9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions.

9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions 3Linear functions 4Linear equations and inequalities 5Quadratic and other nonlinear functions 6Geometric relationships and spatial reasoning 7Two- and three-dimensional representations of geometric relationships and shapes 8Concepts and uses of measurement and similarity 9Percents, proportional relationships, probability, and statistics in application problems 10Mathematical processes and tools used in problem solving

Objective 1: The student will describe functional relationships in a variety of ways.

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (A) describe independent and dependent quantities in functional relationships;

If y is a function of x in the equation y = ½x + 9, which statement is true? A The dependent variable, y, is 9 more than ½ the independent variable, x. B The independent variable, y, is 9 more than ½ the dependent variable, x. C The dependent variable, x, is 9 more than ½ the independent variable, y. D The independent variable, x, is 9 more than ½ the dependent variable, y. Correct Answer - A 2008 Released Item

To find c, the total cost of an order of DVDs from a certain website, the equation c = 19.99n + 4.99 can be used, where n represents the number of DVDs ordered. If c is a function of n, which of the following best describes this relationship? A The value of n is constant in relation to c. B The value of n is dependent on c. C The value of c is constant in relation to n. D The value of c is dependent on n. Correct Answer - D April 2006 #41

For a car traveling at a speed of 50 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function d = 50t. Which statement is true? F The time traveled depends on the distance traveled. GThe distance traveled depends on the time traveled. H The speed of the car depends on the distance traveled. J The speed of the car depends on the time traveled. Correct Answer - G Spring 2003 #42

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (B) [gather and record data and] use data sets to determine functional relationships between quantities;

In many parades, flowers are used to decorate the floats. The table below shows the number of flowers used in each row of a parade float. Which equation best describes these data? An = 2r + 52 Bn = r + 54 Cn = 4r + 50 Dn = 4r + 54 Correct Answer - C April 2006 #25

Which equation could be used to generate this table of values? Ay = -2x By = 2x + 1 Cy = x + 1 Dy = x 2 + 1 Correct Answer - D April 2004 #41

Which equation best describes the relationship between the corresponding values of x and y shown in the table? Fy = x – 10 Gy = 2x – 8 Hy = 3x – 6 Jy = x 2 – 8 Correct Answer - H April 2004 #50

Students in a science class recorded lengths of a stretched spring, as shown in the table below. Which equation best represents the relationship between distance stretched, x, and the weight on the spring, y? Correct Answer - D Spring 2003 #49

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (C) describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

Kimberly wants to complete at least 2/3 of her algebra problems by 8 P.M. If she has x algebra problems to complete, which inequality can Kimberly use to determine y, the number of algebra problems she wants to complete by 8:00 P.M.? Ay ≥ x – 2/3 By < x + 2/3 Cy < 2/3x D y ≥ 2/3x Correct Answer - D 2008 Released Item

Mr. Ross is purchasing a table and chairs for $1350, including tax and interest. He will pay for the furniture with monthly payments of $75. If Mr. Ross has made m payments, which equation best describes r, the amount of the remaining balance? Fr = (1350 – 75)m Gr = 75m + 1350 Hr = 1350 – 75m Jr = 75m - 1350 Correct Answer - H April 2006 #30

The temperature in degrees Celsius, C, is 5/9 of the difference between the temperature in degrees Fahrenheit, F, and the constant 32. Which equation best represents this relationship? April 2004 #27 Correct Answer C

The Alejo family budgeted $2000 for their vacation. Their budget consisted of $800 for travel costs and $75 per day for other expenses. Which inequality represents the number of days, x, the family could have stayed on vacation? A800 + 75x ≤ 2000 B800x + 75 ≥ 2000 C800x – 75 ≥ 2000 D800 – 75x ≤ 2000 Correct Answer - A Spring 2003 #45

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (D) represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

Which inequality best describes the graph shown below? Correct Answer - D April 2006 #5

Jerome received a gift card for $20 worth of video rentals from a video store. If the cost of renting a video is $2.50, which table best describes b, the balance remaining on the gift card after he rents n videos? Correct Answer F April 2004 #24

Correct Answer G Spring 2003 #24 The function f(x) = {(1,2), (2,4), (3,6), (4,8)} can be represented in several other ways. Which is NOT a correct representation of the function f(x)?

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (E) interpret and make decisions, predictions, and critical judgmentsfrom functional relationships.

The kinetic energy of a car can be described by the function KE = ½mv 2, in which the constant m is the mass of the car and v is the car’s velocity. If the velocity keeps increasing, the kinetic energy will – Aremain constant Bcontinually increase Cincrease and the become constant Ddecrease to zero 2008 Released Item Correct Answer – B

The graph below represents Lynne’s car trip from her house to the mall and then back to her house. If each section of the graph represents part of Lynne’s trip, which part of the trip took the least amount of time? ArBpCqDsArBpCqDs April 2006 #37 Correct Answer C

Which graph best represents the relationship between the height of a burning candle and the amount of time that passes as the candle burns? Correct Answer J April 2004 #46

Which is always a correct conclusion about the quantities in the function y = x +4? AThe variable x is always 4 more than y. BWhen the value of x is negative, the value of y is also negative. CThe variable y is always greater than x. DAs the value of x increases, the value of y decreases Correct Answer - C Spring 2003 #25

Objective 2: The student will demonstrate an understanding of the properties and attributes of functions.

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

Which graph below best represents the parent function of a quadratic function? Correct Answer - D 2008 Released Item

Which graph below best represents the linear parent function? Correct Answer - J April 2006 #22

Which is the best representation of the function y = x? Correct Answer - B Spring 2003 #7

(A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (B) identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

The perimeter of an equilateral triangle is 36 meters or less. Which set describes the domain for l, the length of one side of the triangle? Correct Answer - C 2008 Released Item A{0 < l ≤ 3} B {0 < l ≤ 6} C {0 < l ≤ 12} D {0 < l ≤ 36}

(A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (C) interpret situations in terms of given graphs [or create situations that fit given graphs];

Look at the graph. Which is the best interpretation of this graph? AJorge earns $20 for each hour worked. BFor every 10 pieces of candy Stacey buys, she pays $1. CFor every 10 students at a dance, 2 teachers are needed as chaperones. DA runner runs at a constant rate of 2 miles every 30 minutes. Correct Answer - B April 2006 #51

Which statement is true for the graph below? A Ms. Goodlett will earn $500 if she sells $5000 worth of merchandise. B Mr. Murphy will not earn any money if he does not sell any merchandise. C Mr. Laster will earn $1000 if he sells $1000 worth of merchandise. D Ms. Cho will earn $700 if she sells $5000 worth of merchandise. Correct Answer - D April 2004 #47

