.C2 (C) Correct Answer - A Spring 2003 #29

A(c)(2) Linear functions
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. (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)?
A.C2 (D) Correct Answer - J April 2006 #4

Which equation describes the line passing through the points (3, 0) and (0, 4)?
F y = 3x + 4 G x = 4y + 3 H 3x + 4y = 12 J 4x + 3y = 12 A.C2 (D) Correct Answer - J February 2006 #26

Which graph best represents the line that has intercepts at (5, 0) and (0, -4)?
A.C2 (D) Correct Answer - B Fall 2005 #5

What is the equation of the line that passes through the points (-4, 1) and (4, -6)?
A.C2 (D) Correct Answer - F October 2005 #24

Which equation represents the line that passes through the points (-1, 4) and (3, 2)?
A.C2 (D) Correct Answer - F April 2004 #44

Correct Answer - G F f(x) = -3x + 6 G f(x) = -3x + 18
Which function represents the line that contains the point (2, 12) and has a slope of -3? F f(x) = -3x + 6 G f(x) = -3x + 18 H f(x) = -3x + 34 J f(x) = -3x + 38 A.C2 (D) Correct Answer - G July 2004 #42

A(c)(2) Linear functions
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. (E) The student determines the intercepts of linear functions from graphs, tables, and algebraic representations.

Correct Answer - B Find the x- and y-intercepts of -4x + 7y = -28.
A x-intercept: (-4, 0) y-intercept: (0, 7) B x-intercept: (7, 0) y-intercept: (0, -4) C x-intercept: (0, 7) y-intercept: (-4, 0) D x-intercept: (0, -4) y-intercept: (7, 0) A.C2 (E) Correct Answer - B April 2006 #49

What are the coordinates of the x-intercept of the function graphed below?
J (0, -3) A.C2 (E) Correct Answer - F July 2006 #20

What is the y-intercept of the linear function described by the data below?
G (1.25, 0) H (0, -1) J (0, -1.25) A.C2 (E) Correct Answer - F Fall 2005 #20

What are the coordinates of the x-intercept of the equation -3y = 8 – 2x?
G (0, -8/3) H (2/3, 0) J (4, 0) A.C2 (E) Correct Answer - J April 2004 #8

Correct Answer - C A (0, 2) B (0, 5/2) C (0, 5) D (0, 10)
What are the coordinates of the y-intercept of the line represented by the equation 4x + 2y = 10? A (0, 2) B (0, 5/2) C (0, 5) D (0, 10) A.C2 (E) Correct Answer - C July 2004 #3

Correct Answer - C A -24 B -21 C -18 D -9
What is the y-intercept of the function graphed below? A -24 B -21 C -18 D -9 A.C2 (E) Correct Answer - C Spring 2003 #53

A(c)(2) Linear functions
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. (F) The student interprets and predicts the effects of changing slope and y-intercept in applied situations.

Correct Answer - D A \$112 B \$141 C \$143 D \$157
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? A \$112 B \$141 C \$143 D \$157 A.C2 (F) Fall 2005 #27 October 2005 #37 Correct Answer - D

A(c)(2) Linear functions
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. (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?
A.C2 (G) Correct Answer - H April 2006 #28

If y varies directly with x and y is 14 when x is 6, which of the following represents this situation? A.C2 (G) Correct Answer - G July 2006 #42

If y varies directly with x and y is 42 when x is 4, what is the constant of variation expressed in decimal form? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. A.C2 (G) Correct Answer – 10.5 February 2006 #21

Correct Answer - J F \$1.63 G \$2.86 H \$3.01 J \$2.46
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? F \$1.63 G \$2.86 H \$3.01 J \$2.46 A.C2 (G) Correct Answer - J October 2005 #60

Correct Answer - D A 250 m B 175 m C 150 m D 278 m
Matt is a speed skater. His coach recorded the following data during a timed practice period. If matt continues to skate at the rate shown in the table, what is the approximate distance in meters he will skate in 25 seconds? A 250 m B 175 m C 150 m D 278 m A.C2 (G) Correct Answer - D April 2004 #45

Objective 4: The student will formulate and use linear equations and inequalities.

A(c)(3) Linear functions
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? A.C3 (A) Correct Answer - D April 2006 #11

Correct Answer - J F (17 + 26)(x + y) > 300
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 ( )(x + y) > 300 G (17 + x) + (26 + y) > 300 H ( )(x + y) ≤ 300 J 17x + 26y ≤ 300 A.C3 (A) Correct Answer - J July 2006 #52

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? A.C3 (A) Correct Answer - D Fall 2005 #53

Correct Answer - A A x + 6 = ⅔y B x = ⅔y + 6 C x = ⅔(y + 6)
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 A.C3 (A) Correct Answer - A October 2005 #29

Andy drove y miles to work in 0. 5 hour
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 A.C3 (A) Correct Answer - B July 2004 #49

Correct Answer - H F 20(s + e) > 75 G 8s = 75 – 12e H 8s + 12e ≤ 75
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 < s A.C3 (A) Correct Answer - H Spring 2003 #56

A(c)(3) Linear functions
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. (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? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. A.C3 (B) 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?
A.C3 (B) Correct Answer - J July 2006 #30

Correct Answer - D A (4, 0) B (-3, -5) C (7, 2) D (-2, 3)
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) A.C3 (B) Correct Answer - D February 2006 #45

Ms. Barton determined that the total cost of her wedding, c, could be represented by the equation c = 75n , 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 A.C3 (B) Correct Answer - G April 2004 #60

Correct Answer - F F x = -6 G x = -1 H x = 1 J x = 3
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 A.C3 (B) Correct Answer - F July 2004 #20

Anna makes hand-painted plates
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 A.C3 (B) Correct Answer - C Spring 2003 #35

A(c)(3) Linear functions
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. (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
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? A.C3 (C) Correct Answer - B April 2006 #55

