10 th Grade TAKS - Released Tests - by Objective Objective 11 Functional relationshipsFunctional...

10th Grade TAKS - Released Tests - by Objective

Objective1 Functional relationships

2 Properties and attributes of functions

3 Linear functions

4 Linear equations and inequalities

5 Quadratic and other nonlinear functions

6 Geometric relationships and spatial reasoning

7 Two- and three-dimensional representations of geometric relationships and shapes8 Concepts and uses of measurement and similarity

9Percents, proportional relationships, probability, and statistics in application problems10 Mathematical processes and tools used in problem solving

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

A(b)(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

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

If y is a function of x in the equation y = x2 – 9, which statement is true?

F The independent variable x is equal to 9 less than the square of the dependent variable y.

G The independent variable y is equal to 9 less than the square of the dependent variable x.

H The dependent variable y is equal to 9 less than the square of the independent variable x.

J The dependent variable x is equal to 9 less than the square of the independent variable y.

Correct Answer - H April 2006 #10

The volume of a rectangular prism is given by the function V = lwh. Which statement is true?A The volume of the prism depends on the product of only the length and the width.

B The volume of the prism depends on the product of only the length and the height.

C The volume of the prism depends on the product of the length, the width, and the height.

D The volume of the prism depends on the product of only the width and the height.

Correct Answer - C April 2004 #23

A function is described by the equationf(x) = x2 + 5. The replacement set for the independent variable is {1, 5, 7, 12}. Which of the following is contained in the corresponding set for the dependent variable?

A 0

B 6

C 7

D 15

Correct Answer - B Spring 2003 #19


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

The table below shows the relationship between p, the number of cell phones a company produces, and d, the number of cell phones that are defective. Which equation can be used to describe this relationship?

Correct Answer - GApril 2006 #14

Troy borrowed money from his father so that he could buy a used car. The table shows the remaining balance, b, of Troy’s loan after each payment. Which function can be used to describe this relationship?

A b = 3910 + 225p

B b = 4135 – 225p

C b = 2785 + 225p

D b = 3685 – 225p

Correct Answer - B April 2004 #35

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

Correct Answer - D Spring 2003 #45


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

Ms. Adams bought a refrigerator that cost $1200, including tax. The cost of electricity to run this refrigerator is estimated at $78 per year. Which equation best represents c, the total cost of the refrigerator including electricity over n years of operation?

A c = 1200(78n)B c = 1200(n + 78)C c = 1200 – 78nD c = 1200 + 78n

Correct Answer - D April 2006 #5

A candy company sells chocolate-covered cherries in a box. The empty box weighs 4.2 ounces. Each piece of candy weighs at least 1.8 ounces. Which inequality best describes the total weight in ounces, w, of a box of chocolate-covered cherries in terms of c, the number of candies in the box?

A w ≥ 1.8c + 4.2

B w ≥ 1.8c – 4.2

C w ≥ 4.2c + 1.8

D w ≥ 4.2c – 1.8

Correct Answer - A April 2004 #49

Vicki works as a salesclerk in a clothing store. She earns $10 per hour plus a commission of 6% of her total sales. Which equation represents e, her total earnings when she works h hours and sells a total of d dollars in merchandise?

A e = 10h + 0.06d

B e = 10h + 0.6d

C e = 6h + 10d

D e = 0.06h + 10d

Correct Answer - A Spring 2003 #7


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

Which data set is best described by the function y = -2x2 + 5x?

Correct Answer

H

April 2006 #48

Which inequality best describes the graph shown below?F y ≥ -2x

G y ≥ -x – 2

H y ≥ -2x – 2

J y ≥ x – 2

Correct Answer - G April 2004 #20

Which mapping best represents the function y = 2x2 + 1 when the replacement set for x is {-1, 0, 3}?



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

The graph below represents Cheyenne’s bicycle trip from her house to a friend’s house. On which segment of the graph does it appear that Cheyenne was riding her bicycle at the slowest pace?

A r

B s

C t

D u


The graph below represents which of the following relationships between temperature and time?

A Oven temperature whilea cake is baking

B Temperature of waterthat is heated on astove, removed, andthen allowed to cool

C Temperature of acontainer of hot teaafter placing several cubes of ice in it

D Room temperature of a gym after the airconditioner is turned on


Jake studied the parabola shown below. Which is an accurate conclusion that Jake could make about this parabola?A The vertex is at

(-2, 0).

B The minimum value is at (0, -4).

C The maximum value is at (2, 0).

D The axis of symmetry is the x-axis.