Identify the graph that best represents the relationship between the number of gallons of gasoline Mr. Johnson purchased at $1.49 a gallon and the total cost of his gasoline. Correct Answer - F Spring 2003 #48

(A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (D) [collect and] organize data, [make and] interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

The graph shows the relationship between the distance in miles a delivery truck traveled and the number of hours each delivery took. Which best describes the relationship shown in the graph? ANegative trend BPositive trend CConstant trend DNo trend Correct Answer - B April 2006 #33

Monica collected data on the ages and heights of a random sample of sixth-, seventh-, and eighth- grade students at her school. If she plots the data on a scatterplot, what relationship will she most likely see between age and height? AA negative correlation BNo correlation CA positive correlation DA constant correlation Correct Answer - C Spring 2003 #11

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

Ronald wants to buy a shirt that is on sale for 15% off the regular price. The regular price of the shirt is p dollars. Which expression represents the sale price of the shirt? Fp – 0.15p Gp + 0.15p Hp – 15p J0.15p Correct Answer - F April 2006 #6

A class consists of 8 freshmen and 22 sophomores. Freshmen had an average of x points on a test, while the sophomores had an average of y points. Which expression gives the average test score per student for the entire class? Correct Answer - A April 2004 #45

A large room has the dimensions shown below. A partition is to be installed so that 2 classes can use it. The area of the smaller classroom is 38x. How can the area of the larger classroom be expressed in terms of x? Correct Answer - D Spring 2003 #19

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

Sue wants to write an expression that will always produce an even integer. Which of the following will always produce an even integer for any given integer, n? A2n + 1 B2n – 1 Cn + 2 D2n Correct Answer - D April 2004 #43

(A.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. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations.

Given the function f(x) = 3x 2 – 7, what is the value of f(-3)? A-25 B-34 C74 D20 Correct Answer - D 2008 Released Item

Tammy drew a floor plan for her kitchen, as shown below. Which expression represents the area of Tammy’s kitchen floor in square units? F6x 2 + 30x + 5G6x 2 + 13x + 5 H10x + 12J5x + 6 Correct Answer - G April 2006 #16

The area of a rectangle is 3x 2 + 14x + 8, and the width is x + 4. Which expression best describes the rectangle’s length? F3x + 2 G2x + 4 H2x + 2 J3x - 2 Correct Answer - F April 2004 #16

The area of a rectangle is given by the equation 2l 2 – 5l = 18, in which l is the rectangle’s length. What is the length of the rectangle? F1.5 G2 H4.5 J6 Correct Answer - H Spring 2003 #46

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

Simplify the algebraic expression 3(x + 3) – 2(x + 3). Fx + 3 Gx – 3 H-6x 2 – 54 J6x 2 + 3 Correct Answer - F April 2004 #20

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

(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: (A) determine whether or not given situations can be represented by linear functions;

(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: (C) use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

The table below shows various values for x and y. Which equation best describes the relationship between x and y? Correct Answer - A April 2006 #15 Ay = -3x + 5 By = -5x – 7 Cy = -x + 17 Dy = 3x + 41

Which function includes the data set {(2, 4), (6, 6), (12, 9)}? Correct Answer - D April 2004 #13 Ay = 2x By = x/2 Cy = 2x - 9 Dy = x/2 + 3

A math club decided to buy T-shirts for its members. A clothing company quoted the following prices for the T-shirts. Which equation best describes the relationship between the total cost, c and the number of T-shirts, s? Correct Answer - D Spring 2003 #41 Ac = 6.75s Bc = 7.00s Cc = 2s - 20 Dc = 15 + 6s

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

What is the slope of the line described by the equation 8x + 12y = – 18? Correct Answer - A 2008 Released Item A –2/3 B –3/2 C –2/3 D –3/2

What is the slope of the line that contains the coordinate points (8, -3) and (-2, 7)? Correct Answer - A April 2006 #17 A-1 B-9/11 C-5/3 D-2/5

What is the slope of the linear function shown in the graph? Correct Answer - B April 2004 #19

In the distance formula, d = rt, r represents the rate of change, or slope. Which ray on the graph best represents a slope of 55 mph? Correct Answer - A Spring 2003 #39 AWBXCYDZAWBXCYDZ

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (B) interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

The cost of renting a car for 1 day at Cars Plus is $20 plus 10 cents per mile driven. The cost of renting a car for 1 day at Need-A-Car is $20 plus 15 cents per mile driven. In a graph of the cost of a car rental, what does the cost per mile driven represent? Correct Answer - C 2008 Released Item AThe x-intercept BThe y-intercept CThe slope DThe point of intersection

A small business purchased a van to handle its delivery orders. The graph below shows the value of this van over a period of time. Which of the following best describes this situation? Correct Answer - B April 2006 #11 AThe van was purchased for $1,600. BThe van decreases in value by $1,600 per year. CThe van increases in value by $1,600 per year. DThe van has no value after 5 years.

The line segment on the graph shows the altitude of a landing airplane from the time its wheels are lowered to the time it touches the ground. Which of the following best describes the slope of the line segment? Correct Answer - G April 2004 #34 F The plane descends about 1 foot per 8 seconds. G The plane descends about 8 feet per second. H The plane descends about 1 foot per 2 seconds. J The plane descends about 2 feet per second

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (C) investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

The graph of a linear function is shown on the coordinate grid below. If the y-intercept is changed to (0, 5) and the slope becomes -4, which statement best describes the relationship between the two lines when they are graphed on the same coordinate grid? Correct Answer G April 2006 #12 F The y-intercepts are 1 unit apart, and the lines are parallel. G The y-intercepts are 1 unit apart, and the lines intersect at (1, 1). H The y-intercepts are 1 unit apart, and the lines are perpendicular. J The y-intercepts are 1 unit apart, and the lines intersect at (1, 0).