Correct Answer - A A 23 gal B 29 gal C 21 gal D 25 gal
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 A.C3 (C) Correct Answer - A July 2006 #59

Hoaung went to a doughnut shop where jelly-filled doughnuts cost \$0
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 A.C3 (C) Correct Answer - C February 2006 #39

Correct Answer - D A (4, 2) B (2, 3) C (5, 2) D (3, 2)
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) A.C3 (C) Correct Answer - D Fall 2005 #41

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 A.C3 (C) Correct Answer - C October 2005 #59

Correct Answer - H F \$118.75 G \$250.00 H \$272.50 J \$290.25
The amount of an employee’s weekly pay, p, including a bonus, can be represented by the inequality 6.00h < 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.C3 (C) Correct Answer - H April 2004 #48

A waitress at a restaurant calculated her daily pay, p, using the equation p = 0.15f , where f is the total amount of food purchased by customers. If the waitress sold between \$ and \$ 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 \$ and \$125.60 A.C3 (C) Correct Answer - J July 2004 #58

Correct Answer - C A (1, 5) B (2, 3) C (1, 3) D (2, 2)
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.C3 (C) Correct Answer - C Spring 2003 #23

A(c)(4) Linear functions
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 \$ from the sales of brownies and cookies. Which system of linear equations can be used to find b, the number of brownies sold, and c, the number of cookies sold? A b + c = 220 0.50b c = B b + c = 0.75b c = 220 C b + c = 0.50b c = 220 D b + c = 220 0.75b c = A.C4 (A) Correct Answer - D April 2006 #1

An investor has a total of 45 one-ounce ingots, made of either gold or silver, worth \$ The value of a gold ingot is \$280.00, and the value of a silver ingot is \$ 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 = g s = B g + s = g s = C g + s = g s = D g – s = g s = 45 A.C4 (A) Correct Answer - B July 2006 #9

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 + 5 w + m = 53 B 2w + m = 5 w + m = 53 C w = m + 5 w + m = 53 D w = 2m + 5 w + m = 53 A.C4 (A) Correct Answer - D February 2006 #51

Correct Answer - F F 2x + y = 38 y = x – 8 G 2x + 2y = 38 y = x – 8
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 = 38 y = x – 8 G 2x + 2y = 38 y = x – 8 H 2x + y = 38 x = y – 8 J 2x + 2y = 38 x = y – 8 A.C4 (A) Correct Answer - F Fall 2005 #16

Lon caught 24 trout and bass while on a fishing trip
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 + b 2.5t + 8b = 137 B t + b = t + 8b = 137 C t + b = t + 8b = 24 D t = b 2.5t + 8b = 24 A.C4 (A) Correct Answer - B October 2005 #1

Correct Answer - H F m + n = 8 m = 3n + 54 G m + n = 8 m = 3n − 54
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 = 8 m = 3n + 54 G m + n = 8 m = 3n − 54 H m + n = 54 m = 3n + 8 J m + n = 54 m = 3n − 8 A.C4 (A) Correct Answer - H April 2004 #40

Correct Answer - D A 2e – u = 220 e – u = -175
The price, e, of an entertainment system at Extreme Electronics is \$220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is \$175. Which system of linear equations can be used to determine the price of the system at each store? A 2e – u = 220 e – u = -175 B 2e – u = 220 e + u = 175 C 2e – 2u = 440 e – u = -175 D e – 2u = e – u = 175 A.C4 (A) Correct Answer - D April 2004 #53

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 find the number of pounds of each kind of raisin needed to produce the mixture? A c + y = 40 1.50c y = 1.35(40) B c + y = 40 150c + 120y = 1.35(40) C c + y = 40 1.20c y = 1.35(40) D c + y = 40 120c + 150y = 1.35(40) A.C4 (A) Correct Answer - A July 2004 #59

At a restaurant the cost for a breakfast taco and a small glass of milk is \$ The cost for 2 tacos and 3 small glasses of milk is \$ 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 = t + 2m = 5.15 B t + m = t + 3m = 5.15 C t + m = t + 2m = 5.15 D t + m = t + 3m = 5.15 A.C4 (A) Correct Answer - D Spring 2003 #3

A(c)(4) Linear functions
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. (B) The student solves systems of linear equations using [concrete] models, graphs, tables, and algebraic methods.

Correct Answer - J F (0, 4) G (8, 1) H (0, -3) J (10, 2)
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.C4 (B) Correct Answer - J April 2006 #32

A large cheese pizza at Palanzio’s Pizzeria costs \$6. 80 plus \$0
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? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. A.C4 (B) 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? A.C4 (B) Correct Answer - B February 2006 #9

Some students want to order shirts with their school logo
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 A.C4 (B) Correct Answer - B Fall 2005 #17

The equations of two lines are 6x − y = 4 and y = 4x + 2
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 A.C4 (B) Correct Answer - B October 2005 #45

Correct Answer - C A (0, 1) B (5, 6) C (6, 7) D No solution
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 A.C4 (B) Correct Answer - C April 2004 #29

Which of the following is the solution for this system of linear equations?
A.C4 (B) Correct Answer - H July 2004 #16

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 A.C4 (B) Correct Answer - G Spring 2003 #46

A(c)(4) Linear functions
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. (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
Maricella has a bag containing 35 nickels and quarters. The total value of these coins is less than \$ What is the maximum number of quarters that meets these conditions? F 10 G 4 H 3 J 9 A.C4 (C) Correct Answer - H February 2006 #34

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.C4 (C) Correct Answer - B Fall 2005 #9

A certain video rental store rents video games for \$4
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. A.C4 (C) 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
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.