Objective 2:The student will demonstrate an

understanding of the properties and attributes of functions.

A(b)(2) Foundations for functions. The student uses the properties and attributes of functions.

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

Which of these are characteristics of the parent function of a quadratic equation?

I. The parent function of a quadratic equation has the vertex at (0, 0).

II. The parent function of a quadratic equation opens downward.

III.The parent function of a quadratic equation has the y-axis as its line of symmetry.

F I and II only

G I and III only

H II and III only

J I, II, and III



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

The graph shows the path of a golf ball.What is the rangeof this function?

F 0 < y < 100

G 0 ≤ y ≤ 100

H 0 ≤ x ≤ 5

J 0 < x < 5

Correct Answer - G Spring 2003 #


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


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

The coaches of a group of debate teams answered a survey about hours of debate team practice and number of team wins. The graph shows the results of this survey. Based on these results, if a team practices 4 hours per week next season, which is the best estimate of the number of debates the team can expect to win?

F 1

G 12

H 16

J 20

CorrectAnswer

H

April 2004 #12

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.

The area of the shaded portion of the rectangle shown below is 440 square feet. How can the area of the unshaded portion of the rectangle be expressed in terms of x in square feet?

F 440x – 30

G (30 + x)440

H (30 – 440)x

J 30x - 440

Correct Answer - J April 2006 #36

Mrs. Franklin received a 7% raise at her job. If she was earning x dollars per year before, how much is she earning now?

F x + 7

G x + 0.07

H x + 0.7x

J x + 0.07x


Which equation best represents the area, A, of the rectangle below?A A = 2x + 2(x + c)

B A = x2 + (x + c)2

C A = x(x + c)

D A = 2x(x + c)

Correct Answer - C Spring 2003 #53

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 squares below show a pattern. Which expression can be used to determine the number of squares at stage n?

F 5n – 3

G 4n – 2

H 2n2

J n2 + n

Correct Answer - J

April 2006 #38

Which expression can be used to find the values of s(n) in the table below?

F 3n

G 5n

H n + 4

J 3n + 2Correct Answer - J April 2004 #4

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.

A rectangle has a length of 2x + 1 and a width of 5x – 4. Which expression best describes the area of the rectangle?F 7x – 3

G 14x – 6

H 10x2 – 3x – 4

J 10x2 + 13x – 4


In the equation y = 2x2 – 5x – 18, which is a value of x when y = 0?A -18

B 1½

C 2

D 4½


After a ball is dropped, the rebound height of each bounce decreases. The equation y = 5(0.8)x shows the relationship between x, the number of bounces, and y, the height of the bounce, for a certain ball. What is the approximate height of the fifth bounce of this ball to the nearest tenth of a unit?

A 20.0 units

B 4.0 units

C 1.6 units

D 1.3 units


A(b)(4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

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

Simplify the expression 6 – 3(5x + 2) – 10x.

F -25x

G 5x + 6

H 8 – 25x

J 12 – 25x

Correct Answer - F April 2006 #16

Simplify the algebraic expression5(x + 3)(x + 2) – 3(x2 + 2x + 1).

A 2x2 + 7

B 2x2 + 27

C 2x2 + 7x + 7

D 2x2 + 19x + 27


Which expression is equivalent to5(x2 – 4x) – (x + 1)?

A 5x2 – 21x + 1

B 5x2 – 5x – 1

C 5x2 – 21x - 1

D 5x2 – 5x + 1


Simplify the expression 3(x + 1) – 2(3x + 7).

F -3x – 11

G -3x - 10

H -3x - 8

J -3x + 17

Correct Answer - F Spring 2003 #10

Objective 3:The student will demonstrate an

understanding of linear functions.

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

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

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 best describes points on the line graphed below?


Which graph best represents the function y = -1.75x + 5?


Which linear function best describes the graph shown below?


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.

Which line appears to have a slope of zero?


F Line n

G Line k

H Line w

J Line p

What is the rate of change of the graph below?


F 3.5

G 1.67

H 0.6

J -1.67

What is m, the slope of the line that contains the points (2, 0), (0, 3), and (4, -3)?

Correct Answer - J Spring 2003 #46


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

The graph shows the distance a certain motorbike can travel at a constant speed with respect to time. Which of the following best describes the meaning of the slope of the line representing this situation?


F The motorbike travels at a speed of about 8 mph.

G The motorbike travels at a speed of about 2.5 mph.

H The motorbike travels at a speed of about 5 mph.

J The motorbike travels at a speed of about 10 mph.


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

What will happen to the slope of line p if the line is shifted so that the y-intercept increases and the x-intercept remains the same?