The graph of a line that contains the points (-1, -5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? Correct Answer - G Spring 2003 #18

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (D) graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

Which equation describes a line that has a y-intercept of 5 and a slope of ½? Correct Answer - F April 2004 #10

Which linear function includes the points (-3, 1) and (-2,4)? Correct Answer - F Spring 2003 #44

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (E) determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

The ordered pairs in the table are contained in the graph of a linear function. What are the x- and y- intercepts of the graph of this linear function? Correct Answer - D 2008 Released Item Ax-intercept: (2, 0) y-intercept: (0, -3) Bx-intercept: (0, -3) y-intercept: (-2, 0) Cx-intercept: (0, 2) y-intercept: (-3, 0) Dx-intercept: (-3, 0) y-intercept: (0, -2)

Which of the following ordered pairs is the x-intercept or the y-intercept of the function 2x – y = 8? Correct Answer - C April 2006 #19 A(8, 0) B(0, 4) C(4, 0) D(0, 8)

What are the x- and y-intercepts of the function graphed below? Correct Answer - G April 2004 #42 F(4, 0) and (5, 0) G(4, 0) and (0, 5) H(0, 4) and (5, 0) J(0, 4) and (0, 5)

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (F) interpret and predict the effects of changing slope and y-intercept in applied situations;

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected: (G) relate direct variation to linear functions and solve problems involving proportional change.

The amount of chlorine, y, needed for a swimming pool varies directly with the amount of water, x, needed to fill the pool. If 16 units of chlorine are needed for every 1250 gallons of water, which of the following represents the equation of direct variation? Correct Answer - A 2008 Released Item

On a certain day the exchange rate of Mexican pesos for U.S. dollars was approximately 10 pesos for 1 dollar. If an exchange of 4,000 pesos was made that day, what was the approximate value of the exchange in dollars? Correct Answer - G Spring 2003 #2 F$40 G$400 H$4,000 J$40,000

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

(A.7) Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

Joan went to a department store to buy a sweater that was on sale for 25% off the original price, p. Which equation can be used to determine s, the sale price of the sweater, not including tax? As = p + 0.75p B s = p + 0.25p C s = p – 0.75p D s = p – 0.25p Correct Answer - D 2008 Released Item

Brandon has a budget of $58 to spend on clothes. The shirts he wants to buy are on sale for $9 each, and the pair of pants he wants costs $21. All prices include tax. Which inequality could be used to determine s, the maximum number of shirts Brandon can buy if he also buys the pair of pants? F21s + 9 < 58 G9s + 21 ≤ 58 H30s < 58 J9s – 21 ≤ 58 Correct Answer - G April 2006 #38

A weather balloon is launched from a height of 475 feet above sea level. If the balloon rises at a constant rate of 85 feet per minute, which equation could be used to determine t, the time in minutes it will take the balloon to reach a height of 9245 feet above sea level? A9245 = 85 + 475t B9245 = 85(t + 475) C9245 = 475 + 85t D9245 = (475 + 85)t Correct Answer - C April 2004 #7

The number of hours Abe practices golf each week, g, is 2 more than the number of hours he runs, r. Which equation represents the number of hours he runs each week? Fr = g – 2 Gg = r – 2 Hg = 2r Jr = g + 2 Correct Answer - F Spring 2003 #30

Passengers on many commercial flights may make calls from a telephone provided by the airline. On a certain airline a call costs $3 to connect plus $2 for each minute. Which equation best represents c, the total cost for a call that lasts m minutes? Fm = 3 + 2c Gc = 3 + 2m Hm = 2 + 3c Jc = 2 + 3m Correct Answer - G Spring 2003 #50

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

If (-7, y) is a solution to the equation 2x – 7y – 42 = 0, what is the value of y? A-4 B-8 C-3.5 D-6.7 Correct Answer - B 2008 Released Item

If (x, -3.2) is a solution to the equation 4x = 5y – 17, what is the value of x? F0.84 G0.25 H-5.96 J-8.25 Correct Answer - J April 2006 #10

If (x, -4) is a solution to the equation 4x – 5y = 8, what is the value of x? A-4.8 B-3 C1.6 D7 Correct Answer - B April 2004 #17

The graphs of the linear equations y = 2x – 3 and y = 3x – 7 are shown below. If 2x – 3 = 3x – 7, what is the value of x? F4 G5 H9 J10 Correct Answer - F April 2004 #36

Auto-Check Motors charged Mr. Jones $84.00 for an automotive part plus $68.00 per hour that a mechanic worked to install the part. The total charge was $353.00. For about how long did the mechanic work to install the part on Mr. Jones’s car? F6 h G5 h H4 h J3 h Correct Answer - H Spring 2003 #8

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

Harris has $20.92 to spend on video-game rentals at a local video store. The store charges $3.95 per video-game rental plus an 8.125% tax. What is the maximum number of video games that Harris can rent? A5B4C6D3A5B4C6D3 Correct Answer - B April 2006 #27

A florist plans to sell bouquets for $25 each. He wants to use only roses and carnations in each bouquet and needs to charge the following amount for each type of flower. $1.50 per rose $1.25 per carnation Which of these combinations of roses and carnations will result in bouquets that the florist can sell for exactly $25 each? I. 18 roses and 2 carnations II. 6 roses and 10 carnations III. 10 roses and 8 carnations IV. 5 roses and 14 carnations FI and II only GII and III only HIII and IV only JI and IV only Correct Answer - H April 2006 #52

A recycling center pays $0.35 per pound of glass that it receives. If students at Falcon High School want to raise $500 in a glass-recycling project, what is a reasonable number of pounds of glass they must collect? A750 lb B175 lb C500 lb D1500 lb Correct Answer - D April 2004 #5

The cost of renting a DVD at a certain store is described by the function f(x) = 4x + 3 in which f(x) is the cost and x is the time in days. If Lupe has $12 to spend, what is the maximum number of days that she can rent a single DVD if tax is not considered? F1G2H3J7F1G2H3J7 Correct Answer - G Spring 2003 #40

(A.8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations and formulate systems of linear equations in two unknowns to solve problems.

The perimeter of a rectangular volleyball court is 180 feet. The court’s width, w, is half its length, l. Which system of linear equations could be used to determine the dimensions, in feet, of the volleyball court? Correct Answer - B 2008 Released Item

The perimeter of a rectangular wooden deck is 90 feet. The deck’s length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck? F2l + 2w = 90 l = 5 – 4w G 2l + 2w = 90 l = 5w – 4 H 2l + 2w = 90 l = 4 – 5w J 2l + 2w = 90 l = 4w – 5 Correct Answer - J April 2006 #32

The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. Which system of equations could be used to find the number of sundaes, s, and banana splits, b, that the shop sold that day? A2s + 3b = 156 s = b + 8 B2b + 3s = 156 s + b = 8 C2s + 3b = 8 s = b + 156 D2s + 3b = 156 b – s = 8 Correct Answer - A April 2004 #39

Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Mr. Kitts sold a total of 108 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week? Al + t = 108 t = 3l + 6 Bl + t = 108 t = 3l -6 Cl + t = 108 l = 3t – 6 Dl + t = 108 l = 3t + 6 Correct Answer - D Spring 2003 #13

Objective 5: The student will demonstrate an understanding of quadratic and other nonlinear functions.