Correct Answer - F How does the graph of differ from the graph of ?
A.D1 (B) Correct Answer - F April 2006 #46

The graphs below represent functions of the form y = ax2
The graphs below represent functions of the form y = ax2. In which of the following graphs does a have the smallest value? A.D1 (B) Correct Answer - F July 2006 #12

Which of the following functions of the form y = ax2 produces the widest graph and opens upward?
A.D1 (B) Correct Answer - G February 2006 #2

Correct Answer - H F The graph is translated up.
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. A.D1 (B) Correct Answer - H Fall 2005 #44

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. A.D1 (B) Correct Answer - D October 2005 #3

Which equation will produce the widest parabola when graphed?
A y = 2x2 B y = -6x2 C y = -0.6x2 D y = 0.2x2 A.D1 (B) Correct Answer - D April 2004 #59

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. A.D1 (B) Correct Answer - C July 2004 #51

Which shows the functions correctly listed in order from widest to narrowest graph?
A.D1 (B) Correct Answer - B Spring 2003 #49

A(d)(1) 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. (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
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? A.D1 (C) Correct Answer - D April 2006 #7

Correct Answer - A A y = 0.4x2 + 1 B y = 0.7x2 – 2 C y = 0.4x2 + 5
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 A.D1 (C) Correct Answer - A July 2006 #1

The grid below shows parabolas A and B of the form y = ax2 + c
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 narrower than parabola B. G Parabola A is wider than parabola B. H All the points on parabola A are 7 units below the corresponding points on parabola B. J All the points on parabola A are 7 units above the corresponding points on parabola B. A.D1 (C) Correct Answer - J February 2006 #36

Correct Answer - D A y = -x2 + 3 B y = -x2 – 1 C y = x2 + 5
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 A.D1 (C) Correct Answer - D Fall 2005 #7

Correct Answer - G F y = (x – 3)2 + 1 G y = x2 – 2 H y = x2 + 4
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 A.D1 (C) Correct Answer - G October 2005 #58

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. A.D1 (C) Correct Answer - D July 2004 #5

Correct Answer - C A c > 0 B c < 0 C c = 0 D c = 11
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 A.D1 (C) Correct Answer - C July 2004 #55

Correct Answer - H F The slope of the graph changes.
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. A.D1 (C) Correct Answer - H Spring 2003 #4

A(d)(1) 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. (D) For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.

Correct Answer - C A (0, 3) B (-1, 0) C (1, 4) D (3, 0)
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) A.D1 (D) Correct Answer - C April 2006 #43

Correct Answer - B 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. A.D1 (D) Correct Answer - B July 2006 #51

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. 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. A.D1 (D) 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. 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. 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. Correct Answer - B February 2006 #59

Correct Answer - C A 320 kilojoules B 480 kilojoules C 720 kilojoules
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 A.D1 (D) Correct Answer - C Fall 2005 #31

Correct Answer - J F 1 sec G 9 sec H 7 sec J 6 sec
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.D1 (D) Correct Answer - J April 2004 #4

A(d)(2) Quadratic and other nonlinear functions
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
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) A.D2 (A) Correct Answer - G February 2006 #6

Correct Answer - F F {-3, 0.25} G {-3.47, 0.72} H {3, -0.25}
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} A.D2 (A) Correct Answer - F Fall 2005 #24

Correct Answer - A A -4 and 6 B -3 and 2 C 4 and -6 D -2 and 3
What are he zeros of the following function? A -4 and 6 B -3 and 2 C 4 and -6 D -2 and 3 A.D2 (A) Correct Answer - A October 2005 #43

Correct Answer - A F 5°C G 7°C H 10°C J 12°C
The completion of a certain chemical reaction is expressed by the equation y = x - 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 A.D2 (A) Correct Answer - A April 2004 #37

Correct Answer - H F Between 0 seconds and 0.5 second
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 seconds J Between 1 second and 1.5 seconds and between 1.5 seconds and seconds A.D2 (A) Correct Answer - H July 2004 #6

What is the solution set for the equation 4(3x – 2)2 = 36?
A.D2 (A) Correct Answer - C Spring 2003 #47

A(d)(2) Quadratic and other nonlinear functions
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) A.D2 (B) Correct Answer - H April 2006 #18

Correct Answer - A A (x + 6)(x – 2) = y B (x – 2)(x – 16) = y
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 A.D2 (B) Correct Answer - A July 2006 #53

Correct Answer - D A -4 and -3 B -3 and -2 C -2 and -1 D -1 and 0
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 A.D2 (B) Correct Answer - D October 2005 #25

Which ordered pair represents one of the roots of the function f(x) = 2x2 + 3x – 20?
A.D2 (B) Correct Answer - G April 2004 #42

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.D2 (B) Correct Answer - B Spring 2003 #15

A(d)(3) Quadratic and other nonlinear functions
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.

Correct Answer - G What is the simplified form of ? April 2006 #16
A.D3 (A) Correct Answer - G April 2006 #16

The mass of Earth is close to 5
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 A.D3 (A) Correct Answer - A July 2006 #23

Jupiter has an equatorial diameter of about 8
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 A.D3 (A) Correct Answer - H February 2006 #22

Correct Answer - F F 18a6b5c4 G -18a6b3c3 H 18a6b9c4 J -8a6b5c4
Which expression best represents (3a2b3c)(-3ab)(-2a3bc3)? F 18a6b5c4 G -18a6b3c3 H 18a6b9c4 J -8a6b5c4 A.D3 (A) Correct Answer - F Fall 2005 #4

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 A.D3 (A) Correct Answer - J October 2005 #4

Correct Answer - J F 1152 j13k20 units G 152j13k20 units
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 A.D3 (A) Correct Answer - J April 2004 #54

Correct Answer - G F 5x + 6 G 2x2 + 3x H 4x2 + 12x J 4x + 12
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 A.D3 (A) Correct Answer - G July 2004 #36

Which expression best represents the simplification of (3m-2n4)(-4m6n-7)?
A.D3 (A) 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
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
Look at the cube shown below. Which equation best represents the area of the shaded rectangle located diagonally in the cube? G.B4 (A) Correct Answer - D April 2006 #19