F The slope will change from positive to negative.

G The slope will change from negative to positive.

H The slope will increase.

J The slope will decrease.

Which best describes the effect on the graph of f(x) = 4x + 8 if the y-intercept is changed to -3?

Correct Answer - H Spring 2003 #24

F The slope decreases.

G The new line passes through the origin.

H The x-intercept increases.

J The y-intercept increases.


(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 linear equation represents the line passing through points R and S?


F y = 1.5x – 4.5

G y = 1.5x + 4.5

H y = 0.5x – 4.5

J y = 0.5x + 4.5

Which equation describes the line that passes through the point (4, 7) and is parallel to the line represented by the equation -3x + y = 4?


Which of the following describes the line containing the points (0, 4) and (3, -2)?



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

What is the x-coordinate of the x-intercept of the function ⅔y = -6x + 12?


F 12

G 18

H -9

J 2

Which coordinate points represent the x- and y-intercepts of the graph shown below?


F (0, -4) and (6, 0)

G (-4, 0) and (0, 6)

H (6, 0) and (-4, 0)

J (0, 6) and (0, -4)

What is the y-intercept of the function f(x) = 3(x – 2)?


F 3

G 1

H -2

J -6


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


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

Objective 4:

The student will formulate and use linear equations and inequalities.

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

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

A chemist started an experiment with 5 grams of a chemical. The chemical was used at a rate of 0.01 gram per minute. Which equation best describes the relationship between c, the amount of chemical remaining in grams, and t, the time in minutes?F c = 5.01t

G c = 4.99t

H c = 5 – 0.01t

J c = 0.01t – 5


Rita put some hummingbird feeders in her backyard. The table shows the number of hummingbirds that Rita saw compared to the number of feeders. Which equation best describes the relationship between h, the number of hummingbirds, and f, the number of feeders?


A shaded parallelogram is graphed on the coordinate grid below. Which of the following functions describes a line that would include an edge of the shaded parallelogram?

F y = -2x + 5

G y = -2x – 2

H y = -2x + 9

J y = -2x – 1


At Northwest Electronics audiotapes cost $5.00 per package, and videotapes cost $10.00 per package. Which inequality best describes the number of packages of audiotapes, a, and the number of videotapes, v, that can be purchased for $45.00 or less?

F 5a + 10v < 45

G 10a + 5v ≤ 45

H 5a + 10v ≤ 45

J 10a + 5v < 45



(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 length of each leg of an isosceles triangle is 5 centimeters more than twice the length of the base. If the perimeter of this isosceles triangle is 95 centimeters, what is the length of the base?

A 17 cm

B 21 cm

C 30 cm

D 39 cm


What is the value of y if (3, y) is a solution to the equation 5x – 3y = 18?

F 3

G 1

H -1

J -11



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

In 2004 a married couple could have calculated their estimated income tax, t, for that year using the equation t = 0.25c – 6525, in which c represents their combined taxable income. If a married couple had a combined taxable income between $60,000 and $64,000, which of the following is a reasonable amount for their income tax?F $6,525

G $8,975

H $13,869

J $15,500


The 1998 enrollment at a community college was approximately 2500 students. In 2002 the enrollment had increased to 3250 students. If the enrollment continues to increase at this rate, what is a reasonable projection of enrollment for 2010?

F 4750

G 5750

H 6250

J 9000


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.

Norma and Lauretta went to a store to buy DVDs on sale for $5 each, tax included. Norma purchased two and a half times as many DVDs as Lauretta purchased. Together they purchased 14 DVDs. Which system of linear equations can be used to determine n, the number of DVDs Norma purchased, and l, the number of DVDs Lauretta purchased?

F n + l = 14n = ½l

G 5n + 5l = 14l = ½n

H n + l = 14n = (5/2)l

J n + l = 14l = (5/2)n


Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

F 5f + 3g = 3.602f + 10g = 5.70

G 5f + 2g = 5.703f + 10g = 3.60

H f + g = 227f + 13g = 9.30

J 5f + 3g = 5.702f + 10g = 3.60


The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters?

F l = w + 32(l + w) = 85

G l = 3w2l + 6w = 85

H l = 3w2(l + w) = 85

J l = w + 32l + 6w = 85



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

If the system of linear equations 2x + y = 1 and y = (-½)x +1 are graphed on the same coordinate grid, which of the following is the solution to this system of linear equations?

A (2, 0)

B (0, 2)

C (0.5, 0)

D Not here


What is the x-coordinate of the solution to the system of linear equations below?