(A.9) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to: (C) investigate, describe, and predict the effects of changes in c on the graph of y = x 2 + c.

The graph of f(x) and g(x) are shown on the grid below. If f(x) = x 2 + 3, what is the equation for g(x)? Correct Answer - D 2008 Released Item Ag(x) = x 2 + 7 B g(x) = x 2 + 2.5 C g(x) = x 2 – 4 Dg(x) = x 2 – 7

The graph of a function is shown below. If the graph is translated 7 units down, which of the following best represents the resulting graph? Correct Answer - D April 2006 #1

The graph of the function y = x 2 – 3 is shown below. If the graph of the original function is shifted 5 units up, which of the following equations best represents the translation of each point on the curve? Fy = x 2 + 5 Gy = x 2 + 2 Hy = x 2 – 2 Jy = x 2 – 8 Correct Answer - G April 2006 #46

How would the graph of the function y = x 2 + 4 be affected if the function were changed to y = x 2 + 1? FThe graph would shift 3 units up. GThe graph would shift 3 units down. HThe graph would shift 3 units to the right. JThe graph would shift 3 units to the left. Correct Answer - G April 2004 #2

Which graph shows a function y = x 2 + c when c < -1? Correct Answer - G April 2004 #8

In the graph of the function y = x 2 + 5, which describes the shift in the vertex of the parabola if, in the function, 5 is changed to -2? A3 units up B7 units up C3 units down D7 units down Correct Answer - D Spring 2003 #9

When graphed, which function would appear to be shifted 2 units up from the graph of f(x) = x 2 + 1? Fg(x) = x 2 – 1 Gg(x) = x 2 + 3 Hg(x) = x 2 – 2 Jg(x) = x 2 + 2 Correct Answer - G Spring 2003 #52

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

Which expression is equivalent to (-5abc 4 )(-3a 3 c 2 )(-4a 2 b 4 c 3 )? A-12a 6 b 5 c 9 B-12a 6 b 4 c 24 C-60a 6 b 5 c 9 D-60a 9 b 9 c 9 Correct Answer - C 2008 Released Item

For all real numbers m and n, which of the following statements is always true? A(2m) 4 = 8m 4 B(m 3 )(m 4 ) = m 3+4 C(m 4 n 3 ) 2 = m 6 n 5 D (3m 3 )(n 3 ) = (3mn) 3 Correct Answer - B 2008 Released Item

Which expression represents the area of a rectangle with sides measuring 2x 2 y 4 z units and 5xy 4 z 3 units? F7x 2 y 8 z 3 units 2 G7x 3 y 8 z 4 units 2 H10x 3 y 8 z 4 units 2 J10x 2 y 8 z 3 units 2 Correct Answer - H April 2006 #34

What is the simplified form of ? Correct Answer - D April 2006 #47

Which expression is equivalent to A4x9B4x2C2x8D2x4A4x9B4x2C2x8D2x4 Correct Answer - B April 2004 #9

If y = x 3, what is equivalent to x 12 ? Fy 36 Gy 15 Hy 9 Jy 4 Correct Answer - J April 2004 #44

Which expression describes the area in square units of a rectangle that has a width of 4x 3 y 2 and a length of 3x 2 y 3 ? F12x 6 y 6 G12y 5 x 5 H7x 6 y 6 J7x 5 y 5 Correct Answer - G Spring 2003 #10

The area of a rectangle is 30m 11 n 5 square units. If the length of the rectangle is 6m 4 n 2 units, how many units wide is the rectangle? (m ≠ 0 and n ≠ 0) A5m 7 n 3 units B24m 7 n 3 units C36m 15 n 7 units D180m 15 n 7 units Correct Answer - A Spring 2003 #27

Objective 6: The student will demonstrate an understanding of geometric relationships and spatial reasoning.

(8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to (A) generate similar shapes using dilations including enlargements and reductions;

The two figures shown below are similar. Which scale factor was used to transform the smaller figure to the larger figure? Correct Answer - B 2008 Released Item

∆AHP ~ ∆ENK as shown below. Which scale factor was used to transform ∆AHP to ∆ENK? Correct Answer - G April 2006 #20

∆DFG has vertices D(2, 4), F(4, 8), and G(6, 4). ∆DFG is dilated by a scale factor of ¼ and has the origin as the center of dilation. What are the coordinates of F’? Correct Answer - F April 2004 #18

∆MNP ~ ∆RST is shown below. Which scale factor was used to transform ∆MNP to ∆RST? A1/3 B1/2 C2/7 D5 Correct Answer - C April 2004 #31

The pentagon in the graph below is to be dilated by a scale factor of 1/3. Which graph shows this transformation? Correct Answer - H Spring 2003 #32

(8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to (B) graph dilations, reflections, and translations on a coordinate plane.

Point L under the translation (x + 5, y – 3) becomes point L’. Which point on the grid will have the same coordinates as point L’? APoint N BPoint P CPoint T DPoint R Correct Answer - C 2008 Released Item

∆LMN has vertices L(a, b), M(r, s), and N(u, v). What will be the new coordinates of point M if the triangle is translated 7 units to the right and 3 units down? F(r + 3, s – 7) G(r + 7, s – 3) H(r – 7, s + 3) J(r – 3, s + 7) Correct Answer - G April 2006 #40

Triangle XYZ is translated so that X is mapped to X’. Which coordinate pair best represents Y’? Correct Answer - H April 2004 #6 F(-3, -8) G(2, -7) H(2, -6) J(2, -2)

∆RST is shown on the coordinate plane below. Find the coordinates of the vertices of the image of ∆RST reflected across the y-axis. A (-2, -3), (-4, -6), (-5, -1) B (2, 3), (4, 6), (5, 1) C (0, 3), (-2, 6), (-3, 1) D (2, -3), (4, -6), (5, -1) Correct Answer - B Spring 2003 #47

(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (D) locate and name points on a coordinate plane using ordered pairs of rational numbers.