Correct Answer - B A bc – ef B af + ad – de C de + af + ad D af + cd
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 G.B4 (A) Correct Answer - B April 2006 #33

Correct Answer - J F 4n2 G 4n H 2n J n2
The polygon RSTU is shown below. Which expression represents the area of this polygon? F 4n2 G 4n H 2n J n2 G.B4 (A) Correct Answer - J July 2006 #24

Shown below is ∆LMN, an isosceles triangle
Shown below is ∆LMN, an isosceles triangle. Which equation can be used to find the measure of the vertex angle of this isosceles triangle? G.B4 (A) Correct Answer - B February 2006 #43

Mitch drew lines l, k, and t. Lines l and k were parallel to each other. Mitch measured 2 alternate interior angles. He labeled the angles 1 and 2. Which of the following shows angles 1 and 2 correctly labeled? G.B4 (A) 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?
G.B4 (A) Correct Answer - G October 2005 #48

In ∆ABC, m BAC = (6x + 3)° and m ABC = (3x – 6)°
In ∆ABC, m BAC = (6x + 3)° and m ABC = (3x – 6)°. Which equation can be used to find m BCA? G.B4 (A) Correct Answer - B October 2005 #55

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 G.B4 (A) Correct Answer - A April 2004 #7

Correct Answer - J F 100°, 100°, and 160° G 100°, 100°, and 100°
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° G.B4 (A) Correct Answer - J July 2004 #52

Correct Answer - G F y = 90 + x G y = 90 – x H y = 180 – x
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 G.B4 (A) Correct Answer - G Spring 2003 #24

Find the equation that can be used to determine the total area of the composite figure shown below.
G.B4 (A) Correct Answer - A Spring 2003 #51

G(c)(1) Geometric patterns
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 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? G.C1 (A) Correct Answer - H April 2006 #38

Look at the figures and the table below
Look at the figures and the table below. How many triangles will the nth stage contain? G.C1 (A) Correct Answer - G July 2006 #54

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. G.C1 (A) Correct Answer - F February 2006 #10

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 G.C1 (A) February 2006 #13

Parallelogram MPQR is shown below
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 G.C1 (A) Correct Answer - C Fall 2005 #29

Correct Answer - C A (n – 1)n – 1 B (2n – 1)2 C 3n – 1 D n2
According to the table, which expression best represents the number of white triangles at any stage, n, in this geometric pattern? A (n – 1)n – 1 B (2n – 1)2 C 3n – 1 D n2 G.C1 (A) Correct Answer - C October 2005 #33

Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides. G.C1 (A) Correct Answer - C April 2004 #5

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? G.C1 (A) Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Correct Answer - 140 April 2004 #21

On the map below, First Ave and Second Ave are parallel
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° G.C1 (A) Correct Answer - G Spring 2003 #2

Correct Answer - J F 2n G 2n H 2n – 1 J 2n – 1
The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain? F 2n G 2n H 2n – 1 J 2n – 1 G.C1 (A) Correct Answer - J Spring 2003 #34

G(c)(1) Geometric patterns
G(c)(1) Geometric patterns. The student identifies, analyzes, and describes patterns that emerge from two- and three-dimensional geometric figures. (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
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 G.C1 (B) Correct Answer - H April 2006 #8

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° G.C1 (B) Correct Answer - A July 2006 #19

Correct Answer - A A T to U B S to V C W to V D Z to W
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 G.C1 (B) Correct Answer - A July 2006 #31 Fall 2005 #25

Correct Answer - A A 101° B 79° C 54° D 43°
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° G.C1 (B) Correct Answer - A February 2006 #23

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 G.C1 (B) Correct Answer - H Fall 2005 #32

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° G.C1 (B) Correct Answer - B October 2005 #27

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 grid What fraction of the 1-unit-by-1-unit square is shaded after the second iteration? G.C1 (B) Correct Answer - C July 2004 #23

G(c)(1) Geometric patterns
G(c)(1) Geometric patterns. The student identifies, analyzes, and describes patterns that emerge from two- and three-dimensional geometric figures. (C) The student identifies and applies patterns from right triangles to solve problems, including special right triangles ( and ) 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 is closest to the length of the hose in the garden? A 7.8 ft B 9.5 ft C 6.4 ft D 5.5 ft G.C1 (C) Correct Answer - B April 2006 #15

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 G.C1 (C) Correct Answer - A April 2006 #39

A diagonal walkway through a park is 18 meters long
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 G.C1 (C) Correct Answer - B July 2006 #27

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 G.C1 (C) Correct Answer - J July 2006 #46

In ∆PKN, PN = 14 inches, m N = 30°, and m K = 90°
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. G.C1 (C) Correct Answer - G February 2006 #38

In the figure below, circle M and circle R intersect at point P
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 G.C1 (C) Correct Answer - G Fall 2005 #22

The area of this regular polygon is 72 in2
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. G.C1 (C) Correct Answer - A Fall 2005 #39

∆TCL is shown below. If TL = 12 inches, what is the area of ∆TCL?
G.C1 (C) Correct Answer - C October 2005 #13

In the figure shown below, ∆MPQ ~ ∆PQR, MR = 45 units, and RQ = 15 units. What is the length of PR?
G.C1 (C) Correct Answer - G October 2005 #52

Correct Answer - H F 110 ft G 127 ft H 156 ft J 311 ft
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 G.C1 (C) Correct Answer - H April 2004 #12

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. G.C1 (C) Correct Answer - B April 2004 #19

Correct Answer - F F 44 units2 G 110 units2 H 88 units2 J 55 units2
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 G.C1 (C) Correct Answer - F April 2004 #46

Correct Answer - A A 16 ft2 B 32 ft2 C 24 ft2 D 40 ft2
Find the area of triangle RST. A 16 ft2 B 32 ft2 C 24 ft2 D 40 ft2 G.C1 (C) Correct Answer - A July 2004 #7

Correct Answer - D ∆WXY is a right triangle. Find the length of WY.
G.C1 (C) Correct Answer - D July 2004 #17

In the figure below, what is the length of ML in cm?
G.C1 (C) Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Correct Answer - 117 July 2004 #21

Correct Answer - J F 1.7 ft G 18 ft H 10.4 ft J 6 ft
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 G.C1 (C) Correct Answer - J July 2004 #38

A fence around a square garden has a perimeter of 48 feet
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 G.C1 (C) Correct Answer - G Spring 2003 #20

Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet
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.C1 (C) Correct Answer - H Spring 2003 #30

G(e)(3) Congruence and the geometry of size
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.