4x + 5y = 82x – 3y = -18

F -4

G -3

H 3

J 4


Which graph best represents a solution to this system of equations?2x – 3y = 0x + 2y = -7


Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?

A (6, 9)

B (5, 10)

C (9, 6)

D (10, 5)



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

Objective 5:

The student will demonstrate an understanding of quadratic and

other nonlinear functions.

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

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

Which lists the functions of the form y = ax2 in order from the widest to the narrowest graph?


What is the effect on the graph of the equation y = -4x2 when the equation is changed to y = 4x2?A The graph of y = 4x2 is translated 8 units

down.

B The graph of y = 4x2 is a reflection of y = -4x2 across the x-axis.

C The graph of y= 4x2 is translated 8 units up.

D The graph of y = 4x2 is a reflection of y = -4x2 across the y-axis.


The graph of the function y = x2 is given below. How will the graph be affected if the coefficient of x2 is decreased to ¼?

F The parabola will be wider.

G The parabola will be narrower.

H The parabola will be translated up.

J The parabola will be translated down.

Correct Answer - F Spring 2003 #22


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

Shirley graphed a function of the form y = ax2 + c. She then translated the graph 8 units up, resulting in the function y = –⅔x2 + 5. Which of the following best represents Shirley’s original function?

F y = –⅔x2 + 13

G y = –⅔x2 – 13

H y = –⅔x2 + 3

J y = –⅔x2 – 3


How does the graph of y = x2 differ from the graph of y = x2 – 4?

A The graph of y = x2 – 4 is wider than the graph of y = x2.

B The graph of y = x2 – 4 is shifted to the left of the graph of y = x2.

C The graph of y = x2 – 4 is shifted down from the graph of y = x2.

D The graph of y = x2 – 4 is narrower than the graph of y= x2.



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

An object was dropped from a height of 250 meters and fell to the ground. The graph below shows the change in h, the objects height in meters, with respect to t, the time in seconds. According to the graph, which time interval best represents when the object was at 140 meters above the ground?

F Between 3 seconds and 3.25 seconds

G Between 3.75 seconds and 4 seconds

H Between 3.5 secondsand 3.75 seconds

J Between 3.25 secondsand 3.5 seconds


The graph below shows h, the height in meters of a model rocket, versus t, the time in seconds after the rocket is launched. From the graph, what conclusion can be made about the flight of the rocket?

A The rocket reached its maximum height after 2.5 seconds.

B At 0 seconds, the rocket was 2 meters off the ground.

C The height of the rocket was 0 meters when it was

launched.

D The rocket was in flight for 5 seconds.


The sales record for a recent hit CD at Tony’s Music Store is shown on the graph below. Which statement best describes the sales of this CD?A Sales rapidly increased, reached a peak, and then gradually decreased.

B Sales gradually increased, reached a peak, and then leveled off.

C Sales rapidly increased, reached a peak, and then rapidly decreased.

D Sales remained constant throughout the time period.


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 polynomial x2 + x – 6 is modeled below using algebraic tiles. What are the solutions to the equation x2 + x = 6?

A -3 and -2

B -3 and 2

C 3 and -2

D 3 and 2


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 graph best represents an equation that has the roots x = -7/2 and x = 1/2?


What are the roots of the function graphed below?

F (-1, -9) and (0, -8)

G (0, -4) and (2, 0)

H (-4, 0) and (2, 0)

J (0, 2) and (0, -4)


What are the roots of the quadratic equation x2 – 3x + 2 = 0?

A -2 and -1

B -2 and 1

C 2 and -1

D 2 and 1


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.

Marlena was asked to find an expression that is not equivalent to 212. Which of the following is not equivalent to the given expression?

F (22)6

G (28)4

H (26)(26)

J (23)(29)


Which expression is equivalent to ?


The area of a rectangle is 144a8b4 square units. If the width of the rectangle is 8a2b2 units, what is the length in units?

A 18a6b2 units

B 136a6b2 units

C 152a10b6 units

D 1152a10b6 units


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;

Look at the cylinder shown below.


Which of the following cylinders is similar to the one shown?

A copy machine can enlarge or reduce letters proportionately. Which would not be an enlargement or reduction of the letter below?


Identify the drawing that shows Figure 1 under dilation to produce Figure 2, using center of dilation (0, 0) and a scale factor of ½.


The graph below shows ∆XYZ and similar ∆X’Y’Z’. Which statement is true when transforming ∆XYZ to ∆X’Y’Z’.

F All the correspondingangles will increaseby a multiple of 3.

G All the correspondingangles will increaseby a scale factor of ⅓.