Which point on the graph satisfies the conditions that x > 1½ and y > 2½? APoint S BPoint T CPoint U DPoint V Correct Answer - B 2008 Released Item

Points K and L are shown on the grid below. If point K is the midpoint of JL, what are the coordinates of endpoint J? F(6, -5) G(-6, 7) H(0, 1) J(-4, 5) Correct Answer - G April 2006 #2

Which point on the grid below best represents the coordinates ? APoint K BPoint M CPoint R DPoint U Correct Answer - A April 2006 #39

∆KLM has coordinates K (−8, 3), L (−4, 1), and M (−2, 7). What will be the new coordinates of point M if the triangle is translated 4 units to the right and 3 units down? F(0, -2) G(2, 4) H(-4, 0) J(-6, 4) Correct Answer - G April 2004 #52

Which circle has a center located at coordinates (-3, 2)? Correct Answer - D Spring 2003 #3

Jake made a map of his neighborhood for a school project. He placed a grid over the map. Which coordinate point best represents the post office? A(6, 12) B(12, 6) C(1.2, 0.6) D(0.6, 1.2) Correct Answer - D Spring 2003 #43

Objective 7: The student will demonstrate an understanding of two- and three- dimensional representations of geometric relationships and shapes.

(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (A) draw three-dimensional figures from different perspectives;

The drawing below shows a 3-dimensional structure built from identical cubes. Which of the following does not represent a top, front, or right-side view of this 3- dimensional structure? Correct Answer - D 2008 Released Item

The drawing below shows both the top view of a solid structure built with identical cubes as well as the number of cubes in each column of the structure. Correct Answer - F April 2006 #4

The drawing below shows a solid with hexagonal bases. Which drawing best represents the top view of this hexagonal solid? Correct Answer - H April 2006 #48

The drawing shows a 3-dimensional solid. Which best represents the shape of the solid when viewed from the top? FPentagon GHexagon HHeptagon JOctagon Correct Answer - G April 2004 #4

Match the three views of this solid to its 3-dimensional sketch. Correct Answer F Spring 2003 #12

(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (B) use geometric concepts and properties to solve problems in fields such as art and architecture;

The dimensions on the blueprints of Mrs. Dunn’s house are proportional to the house’s actual dimensions. The blueprints show the house’s rectangular foundation to be 5.5 inches wide by 9 inches long. If the foundation actually measures 36 feet long, what is the width in feet of the actual foundation? Correct Answer - 22 2008 Released Item Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Olga plans to take a trip from her house in San Marcos, Texas, to a friend’s house in Zapata, Texas. She measured the distance between the two places on a map and found it to be 8 inches. If the scale on the map is ½ inch represents 14 miles, which is closest to the actual distance in miles between the two places? F112 mi G224 mi H56 mi J44 mi Correct Answer - G April 2006 #8

An artist made a drawing of a house with a tree next to it. The drawing is 1/18 the size of the actual house and tree. The tallest point of the house is 12 feet 8 inches, and the tree is 27 feet tall. How many inches tall is the tree in the drawing? F8.4 in. G18 in. H23.4 in. J486 in. Correct Answer - G April 2004 #30

Ms. Hill wants to carpet her rectangular living room, which measures 14 feet by 11 feet. If the carpet she wants to purchase costs $1.50 per square foot, including tax, how much will it cost to carpet her living room? A$50 B$75 C$154 D$231 Correct Answer - D April 2004 #49

A lawn is shaped like a parallelogram with a base of 32 feet and a height of 15 feet. Covering the lawn with grass will cost $2.60 per square foot. How much money will it cost to cover the lawn with grass? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Correct Answer - 1248 Spring 2003 #21

A 12- by 16-foot rectangular floor will be covered by square tiles that measure 2 feet on each side. If the tiles are not cut, how many of them will be needed to cover the floor? A192 B96 C48 D14 Correct Answer - C Spring 2003 #31

(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (C) use pictures or models to demonstrate the Pythagorean Theorem.

The drawing below shows how 3 squares can be joined at their vertices to form a right triangle. What is the area in square centimeters of the largest square? A37 cm 2 B210 cm 2 C420 cm 2 D1369 cm 2 Correct Answer - D 2008 Released Item

Look at the drawing shown below. If ∆KMP is a right triangle formed by the placement of 3 squares, what is the area of the shaded square? A135 in. 2 B24 in. 2 C66 in. 2 D81 in. 2 Correct Answer - C April 2006 #23

The drawing below shows 3 square parking lots that enclose a grassy area shaped like a right triangle. If Lot A’s perimeter is 300 yards and Lot B’s perimeter is 400 yards, what is the perimeter of Lot C? A500 yd B700 yd C1400 yd D2000 yd Correct Answer - A April 2004 #33

What is the area of the largest square in the diagram? F 5 square units G 9 square units H 16 square units J 25 square units Correct Answer - J Spring 2003 #14

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

(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to (A) find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two- dimensional models);

Look at the cylinder shown below. What is the total surface area of this cylinder in terms of π? A273π ft 2 B371π ft 2 C322π ft 2 D956π ft 2 Correct Answer - B 2008 Released Item

The net of a cube is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cube to the nearest tenth of a centimeter. Which is closest to the total surface area of the cube represented by this net? A74 cm 2 B11 cm 2 C43 cm 2 D12 cm 2 Correct Answer - A April 2006 #9 Like April 2004 #35 0 1 2 3 4

The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest ⅛ inch. Which is closest to the total surface area of this cylinder? F4 in. 2 G11 in. 2 H14 in. 2 J25 in. 2 Correct Answer - H Spring 2003 #26 0 1 2 3 4

(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to (B) connect models of prisms, cylinders, pyramids, and cones to formulas for volume of these objects;

The net of a cube is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cube to the nearest tenth of a centimeter. Which best represents the volume of this cube to the nearest cubic centimeter? A11 cm 3 B13 cm 3 C30 cm 3 D42 cm 3 Correct Answer - A Spring 2003 #29 0 1 2

(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to (C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

Mrs. Lee bought a small rectangular box that contains 10 tightly packaged erasers shaped like rectangular prisms, as shown below. What is the approximate volume in cubic centimeters of this rectangular box? F19 cm 3 G97 cm 3 H192 cm 3 J513 cm 3 Correct Answer - H April 2006 #14

The student council members are making decorative labels to cover 20 identical empty coffee cans for a charity drive. Each label will cover the entire lateral surface area of a can. Which is closest to the lateral surface area of a single coffee can? A186 in. 2 B157 in. 2 C195 in. 2 D128 in. 2 Correct Answer - D April 2006 #31

A cylindrical water tank has a radius of 2.8 feet and a height of 5.6 feet. The water tank is filled to the top. If water can be pumped out at a rate of 36 cubic feet per minute, about how long will it take to empty the water tank? F3 h G2 h H4 min J1 min Correct Answer - H April 2004 #22

A 72-inch piece of wire was cut into equal segments, which were then soldered at the ends to form the edges of a cube. What is the volume of the cube? A216 in. 3 B576 in. 3 C729 in. 3 D1728 in. 3 Correct Answer - A Spring 2003 #37