Correct Answer - G 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 then translated 4 units down to become parallelogram W’B’M’P’, what will be the coordinates of M’? F (-6, -7) G (6, -1) H (6, 7) J (6, 3) G.E3 (A) Correct Answer - G April 2006 #36

Correct Answer - D A (6, -4) B (4, -5) C (5, -5) D (6, -5)
The graph shows quadrilateral TUVW, KN, and KL. At what coordinate point should vertex M be placed to make quadrilateral KLMN congruent to quadrilateral TUVW? A (6, -4) B (4, -5) C (5, -5) D (6, -5) G.E3 (A) Correct Answer - D July 2006 #7

Correct Answer - D A ∆KLM ∆PNM B ∆KRM ∆PQM C ∆KRM ∆PNM D ∆KLM ∆KRM
Look at the triangles graphed on the grid below. Which of the following correctly describes two triangles, one a single reflection of the other across the x-axis? A ∆KLM ∆PNM B ∆KRM ∆PQM C ∆KRM ∆PNM D ∆KLM ∆KRM G.E3 (A) Correct Answer - D February 2006 #19

Look at the triangle graphed on the coordinate grid below
Look at the triangle graphed on the coordinate grid below. Which coordinates are the vertices of a triangle congruent to this figure? 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) G.E3 (A) Correct Answer - A Fall 2005 #11

Correct Answer - B A M’(-2, -6) B P’(3, 8) C P’(4, -7) D M’(-7, -3)
∆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) G.E3 (A) Correct Answer - B October 2005 #17

Correct Answer - J F A and C G B and D H A and B J B and C
Which pair of the following polygons is congruent? F A and C G B and D H A and B J B and C G.E3 (A) Correct Answer - J April 2004 #10

Which coordinates are the vertices of a triangle congruent to ∆MNP?
J (-15,14), (-18,17), (-17,22) G.E3 (A) Correct Answer - G July 2004 #50

Figure MNPQ is shown on the coordinate plane
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 G.E3 (A) Correct Answer - D Spring 2003 #27

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
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?
G.D1 (B) Correct Answer - C April 2006 #31

Which net best represents the hexagonal prism shown below?
G.D1 (B) Correct Answer - J July 2006 #4

The net below can be folded to form a cube
The net below can be folded to form a cube. Which cube could be formed from this net? G.D1 (B) Correct Answer - H Fall 2005 #6 October 2005 #26

Correct Answer - J F Faces R and S are parallel.
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. G.D1 (B) Correct Answer - J April 2004 #38

The net shows the surface of a 3-dimensional figure
The net shows the surface of a 3-dimensional figure. Which 3-dimensional figure does this net represent? G.D1 (B) Correct Answer - B Spring 2003 #1

G(d)(1) Dimensionality and the geometry of location
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? G.D1 (C) Correct Answer - H April 2006 #14

The illustration shows a 3-dimensional view of a screw
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? G.D1 (C) Correct Answer - G April 2006 #60

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? G.D1 (C) Correct Answer - G July 2006 #60

The figure shown is a cube with a corner sliced off
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? G.D1 (C) Correct Answer - H February 2006 #8

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? G.D1 (C) Correct Answer - D February 2006 #49 Fall 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? G.D1 (C) Correct Answer - D October 2005 #57

Which of the following best represents the front view of the solid shown below?
G.D1 (C) Correct Answer - D April 2004 #15

The front, side, and top views of a solid built with cubes are shown
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 G.D1 (C) Correct Answer - B July 2004 #39

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.D1 (C) Correct Answer - G Spring 2003 #44

G(d)(2) Dimensionality and the geometry of location
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.

Correct Answer - C A DF + FQ + QR = DR B DQ + QR = DR C DQ + FR = DR
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 G.D2 (A) Correct Answer - C April 2006 #9

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) G.D2 (A) Correct Answer - B July 2006 #43

Correct Answer - H F y – x G x + y H a + x J x – a
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 G.D2 (A) Correct Answer - H February 2006 #20

Correct Answer - C A (4, 2) B (2, 4) C (2, 1) D (1, 2)
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) G.D2 (A) 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 G.D2 (A) Correct Answer - H October 2005 #46

A hexagon is graphed on the coordinate grid
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) G.D2 (A) Correct Answer - J April 2004 #50

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 J G.D2 (A) July 2004 #60

Correct Answer - G F Rectangle G Rhombus H Trapezoid J Square
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 G.D2 (A) Correct Answer - G Spring 2003 #58

G(d)(2) Dimensionality and the geometry of location
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. (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 of the equation ?
G.D2 (B) Correct Answer - B April 2006 #45

∆RST is a right triangle
∆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? G.D2 (B) Correct Answer - G July 2006 #40

A right triangle has two vertices with coordinates (0, 3) and (4, 1)
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) G.D2 (B) Correct Answer - C February 2006 #35

Correct Answer - G F 6x – 2y = -8 and 3x+ y = -4
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 G.D2 (B) Correct Answer - G Fall 2005 #52

Correct Answer - B A (0, -8) B (0, -2) C (0, 2) D (0, 8)
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) G.D2 (B) Correct Answer - B October 2005 #39