H All the correspondingsides are proportional,with a scale factor of 3.

J All the correspondingsides are proportional,with a scale factor of ⅓.


(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.

∆KQR is translated so that R is mapped to R’. Which ordered pair best represents either point K’ or point Q’?

F K’ (-3, 6)

G Q’ (-4, -1)

H K’ (5, -2)

J Q’ (-3, -2)Correct Answer - J April 2006 #4

Pentagon PQRST is graphed on the coordinate grid below. Which of the following points would be the location of S’ if pentagon PQRST is dilated by a scale factor of 2 and has a center of dilation at (0, 0)?

F (-6, 4)

G (2, -6)

H (4, -6)

J (4, -3)


At what coordinates should vertex Z be placed to create a quadrilateral WXYZ that is similar to quadrilateral PQRS?

F (24, 16)

G (24, 24)

H (20, 20)

J (16, 24)


If quadrilateral TUVW is reflected across the x-axis, to become quadrilateral T’U’V’W’, what will be the coordinates of W’?

F (-4, -2)

G (-4, 2)

H (2, -4)

J (4, -2)


Identify the location of point P under translation (x + 3, y – 2).

A (3, -2)

B (2, 3)

C (-1, 0)

D (2, 0)


∆RST is translated so that R is mapped to R’. Which set of ordered pairs best identifies points S’ and T’.

F S’ (8, 3), T’(3, 8)

G S’(4, 3), T’(9, 8)

H S’(10,-1), T’(12,-9)

J S’(10,3), T’(5,4)

Correct Answer - G Spring 2003 #54

(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 of the following ordered pairs best represents the location of point T?


The circle shown below has a diameter of 10 units. Which of the following ordered pairs best represents the location of the center of the circle?


A portion of isosceles trapezoids NPRT is shown on the grid below. At what coordinate should vertex T be placed to make NP parallel to RT in order to complete isosceles trapezoid NPRT?

A (-2, -2)

B (-3, -2)

C (-2, -3)

D (-4, -5)


Which point on the grid satisfies the conditions x ≥ 5 and y < -1?

F W

G X

H Y

J Z


A M

B N

C P

D Q


Objective 7:

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

geometric relationships and shapes.


(A) draw solids from different perspectives;

The drawing shows the top view of a 3-dimensional object.Which of the following drawings best represents this 3-dimensional object?


Which of the following shapes could not represent a top, front, or side view of a trapezoidal prism?

A A square

B A trapezoid

C A rectangle

D A triangle


Lee designed a table that appears to be a cone with a wooden board passing through it, as shown below. Which of the following best represents a top view of this table?


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


The drawing shows a view of a building. Which drawing best represents the top view of this building?



(B) use geometric concepts and properties to solve problems in fields such as art and architecture;

An artist painted a mural from the photograph shown below. If the artist used a scale of ½ inch to represent 1 foot, which of thefollowing best represents thedimensions in feet of the mural?


The blueprint dimensions for a newly constructed house are proportional to the house’s actual dimensions. On the blueprints the house’s foundation measures 75 centimeters long by 40 centimeters wide. If the house’s foundation measures 15 meters long, what is the foundation’s actual width?

A 8 m

B 28.1 m

C 50 m

D 200 m


Near the downtown area of a city, there is a vacant triangular plot of land with sides that measure 22 feet, 27 feet, and 17 feet. If the city council decides to plant an oak tree in the corner with the smallest angle, where should the tree be planted?

A In the corner opposite the side that is 17 feet

B In the corner opposite the side that is 22 feet

C In the corner opposite the side that is 27 feet

D In the center of the triangular plot


Mr. Harrison wants to calculate the cost of buying a carpet to cover his rectangular living room floor. He knows the cost per square foot of carpet, and he knows the length, width, and height of the living room. Which geometric formula should Mr. Harrison use to determine the cost of the carpet he needs?

F c2 = a2 + b2

G V = Bh

H A = lw

J P = 2l + 2w


A blueprint of a house plan uses a scale in which ¼ inch equals 1 foot. If the length of one side of the house is 65 feet, how many inches will the length be on the blueprint?

F 4 in.

G 16¼ in.

H 65¼ in.

J 260 in.


A regular hexagon is drawn in a circle as a design on a window. Opposite vertices are connected by line segments.

What is the measure of angle Y in degrees?

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

Correct Answer - 60 Spring 2003 #21


(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.Which is closest to the area in squareinches of the largest square?

A 1914 in.2

B 233 in.2

C 210 in.2

D 1073 in.2


Look at the right triangle shown below. Which of the following could be the triangle’s dimensions?