(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to (A) use the Pythagorean Theorem to solve real-life problems;

The drawing below shows Jeremy’s mailbox and the brace he used to secure it to the post. If the length of the brace is approximately 18 inches, which is closest to x, the distance between the bottom of the mailbox and the point on the post where Jeremy secured the brace? A17 in. B25 in. C19 in. D11 in. Correct Answer - A 2008 Released Item

Mr. Carpenter built a wooden gate, as shown below. Which is closest to the length in feet of the diagonal board that Mr. Carpenter used to brace the wooden gate? A4.9 ft B5.3 ft C6.1 ft D6.9 ft Correct Answer - B April 2006 #35

A square park has a diagonal walkway from 1 corner to another. If the walkway is about 38 yards long, what is the approximate length of each side of the park? F6 yd G19 yd H27 yd J54 yd Correct Answer - H April 2004 #26

In a town, there is a small garden shaped like a triangle, as shown below. The side of the garden that faces Sixth Street is 80 feet in length. The side of the garden that faces Third Avenue is 30 feet in length. What is the approximate length of the side of the garden that faces Elm Street? F35 ft G40 ft H85 ft J110 ft Correct Answer - H Spring 2003 #38

(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to (B) use proportional relationships in similar two-dimensional figures or three-dimensional figures to find missing measurements.

What is the length of YZ if ΔRST is similar to ΔXYZ? A1.2 units B7.5 units C10 units D18 units Correct Answer - B 2008 Released Item

∆MNQ is similar to ∆MLP. If ML = 10 centimeters, what is the length of MN? F6.25 cm G8.3 cm H7.5 cm J4 cm Correct Answer - F April 2006 #44

If ΔTSR is similar to ΔTNM, what is the length of x? Correct Answer - B April 2004 #1 A240 units B140 units C120 units D70 units

Kate has 2 similar triangular pieces of paper, as shown below. Using the dimensions given, find the approximate length of the side labeled p. F2.4 cm G7.3 cm H16.5 cm J19.6 cm Correct Answer - G Spring 2003 #6

(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to (A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally;

If the dimensions of a rectangle are tripled, which of the following best describes an effect on the rectangle? A The new area will be 3 times as large as the original area. B The new area will be 9 times as large as the original area. C The new perimeter will be 1.5 times as large as the original perimeter. D The new perimeter will be 9 times as large as the original perimeter. Correct Answer - B 2008 Released Item

If the dimensions of a rectangle are doubled, which of the following best describes an effect on the rectangle? F The new area will be 2 times as large as the original area. G The new area will be 8 times as large as the original area. H The new perimeter will be 4 times as large as the original perimeter. J The new perimeter will be 2 times as large as the original perimeter. Correct Answer - J April 2006 #26

Tony and Edwin each built a rectangular garden. Tony’s garden is twice as long and twice as wide as Edwin’s garden. If the area of Edwin’s garden is 600 square feet, what is the area of Tony’s garden? A1200 ft 2 B2400 ft 2 C3600 ft 2 D4800 ft 2 Correct Answer - B April 2004 #29

The scale factor of two similar polygons is 2:3. The perimeter of the larger polygon is 150 centimeters. What is the perimeter of the smaller polygon? A100 cm B75 cm C50 cm D150 cm Correct Answer - A April 2004 #37

Describe the effect on the area of a circle when the radius is doubled. FThe area is reduced by ½. GThe area remains constant. HThe area is doubled. JThe area is increased four times. Correct Answer - J Spring 2003 #16

(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to (B) describe the resulting effect on volume when dimensions of a solid are changed proportionally.

Objective 9: The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

(8.1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to (B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.

On a weekly basis Tara sets aside ½ of her weekly salary for rent, 1/5 for credit card payments, ¼ for groceries and utilities, and the rest, approximately $15, for entertainment. Which of the following is closest to Tara’s weekly salary? A$75 B$300 C$379 D$158 Correct Answer - B 2008 Released Item

(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to (B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.

During a softball game Kendra threw 85 pitches, 34 of which the umpire called strikes. What percent of Kendra’s pitches did the umpire not call strikes? A51% B40% C25% D60% Correct Answer - D 2008 Released Item

If a wheel spins at a rate of 36 revolutions per minute, how many revolutions per hour does the wheel spin? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Correct Answer - 2160 April 2006 #21

Antonio works 40 hours per week at Electronics Warehouse. He earns $6.50 per hour plus a 3% commission on the total dollar value of the service contracts he sells. If Antonio’s hourly rate were increased by $0.15 and his commission were raised to 5%, how much would he earn if he sold $4000 worth of service contracts for the week? A$126.50 B$206.65 C$466.00 D$580.00 Correct Answer - C April 2004 #11

A couple bought a house and calculated that they would pay 30% of their combined monthly income of $5,569.75 toward the monthly mortgage payment on the house. Approximately how much will the couple pay for their monthly mortgage payment? A$186 B$1,671 C$3,899 D$18,566 Correct Answer - B Spring 2003 #17

A watch loses 3 minutes every 24 hours. How much time till it lose in 2 hours? A1.6 seconds B5 seconds C15 seconds D22.5 seconds Correct Answer - C Spring 2003 #35

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

A jar contains 6 red marbles and 10 blue marbles, all of equal size. If Dominic were to randomly select 1 marble without replacement and then select another marble from the jar, what would be the probability of selecting 2 red marbles from the jar? Correct Answer - B April 2006 #45

At Reyna High School 50% of the students eat lunch in the school cafeteria. In the same school 10% of the students participate in sports. What is the probability that a student selected at random eats in the school cafeteria and participates in sports? Correct Answer - H Spring 2003 #36

(8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to (B) use theoretical probabilities and experimental results to make predictions and decisions.

A spinner was spun 20 times. The results are shown in the table below. Which color on the spinner has the same experimental probability as theoretical probability? FRed GWhite HBlue JYellow Correct Answer - G April 2004 #32

Last basketball season Ricky made 58% of the free throws he attempted. In the first game this season, Ricky went to the free-throw line 10 times. About how many free throws did Ricky make if his success rate from last season continued? F58 G10 H6 J4 Correct Answer - H Spring 2003 #4

(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 or range to describe a set of data and justify the choice for a particular situation;

Ms. Díaz asked each of her 27 statistics students to write down an integer from 1 to 10. To determine the most common number the students picked, which measure of central tendency should Ms. Díaz use? AMode BMean CMedian DRange Correct Answer - A April 2006 #29

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

The table below shows the number of student absences for the school year in Mr. Cruz’s math classes. Which of the following graphs best represents the data shown in the table? Correct Answer - J April 2006 #50

Students in two honors history classes took their first test. Of 40 students taking the test, 12 received an A, 16 received a B, 8 received a C, 2 received a D, and the remaining received an F. Which circle graph best represents these data? Correct Answer - H April 2004 #40

Which histogram best reflects the data shown in the table? Correct Answer - C Spring 2003 #51

(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.