Correct Answer - J F The lines have the same y-intercept.
Which of the following best describes the graph of the equations below? 2y =3x + 2 4y = 6x + 1 F The lines have the same y-intercept. G The lines have the same x-intercept. H The lines are perpendicular. J The lines are parallel. G.D2 (B) Correct Answer - J April 2004 #16

Line q is shown. Which equation best represents a line parallel to line q?
G.D2 (B) Correct Answer - D April 2004 #57

Correct Answer - G F 2x + 5y = 6 and 5x + 2y = 10
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 G.D2 (B) Correct Answer - G July 2004 #8

Correct Answer - H F The lines have the same x-intercept.
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. G.D2 (B) Correct Answer - H July 2004 #18

Which graph best represents a line parallel to the line with the equation y = 3x + 4?
G.D2 (B) Correct Answer - J Spring 2003 #6

Which graph best represents the line passing through the point (0, 4) and perpendicular to y = –½x?
G.D2 (B) Correct Answer - F Spring 2003 #36

G(d)(2) Dimensionality and the geometry of location
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. (C) The student [develops and] uses formulas, including distance and midpoint.

Correct Answer - C A 3.1 units B 4.3 units C 6.1 units D 12.2 units
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 G.D2 (C) Correct Answer - C April 2006 #25

What is the approximate distance between points (-7, 2) and (11, -5)?
A units B units C units D 8.06 units G.D2 (C) Correct Answer - B July 2006 #11

The midpoint of the diagonals of rectangle PTQW is (-0. 5, 1)
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) G.D2 (C) Correct Answer D July 2006 #57

Correct Answer - A A (-5, -5) B (2, -10) C (-3¼, -1½) D (-5, 5)
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) G.D2 (C) Correct Answer - A February 2006 #17

Correct Answer - A A (-5.5, 3) B (-9.5, 9.25) C (-11, 6) D (-19, 18.5)
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) G.D2 (C) Correct Answer - A Fall 2005 #59 October 2005 #16

Rectangle MNPQ has diagonals that intersect at point X
Rectangle MNPQ has diagonals that intersect at point X. What are the coordinates of point X? G.D2 (C) Correct Answer - F April 2004 #56

Correct Answer - G F 2.4 units G 4.5 units H 10.8 units J 17.2 units
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 G.D2 (C) Correct Answer - G July 2004 #14

Correct Answer - H F (2, -1) G (4, -2) H (5, -1) J (10, -2)
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) G.D2 (C) Correct Answer - H July 2004 #34

A coordinate grid is placed over a map
A coordinate grid is placed over a map. City A is located at (–3, 2), and City B is located at (4, 8). If City C is at the midpoint between City A and City B, which is closest to the distance in coordinate units from City A to City C? A 4.61 units B 6.52 units C 9.22 units D units G.D2 (C) Correct Answer - A Spring 2003 #19

G(e)(2) Congruence and the geometry of size
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 G.E2 (D) Correct Answer - J April 2006 #10

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 G.E2 (D) Correct Answer - B July 2006 #47

Which set of figures can be used to construct a representation of the surface area of the triangular prism shown below? G.E2 (D) Correct Answer - G February 2006 #24

Correct Answer - J F Cone G Sphere H Cylinder J Hemisphere
Which of the following describes a solid with 1 base and no vertices? F Cone G Sphere H Cylinder J Hemisphere G.E2 (D) Correct Answer - J Fall 2005 #30

Which set of figures can be used to construct a representation of the surface area of the solid shown? G.E2 (D) Correct Answer - B Fall 2005 #47

Which of these 3-dimensional figures has the following characteristics: 12 faces, 8 vertices, and 18 edges? G.E2 (D) Correct Answer - H October 2005 #10

Correct Answer - F F A triangular prism and a square pyramid
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 G.E2 (D) Correct Answer - F April 2004 #24

Correct Answer - H F 4 faces, 6 edges, and 4 vertices
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 G.E2 (D) Correct Answer - H Spring 2003 #14

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
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
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 G.E1 (A) Correct Answer - A April 2006 #35

Correct Answer - G F 57.9 yd2 G 76.8 yd2 H 115.9 yd2 J 154.5 yd2
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 yd2 J yd2 G.E1 (A) Correct Answer - G July 2006 #6

Linda has divided her garden into 3 parts as shown
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 G.E1 (A) Correct Answer - A February 2006 #47

The figure shows a triangle on top of a rectangle
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 G.E1 (A) Correct Answer - C Fall 2005 #43

Correct Answer - H F 42 ft2 G 30 ft2 H 39 ft2 J 24 ft2
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 G.E1 (A) Correct Answer - H October 2005 #44

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 G.E1 (A) Correct Answer - D April 2004 #43

Correct Answer - G F 9 cm2 G 21 cm2 H 25 cm2 J 69 cm2
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 G.E1 (A) Correct Answer - G July 2004 #46

G(e)(1) Congruence and the geometry of size
G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to find area, perimeter, and volume in problem situations. (B) The student finds area of sectors and arc lengths of circles using proportional reasoning.

Correct Answer - J 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? F 545 mm G 157 mm H 22 mm J 44 mm G.E1 (B) Correct Answer - J April 2006 #22

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 in. B in. C 4.32 in. D 2.16 in. G.E1 (B) Correct Answer - C July 2006 #45 Fall 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 G.E1 (B) Correct Answer - G February 2006 #56

Correct Answer - A What is the approximate length of arc PQ? A 13 cm
B 98 cm C 94 cm D 7 cm G.E1 (B) Correct Answer - A October 2005 #35

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. G.E1 (B) Correct Answer - J April 2004 #52

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 G.E1 (B) Correct Answer - C July 2004 #4

G(e)(1) Congruence and the geometry of size
G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to find area, perimeter, and volume in problem situations. (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 G.E1 (C) Correct Answer - H April 2006 #2 Fall 2005 #3

Which of the following sets of numbers represents the side lengths in units of a right triangle?
G.E1 (C) Correct Answer - B July 2006 #29