F 12, 16.8, 18.2

G 5.4, 10.6, 16

H 1.2, 1.6, 2

J 8, 10, 12.5


The sides of squares can be used to form triangles. The areas of the squares that form right triangles have a special relationship. Using the dimensions of the squares shown below, determine which set of squares will form a right triangle.

Correct Answer

C

Spring 2003 #13

Use the Pythagorean theorem to find the figure that is a right triangle.


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 solids. The student is expected to

(A) find surface area of prisms and cylinders using [concrete] models and nets (two-dimensional models);

The net of a right triangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the right triangular prism to the nearest centimeter. Which is closest to the total surface area of this right triangular prism?

A 18 cm2

B 60 cm2

C 48 cm2

D 36 cm2

Correct Answer

C

0 1 2 30

1

2 3

0 1 2 3

0

1

2

3

0

1

2

3

4

0 1

2 3 4

5

April 2006 #25

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 tenth of a centimeter. Which of the following best represents the total surface area of this cylinder?

F 137 cm2

G 93 cm2

H 23 cm2

J 14 cm2

Correct Answer

FApril 2004 #38

0 1 2 3 4 5 6 7 8 9 10 11 12 13 140

1 2 3 4

5 6

7 8

9 10 11 12 13 14

0 1 2 3 4


(B) connect models to formulas for volume of prisms, cylinders, pyramids, and cones;

Look at the cylinder shown below. Which equation best represents the volume, V, of this cylinder in terms of π?

A V = 16πr2

B V = 8πr2

C V = 4πr2

D V = 4πr3


A triangular prism is shown below. What is the volume of this triangular prism?

A 192 in.3

B 240 in.3

C 384 in.3

D 480 in.3


Steven has a cylindrical fish tank with a diameter of 8 inches and a height of 14 inches. He placed some rocks that took up 50 cubic inches at the bottom of the tank. Then he filled the tank with springwater to 2 inches from the top. Which is the best strategy for determining the volume of water the fish has for swimming?

F π(8)2(14) – 50

G π(8)2(14 – 2) – 50

H π(4)2(14 – 2) – 50

J π(14 – 2)2(4) – 50


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 quarter inch. Which best represents the volume of this cube to the nearest cubic inch?

A 2 in.3

B 9 in.3

C 12 in.3

D 18 in.3


0 1 2


(C) estimate answers and use formulas to solve application problems involving surface area and volume.

Mr. Bergman built a rectangular sandbox for his children, as shown below. If each 50-pound bag contains approximately 0.70 cubic foot of sand, which is closest to the number of bags of sand that Mr. Bergman used to completely fill this sandbox?

A 81

B 19

C 972

D 116


The owners of Neatly Packaged Company make a cylindrical container that has the dimensions shown below. What is the approximate lateral surface area available for the package label?

A 131.95 in.2

B 151.19 in.2

C 263.89 in.2

D 115.45 in.2


Ginny made a cylindrical clay vase for her art project. If the vase has a volume of 339 cubic inches and a diameter of 6 inches, which is closest to the height of the vase?

F 36 in.

G 18 in.

H 12 in.

J 3 in.


(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;

A slide was installed at the local swimming pool, as shown below. Which is closest to the length of the slide?

A 29 ft

B 16 ft

C 21 ft

D 81 ft


Mrs. Cheung hired a landscaping service to plant a row of bushes around her triangular backyard. If the bushes must be planted 3 feet apart, approximately how many bushes are needed for Mrs. Cheung’s backyard?

A 23

B 25

C 28

D 32


The drawing shows part of the plan for a new underground lawn-sprinkler system. Which is closest to the length of the section of plastic pipe from point A to point C?

A 4.7 ft

B 5.7 ft

C 6.7 ft

D 7.7 ft


(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to

(B) use proportional relationships in similar shapes to find missing measurements.

Trapezoid KMPR is similar to trapezoid LNQS. Which is closest to the perimeter of trapezoid LNQS?

A 23 units

B 31 units

C 25 units

D 63 units


Jeremy’s house is 45 feet wide. In a photograph the width of the house was 2.5 inches, and its height was 2 inches. What is the actual height of Jeremy’s house?

A 18 ft

B 26 ft

C 32 ft

D 36 ft


To estimate the height of her school’s gym, Nicole sights the top of the gym wall in a mirror that she has placed on the ground. The mirror is 3.6 meters from the base of the gym wall.Nicole is standing 0.5 meterfrom the mirror, and herheight is about 1.8 meters.What is the height of thegym wall?