The table below shows the highest and lowest points in elevation for 5 of the 7 continents. Based on the information in the table, which of the following statements is true? Correct Answer - C 2008 Released Item A Asia’s lowest point is more than 3 times lower than Africa’s lowest point. B North America’s highest point is more than 2,000 feet higher than South America’s highest point. C Asia’s highest point is more than 1.5 times as high as Europe’s highest point. D Europe has the lowest point of all 5 continents.

When Memorial Elementary held its annual spring festival, Benjamin surveyed 100 students to see which activity they preferred. The graph below shows the results of Benjamin’s survey. Which of the following statements is supported by these data? Correct Answer - F April 2006 #28 F Close to half the students surveyed preferred either the moon walk or the dunking booth. G More than 25% of the students surveyed preferred the pony ride or the pie toss. H The ratio of students who preferred musical chairs to the pie toss was 1:3. J More students preferred musical chairs than preferred all the other activities combined. F Close to half the students surveyed preferred either the moon walk or the dunking booth. G More than 25% of the students surveyed preferred the pony ride or the pie toss. H The ratio of students who preferred musical chairs to the pie toss was 1:3. J More students preferred musical chairs than preferred all the other activities combined.

The table shows the results of a survey given to 450 graduating seniors about their educational plans after high school. Based on these data, which of the following statements is true? A Only 15 students have no future educational plans. B More students plan to attend a community college or technical school than plan to attend a university. C Fewer than half of the students plan to attend a university. D Fewer than one-fourth of the students plan to attend a community college. Correct Answer - C April 2004 #3

The graph below shows the amount of time Dennis spent studying over a 2-week period in October. Which of the following statements would be an invalid conclusion for these data? F Dennis spent a total of 660 minutes studying. G Dennis studied for an average of about 47 minutes per day. H Dennis studied for an average of 330 minutes per week. J Dennis earned good grades during this 2-week period.` Correct Answer - F April 2004 #14

Objective 10: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.

(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

The astronomy club rented a bus to visit the planetarium. The club rented the bus at a rate of $24.95 per day plus $0.45 per mile driven over 50 miles. If the astronomy club rented the bus for 1 day, what additional information is needed to determine the total cost of renting the bus? A The total number of students in the astronomy club B The number of hours the bus was driven each day C The number of days the bus was rented D The total number of miles the bus was driven Correct Answer - D April 2006 #13

Narong’s family bought 3 shirts, 2 pairs of jeans, and 2 pairs of shoes. Each shirt cost $18, and each pair of shoes cost $35. The jeans were marked down from their original price of $40. What other information, if any, is needed to find the total cost of the 7 items before tax? AThe percent markdown for the shirts BThe original price of the jeans CThe percent markdown for the jeans DNo additional information is needed Correct Answer - C April 2006 #43

Adam’s age is 4 years less than twice Blanca’s age. If Adam is 16 years old, which equation can be used to determine Blanca’s age? F2(x – 4) = 16 G2x – 4 = 16 H4 – 2x = 16 J2(4 – x) = 16 Correct Answer - G April 2004 #38

A newspaper reported that the mean height of waves in the Norwegian Sea increased by 4 inches per year from 1955 to 1994. What additional information is needed to calculate the mean wave height in 1994? FThe mean height of waves in 1955 GThe range of wave heights from 1955 to 1994 HThe projection of the mean height of waves for the next year JThe distance from land to where the wave measurements were taken Correct Answer - F Spring 2003 #20

Trina was recording the calorie content of the food she ate. For lunch she had 3 ounces of chicken, 2 slices of cheese, 2 slices of wheat bread, one-half tablespoon of mayonnaise, a 16-ounce glass of lemonade, and an apple for dessert. According to the chart below, which equation best represents the total number of calories she consumed during lunch? Correct Answer - C Spring 2003 #23

Mr. McGregor wanted to cover the floor in his living room with carpet that cost $12 per square yard. The blueprint shows the area of the living room relative to the area of the house. What information must be provided in order to find the total cost of the carpet? FThe lengths and widths of the adjoining rooms in the blueprint GThe scale of yards to inches in the blueprint HThe total area of the house in the blueprint JThe thickness of the carpeting in inches Correct Answer - G Spring 2003 #34

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

A group of girls is attempting to break the school record for the longest gum-wrapper chain. The girls’ chain already measures 4182 feet. The school record chain is 5967 feet. What additional information is needed to determine how many gum wrappers the girls still need in order to break the record? AThe amount of time it took to complete the current school- record chain B The number of gum wrappers each girl has collected C The number of gum wrappers needed to complete a foot of the chain D The amount of time needed to complete the chain Correct Answer - C 2008 Released Item

Mr. Rivera wants to build a barbed-wire fence containing 5 rows of barbed wire around the irregularly shaped area shown in the drawing below. Mr. Rivera wants to purchase rolls of barbed wire that contain 1380 linear feet of wire per roll and purchase an extra 500 linear feet of wire for a gate for the fence. Which of the following is a correct method for Mr. Rivera to calculate the total number of rolls of barbed wire he will need to purchase? FDetermine the area of the property, multiply by 5, and then divide by the sum of 1380 and 500 G Determine the perimeter of the property, multiply by 5, add 500, and then divide by 1380 H Determine the area of the property, multiply by 5, add 500, and then divide by 1380 J Determine the perimeter of the property, multiply by 5, and then divide by the sum of 1380 and 500 Correct Answer - G April 2006 #18

Heidi has a main-course choice of a hamburger, a hot dog, an egg roll, a taco, a fish sandwich, or a chicken sandwich. She has a side-order choice of French fries, corn chips, potato chips, or a salad. Heidi’s beverage choice can be a soda, fruit punch, milk, or water. Which is the best method to determine how many different combinations Heidi could choose? F Add the total number of items in the 3 categories together G Multiply the total number of main-course choices by the total number of side-order choices and add the product to the total number of beverage choices H Multiply the sum of the total number of main-course choices and the total number of side-order choices by the total number of beverage choices J Multiply the total number of items in each of the 3 categories together Correct Answer - J April 2006 #36