Mr. Krueger attended an event at the Good Time Sports Arena
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 to his parked car. About how far away was his parked car from the exit at point D? F 200 ft G 403 ft H 492 ft J 650 ft G.E1 (C) Correct Answer - G February 2006 #16

Correct Answer - J F 7 inches G 20 inches H 12 inches J 9 inches
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 G.E1 (C) Correct Answer - J October 2005 #40

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? G.E1 (C) Correct Answer - D April 2004 #25

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 G.E1 (C) Correct Answer - A April 2004 #51

Correct Answer - A A 20 mi B 30 mi C 35 mi D 60 mi
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 G.E1 (C) Correct Answer - A July 2004 #25

Correct Answer - D 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 G.E1 (C) Correct Answer - D July 2004 #41

The total area of trapezoid FGHJ is 52 square inches
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. G.E1 (C) Correct Answer - B Spring 2003 #41

G(e)(1) Congruence and the geometry of size
G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to find area, perimeter, and volume in problem situations. (D) The student finds surface area and volumes of prisms, pyramids, spheres, cones, and cylinders in problem situations.

Correct Answer - A A 121 ft2 B 181 ft2 C 154 ft2 D 91 ft2
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 G.E1 (D) Correct Answer - A April 2006 #27

Correct Answer - A A 11,000 cm2 B 22,000 cm2 C 36,000 cm2 D 9,000 cm2
Mrs. Wong has a bookcase shaped like an isosceles trapezoid. The height of the bookcase is approximately 150 centimeters. The other dimensions are shown. Which of the following is closest to the surface area of the top, left, and right rectangular sides of Mrs. Wong’s bookcase? A 11,000 cm2 B 22,000 cm2 C 36,000 cm2 D 9,000 cm2 G.E1 (D) Correct Answer - A February 2006 #7

Correct Answer - H F 255 ft3 G 122 ft3 H 98 ft3 J 28 ft3
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 G.E1 (D) Correct Answer - H Fall 2005 #46

Mr. Martinez bought a solid-glass globe with a stand
Mr. Martinez bought a solid-glass globe with a stand. If the diameter of the globe is 7 centimeters, which is closest to the volume of glass in the globe? A 51 cm3 B 180 cm3 C 154 cm3 D 101 cm3 G.E1 (D) Correct Answer - B October 2005 #41

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 G.E1 (D) Correct Answer - H July 2004 #30

Correct Answer - H F 471 cm3 G 566 cm3 H 1413 cm3 J 5655 cm3
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.E1 (D) Correct Answer - H Spring 2003 #42

G(f)(1) Similarity and the geometry of shape
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
A parallelogram is graphed on the grid. Which set of coordinates identifies the vertices of a similar figure? Correct Answer H G.F1 (A) 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) February 2006 #30

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 G.F1 (A) Correct Answer - J April 2004 #6

Which statement best describes why pentagon PQRST is similar to pentagon VWXYZ?
A The ratio of the length of PT to YZ equals the ratio of the length of RS to WV. B Both pentagons have corresponding right angles. C Pentagon VWXYZ is the result of a translation of pentagon PQRST. D The ratio of the corresponding sides of pentagons PQRST and VWXYZ is 2:1. G.F1 (A) Correct Answer - D July 2004 #9

Use the information in each diagram to find the pair of similar polygons.
G.F1 (A) Correct Answer - B Spring 2003 #13

G(f)(1) Similarity and the geometry of shape
G(f)(1) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. (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 square units B 87.5 square units C square units D square units G.F1 (B) Correct Answer - A April 2006 #51

In 2002, people in Laredo, Texas, erected the tallest flagpole in the United States. It can be seen from miles away. According to the information shown in the drawing, what is the approximate height of the flagpole? (The drawing is not drawn to scale.) A 308 feet B 295 feet C 205 feet D 197 feet G.F1 (B) Correct Answer - A July 2006 #39

Troy used chalk to outline a triangular plot of land in his backyard
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. G.F1 (B) Correct Answer - H February 2006 #14

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? G.F1 (B) Correct Answer - J Fall 2005 #38 October 2005 #32

A rectangle has a length of 4 feet and a perimeter of 14 feet
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 G.F1 (B) Correct Answer - B April 2004 #23

In ∆STR, QP and TR are parallel
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 G.F1 (B) Correct Answer - B July 2004 #33

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 G.F1 (B) Correct Answer - D Spring 2003 #39

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

Correct Answer - H F 15 ft2 G 30 ft2 H 60 ft2 J 120 ft2
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 G.F1 (C) Correct Answer - H July 2006 #10

Correct Answer - H F 15.52 in. G 9.81 in. H 7.79 in. J 12.04 in.
If ∆KLM ~ ∆RST, which is closest to the length of ST? F in. G 9.81 in. H 7.79 in. J in. G.F1 (C) Correct Answer - H Fall 2005 #12

In the figure, ∆QNP ~ ∆PQH, and NM = 12. 5 centimeters
In the figure, ∆QNP ~ ∆PQH, and NM = 12.5 centimeters. What is the area of ∆PQN? A cm2 B cm2 C cm2 D cm2 G.F1 (C) Correct Answer - A October 2005 #47

G(f)(1) Similarity and the geometry of shape
G(f)(1) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. (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. G.F1 (D) Correct Answer - B April 2006 #3

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? 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. G.F1 (D) Correct Answer - H July 2006 #32

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 G.F1 (D) Correct Answer - H February 2006 #32

Correct Answer - C A 37 cm2 B 113 cm2 C 1,923 cm2 D 24,542 cm2
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 G.F1 (D) Correct Answer - C Fall 2005 #55 October 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. G.F1 (D) Correct Answer - F April 2004 #26

A rectangular solid has a volume of 24 cubic decimeters
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 G.F1 (D) Correct Answer - A Spring 2003 #33

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
(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.