F 1 m

G 5.9 m

H 7.2 m

J 12.96 m


A certain parallelogram has the dimensions shown. Which set of dimensions would produce a similar figure?

F 17.6 cm, 88 cm

G 70.4 cm, 176 cm

H 105.6 cm, 132 cm

J 140.8 cm, 220 cm


(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;

The owner of an amusement park created a circular maze that has a diameter of 50 feet. If the owner doubles the radius of the maze, which statement describes what will happen to the circumference and area of the maze?

A The circumference and the area will double.

B The circumference and the area will quadruple.

C The circumference will double, and the area will quadruple.

D The circumference will quadruple, and the area will double.


If the dimensions of a rectangle with a perimeter of 24 inches are tripled, what will be the perimeter in inches of the new rectangle?

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

Correct Answer - 72 April 2004 #21

The scale of two similar quadrilaterals is 1:2. The perimeter of the smaller quadrilateral is 80 centimeters. What is the perimeter of the larger quadrilateral?

A 40 cm

B 80 cm

C 160 cm

D 320 cm


(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.

The edges of a large cube are 4 times longer than the edges of a small cube. How many times greater is the volume of the large cube?

F 4 times

G 12 time

H 16 times

J 64 times


Objective 9:

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

in application problems.

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

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

Bruce went to a barbershop for a haircut. The price for a haircut at this barbershop is $15, tax included. If Bruce tipped the barber 15% of the cost of the haircut and the tax, how much change in dollars and cents should he have received if he paid with a $20 bill?

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

Correct Answer – 2.75 April 2006 #21

Of the 32 students in Mrs. Zane’s class, 25% have brown hair. Of the remaining students, 12.5% have red hair. How many students in Mrs. Zane’s class have red hair?

A 3

B 4

C 21

D Not here


The world’s fastest flying insect is the dragonfly. It can fly 36 miles per hour. If a dragonfly flew in a straight path at this rate, what distance would it fly in 15 minutes?

F 2 mi

G 9 mi

H 25 mi

J 540 mi


Mr. Salinas, a real estate agent, received a 5% commission on the selling price of a house. If his commission was $6,975, what was the selling price of the house?

F $7,342

G $34,875

H $139,500

J $662,625


(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 compound events (dependent and independent);

Jerry has a CD case that contains 4 country music CDs, 1 rock-and-roll CD, 2 rap CDs, and 3 Tejano CDs. What is the probability of Jerry randomly selecting a Tejano CD and then, without replacing it, randomly selecting a rap CD from his case?


Jared has a white cube and a red cube. The surfaces of each cube are numbered with a unique number from 1 to 6. If Jared tosses the cubes, what is the probability he will get a 4 on the white cube and an odd number on the red cube?


(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.

The table below shows the results of rolling a fair number cube 50 times during a classroom activity. What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results recorded in the table?

F 8%

G 79%

H 58%

J 29%


The table shows the results of a number cube being rolled. Based on the results, what is the experimental probability of rolling a 1?


(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;

Nicholas earned the following grades on his science exams: 83, 88, 87, and 83. If Nicholas scores a 90 on his last exam, which measure of central tendency will give him the highest score?

F Mode

G Median

H Range

J Mean


Given the set of data {20, 15, 10, 20, 15, 10, 20, 20, 50}, which statement best interprets the data?

F Only the mean is 20.

G The range of the set of data is 20.

H The mean, median, and mode are all 20.

J The mode and median are not the same.


(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 table shows a math department’s budget for the upcoming school year. Which bar graph best represents the data given in the table?


Of the 800 students at a local high school, 200 students have no siblings, 318 students have one sibling, 160 students have two siblings, and the rest of the students have three or more siblings. Use the key below to find the circle graph that best represents this information.


The student election committee at Chesterfield High School recorded the number of votes that each of 4 presidential candidates received in the student council election. A total of 240 students voted. Charlene received 12.5% of the votes, Jimmy received 33.3%, Stephen received 16.7%, and Lupe received 37.5%. Which bar graph best represents the number of votes each presidential candidate received in the student council election?


(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.

Richard budgets $1200 of his job earnings on a monthly basis. The graph below shows his monthly budget. Which conclusion can be drawn from the information given?

A More than 30% of Richard’s budget is for credit card payments, insurance, and food combined.

B Richard budgets $384 for utilities, insurance, and his car payment combined.

C Less than 50% of Richard’s budget is for rent, food, and utilities combined.

D Richard budgets $228 for savings, entertainment, and clothes combined.