Alonso’s family rented a car when they flew to Orlando for a 4-day vacation. They paid $39 per day and $0.09 for each mile driven. How much did it cost to rent the car for 4 days and drive 350 miles, not including tax? A$70.50 B$124.50 C$156.00 D$187.50 Correct Answer - D Spring 2003 #5

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

The horizontal distance and the vertical distance between the pegs on the geoboard shown below each represent 1 unit. Which is closest to the area of the polygon modeled on the geoboard? A34 units 2 B27 units 2 C21 units 2 D17 units 2 Correct Answer - C April 2006 #7

Mrs. Shawnee wants to buy fresh cherries to make some cherry pies for the school bake sale. The table below shows the sale prices of fresh cherries at 4 local markets. According to the table, which market has the best sale price per cup of cherries? FRosie’s Fruit Stand GFruits and More HNicky’s Fruit Store JFreshly Picked Fruits Correct Answer - G April 2006 #42

Jake’s square backyard covers an area of 104 square meters. How can Jake best determine the length of each side of his backyard? FDivide the area by the number of sides GSquare the area HFind the square root of the area JDivide the area in half Correct Answer - H April 2004 #48

Which of the following equations below represents the second step of the solution process? Step 1.5(6x + 4) + 1 = -39 Step 2. Step 3.30x + 21 = -39 Step 4.30x = -60 Step 5.x = -2 A5(6x + 1) + 4 = -39 B5(6x + 5) = -39 C30x + 4 + 1 = -39 D30x + 20 + 1 = -39 Correct Answer - D Spring 2003 #1

(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

The amount of material needed to make a basketball best represents the ball’s - Avolume Bsurface area Ccircumference Dperimeter Correct Answer - B April 2004 #23

A middle school band must be at the contest site by 8:00 A.M. to participate in a competition. It takes 45 minutes to load the bus with the band’s equipment, and it takes 1 hour 45 minutes to travel to the contest site. What should be the first step in determining the band’s departure time? A Add the time it takes to travel to the contest site to 8:00 A.M. B Add the time it takes to load the bus to 8:00 A.M. C Add the travel time and loading time together D Subtract the loading time from the travel time Correct Answer - C April 2004 #51

The function g(x) = 1.25 + 0.70(x – 1) represents the charge for parking in the mall garage for x number of hours. Which statement best represents the formula for this charge? A The charge consists of a set fee of $1.25 plus $0.70 for every hour parked. B The charge consists of a flat rate of $0.70 for every hour parked. C The charge consists of $1.25 for the first hour parked and $0.70 for each additional hour. D The charge consists of $1.25 for every hour parked plus a set fee of $0.70. Correct Answer - C Spring 2003 #15

Which problem is best represented by the number sentence 19 + 3(12 – x) = 40? FRicardo spent $19, and Lydia spent 3 times $12 less than Ricardo. Together they spent $40. How much did Lydia spend? GGail earned $19 baby-sitting and mowed 3 lawns in less than 12 hours. She earned a total of $40. How much did she earn per lawn? HJuan earned $19 baby-sitting and sold 3 boxes of apples for $12 each. Now he has $40. How much did he earn? JDenise paid $19 for 1 regularly priced item and bought 3 items on sale that were regularly priced at $12. She spent $40 in all. What was the price reduction on the 3 sale items? Correct Answer - J Spring 2003 #22

A store sells milk in two different containers. The first container is a rectangular prism that has a height of 8 inches and a square base with a side length of 2 inches. The other container is a cylinder with a radius of 1.75 inches and a height of 8 inches. Which best describes the relationship between the two containers? AThe prism has the greater volume. BThe cylinder has the greater volume. CThe volumes are equivalent. DThe volumes cannot be determined. Correct Answer - B Spring 2003 #33

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to (A) make conjectures from patterns or sets of examples and nonexamples;

Which of the following is true of all squares and all rectangles? I. All squares and all rectangles are equilateral. II.All squares and all rectangles are equiangular. III.All rectangles are squares AII only BIII only CII and III only DI, II, and III Correct Answer - A 2008 Released Item

The integers 1881, 353, 2002, and 787 are palindrome integers. Which of the following is also a palindrome integer? F1961 G828 H2525 J783 Correct Answer - G April 2006 #24

The figure below shows a partial view of Pascal’s triangle. Which row of numbers best represents the seventh row in Pascal’s triangle? F1 5 10 10 5 1 G1 6 15 20 15 6 1 H1 7 21 35 35 21 7 1 J1 8 28 56 70 56 28 9 1 Correct Answer - G April 2004 #12

Mr. Collins invested some money that will double in value every 12 years. If he invested $5,000 on the day of his daughter’s birth, how much will the investment be worth on his daughter’s 60th birthday? A$300,000 B$160,000 C$80,000 D$320,000 Correct Answer - B April 2004 #15

The table shows the number of sides and diagonals in certain polygons. Based on the table, how many diagonals should a 9-sided convex polygon have? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Correct Answer - 27 April 2004 #21

Which of the following is a valid conclusion based on the diagram? A All rhombuses are squares. B All rhombuses are rectangles. C All quadrilaterals are parallelograms. D All rectangles are parallelograms. Correct Answer - D April 2004 #25

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to (B) validate his/her conclusions using mathematical properties and relationships.

If x > 0 and y < 0, which statement must be true for the expression x/y? AThe result of the expression is undefined. BThe result of the expression is zero. CThe result of the expression is negative. DThe result of the express is positive. Correct Answer - C 2008 Released Item

If a < b and b = c, which statement must be true? AThe values of a, b, and c are positive. BThe values of a, b, and c are negative. CThe value of a is less than the value of c. DThe value of a is greater than the value of c. Correct Answer - C April 2006 #3

Line t intersects parallel lines l 1 and l 2, as shown below. According to the information provided, which of the following pairs of angles are not always congruent? A Same-side interior angles 4 and 5 B Alternate interior angles 3 and 5 C Corresponding angles 2 and 6 D Vertical angles 5 and 7 Correct Answer - A April 2006 #49

Sean is an Algebra I student who believes that xy 2 = (xy) 2. Rudy informs Sean that this theory is not always true. Which pair of values for x and y could Rudy use to disprove Sean’s theory? Fx = 0 and y = 2 Gx = 1 and y = 2 Hx = 2 and y = 0 Jx = 2 and y = 1 Correct Answer - J April 2004 #28

If the variables x and y are related so that x – y > x + y, which statement must be true? FThe variable x is greater than the variable y. GThe variable x is a negative number. HThe variable y is a negative number. JThe variable y is a positive number. Correct Answer - H Spring 2003 #28

9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions.

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9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions.

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