Correct Answer - F F 2.18 joules G 1.68 joules H 3.02 joules
The energy of a certain particle is 3.86 joules. If this particle loses 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 8.3 (B) Correct Answer - F April 2006 #42

Correct Answer - D A 53% B 60% C 38% D 63%
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% 8.3 (B) Correct Answer - D July 2006 #35

Correct Answer - A A \$4275.34 B \$5947.07 C \$2115.93 D \$1371.75
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 \$ in a week, what was the amount of his sales for the week? A \$ B \$ C \$ D \$ 8.3 (B) Correct Answer - A July 2006 #41

Correct Answer - D A 27% B 24% C 53% D 47%
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% 8.3 (B) Correct Answer - D February 2006 #5

Correct Answer - B A \$960 B \$1200 C \$1128 D \$1410
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 8.3 (B) Correct Answer - B Fall 2005 #37

Correct Answer - B A \$35,300 B \$29,700 C \$32,500 D \$26,000
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 8.3 (B) Correct Answer - B October 2005 #5

Correct Answer - B A Between 180 mph and 185 mph
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 8.3 (B) Correct Answer - B April 2004 #35

Amber is making a patchwork quilt using 3 different types of fabric
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. 8.3 (B) Correct Answer - B April 2004 #39

Correct Answer - D A 67% B 75% C 78% D 80%
This year’s price for a certain car is 25% higher than last year’s price of \$ What percent of this year’s price is last year’s price? A 67% B 75% C 78% D 80% 8.3 (B) Correct Answer - D July 2004 #37

Correct Answer - B A \$2000 B \$3125 C \$5200 D \$8125
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 8.3 (B) Correct Answer - B July 2004 #53

Correct Answer - G F 17% G 30% H 43% J 70%
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 \$ 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% 8.3 (B) Correct Answer - G Spring 2003 #18

(8. 11) Probability and statistics
(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? 8.11 (A) Correct Answer - A February 2006 #25

The jar contains 24 solid-colored marbles of equal size
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 first marble will be blue and the second will be white? 8.11 (A) Correct Answer - G October 2005 #22

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? 8.11 (A) Correct Answer - H April 2004 #2

Jamal has a game with 2 groups of tiles
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 (A) Correct Answer - F April 2004 #14

(8. 11) Probability and statistics
(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
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 8.11 (B) Correct Answer - J April 2006 #34

A basketball player made 12 free throws in his last 36 attempts
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 8.11 (B) Correct Answer - G July 2006 #2

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 8.11 (B) Correct Answer - C February 2006 #1

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 8.11 (B) Correct Answer - G Fall 2005 #60

A high school is changing its school colors
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 8.11 (B) Correct Answer - F October 2005 #20

Marcos has a spinner with 12 equal sections colored either blue or red
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 8.11 (B) Correct Answer - H July 2004 #28

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 8.11 (B) Correct Answer - F Spring 2003 #26

(8. 12) Probability and statistics
(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;

Correct Answer - B A Mean B Median C Mode D Range
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 8.12 (A) Correct Answer - B April 2006 #23

Correct Answer - F F Mode G Mean H Range J Median
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 8.12 (A) Correct Answer - F Fall 2005 #40

Correct Answer - H F Mean G Median H Mode J Range
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 (A) Correct Answer - H Spring 2003 #8

(8. 12) Probability and statistics
(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? 8.12 (C) Correct Answer - D April 2006 #53

Correct Answer - B A W B X C Y D Z
An orange-drink label reads “20% real fruit juice.” The other ingredients are water, sugar, and flavoring. Which section of the circle graph best represents the amount of real fruit juice in the orange drink? A W B X C Y D Z 8.12 (C) Correct Answer - B Fall 2005 #45

The senior class at Lambert High School raised \$950 for a class trip
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 \$ H The bake sale earned \$ J School logo mugs earned \$209. 8.12 (C) Correct Answer - H October 2005 #8

Correct Answer - C A 270° B 75° C 54° D 15°
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° 8.12 (C) Correct Answer - C Spring 2003 #5

(8. 13) Probability and statistics
(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 Linda competed in a biathlon consisting of running and swimming events. The table shows the number of seconds each of them took to complete the parts of the competition. The top rankings are awarded to the individuals with the fastest combined times. Based on the information in the table, which event probably determined the outcome of the competition? Correct Answer B 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 8.13 (B) April 2006 #5

A physical education class had 20 students
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 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. 8.13 (B) Correct Answer - D July 2006 #49

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. 8.13 (B) Correct Answer - C Fall 2005 #13

The table shows the monthly sales at a pizza parlor for a 6-month period. Which is the best inference that can be made from the table? A January had the lowest sales. B The period with the greatest increase in monthly sales was 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. 8.13 (B) Correct Answer - C October 2005 #51

The table shows the cost of fertilizer, depending on the amount purchased. Which conclusion can be made based on the information in the table? A The cost of 10 pounds of fertilizer would be more than \$4.00. B The cost of 200 pounds of fertilizer would be less than \$57.00. C The cost of fertilizer is always more than \$0.35 per pound. D The cost of fertilizer is always less than \$0.30 per pound. 8.13 (B) Correct Answer - B April 2004 #49

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. 8.13 (B) Correct Answer - D July 2004 #47

In a survey of 80 nutritionists, 8 said they eat tacos
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. 8.13 (B) Correct Answer - H Spring 2003 #38

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
(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;

Correct Answer - B A \$4.00 B \$1.50 C \$3.00 D \$13.50
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 8.14 (A) Correct Answer - B April 2006 #41

The owners of Crispy Sweet Doughnut Shop want to open a shop centrally located to the police station, the high school, the fire station, and the factory. Based on the information given, which of the following points best represents the location where the new Crispy Sweet Doughnut Shop should open? F (9, 12) G (5, 13) H (6, 10) J (8, 13) 8.14 (A) 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 8.14 (A) Correct Answer - B July 2006 #3