The table shows the population and the area in square miles of some U.S. states. Which statement best describes the relationship between the population and the area of the state?

A The larger a state’s area, the larger its population is.

B No relationship can be determined from the data in the table.

C New Jersey has the smallest population of the states in the table because it has the smallest area.

D Texas is the largest U.S. state.


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;

Mr. Harmon is planning to sell his house and wants to paint all the rooms. A can of paint costs $12.95 plus 7.75% sales tax and covers about 476 square feet. What other information is needed to determine the number of cans of paint Mr. Harmon needs to purchase?

F The number of rooms in the house

G The area in square feet to be painted

H The total cost of each can of paint

J The name of the store where Mr. Harmon will buy the paint


Jerry and Dan are recycling newspaper for a school project. Together they made 21 stacks of newspaper. Each stack is 4 feet tall. Dan can load a stack in 15 minutes, and Jerry can load a stack in 10 minutes. What information is NOT needed to find whether they can load all the newspaper in 2 hours if they work together?

F The time it takes to load the newspaper.

G The rate at which each boy loads the newspaper.

H The height of each stack of newspaper.

J The number of stacks of newspaper.


Greta and her friends are having lunch at Joe’s Diner. The total cost of their lunch, including tax, is $54.63. Greta and her friends have $65.00 altogether and want to leave a tip equal to 15% of the total bill. Is $65.00 enough to cover the cost of their lunch and the 15% tip for the server?

F No, they need $0.56 more.

G No, they need $3.29 more.

H Yes, and they have $2.18 left over.

J Yes, they have the exact amount.



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

The price for this year’s season tickets to a city hockey team’s games was reduced by 15% from last year’s ticket price, x. As a result, there was a 22% increase in the number of season-tickets sold this year. If a total of 4000 season tickets were sold last year and each season ticket is equally priced, which expression could be used to determine the total sales from this year’s season tickets?

A 4000(1 + 0.22)(1 + 0.15)x

B 4000(1 + 0.22)(1 – 0.15)x

C 4000(1 – 0.22)(1 – 0.15)x

D 4000(1 – 0.22)(1 + 0.15)x


For a spring break special, an amusement park charged $10 per person for admission with unlimited rides. The regular admission price is $5 per person plus $0.50 per ride. Which of the following statements is true?

A If a person plans to get on 10 rides, the spring break special costs less.

B If a person plans to get on 10 rides, the regular admission price costs less.

C If a person plans to get on fewer than 10 rides, the regular admission price costs less.

D The spring break special costs less no matter how many rides a person plans to get on.


A triangle is inscribed in a square, as shown below. What is the area of the shaded triangle inscribed in the square?


The school drama club plans to attend a Shakespeare festival in 6 weeks. The total cost per person is $185.75. The club has $296 in its account and will divide the money equally among the 8 members who attend the festival. Troy is planning to attend the festival and has already saved $55. How much more money does Troy need in order to cover his cost to attend the festival?

A $93.75

B $110.25

C $148.75

D Not here


In the system of equations 4x + 2y = 10 and 3x + 7y = -18, which expression can be correctly substituted for y in the equation 3x + 7y = -18?

A 10 – 2x

B 10 + 2x

C 5 – 2x

D 5 + 2x


What is the perimeter to the nearest centimeter of the regular octagon drawn below?

F 41 cm

G 36 cm

H 27 cm

J 18 cm


Mitch wants to use 40 feet of fencing to enclose a flower garden. Which of these shapes would use all the fencing and enclose the largest area?

F A rectangle with a length of 8 feet and a width of 12 feet

G An isosceles right triangle with a side length of about 12 feet

H A circle with a radius of about 5.6 feet.

J A square with a side length of 10 feet



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

A toad is 25 feet north of a bullfrog. Every time the toad jumps 1 foot, the bullfrog jumps 3 feet. If both the toad and the bullfrog jump due north, how many jumps will it take for the bullfrog to pass the toad?

A 12

B 9

C 13

D 7


A rectangle has an area of 144 square inches and a perimeter of 50 inches. What are the dimensions of the rectangle?

A 10 in. by 15 in.

B 9 in. by 16 in.

C 8 in. by 18 in.

D 4 in. by 36 in.


Manuel has 5 more CDs than Pedro has. Bob has twice as many CDs as Manuel has. Altogether the boys have 63 CDs. Which equation can be used to find how many CDs each person has?

A 5x + 2x + x = 63

B x + (x + 5) + 2x = 63

C x + (x + 5) + 2(x + 5) = 63

D x + 2(5x) + 5x = 63


(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.

Mrs. Aman asked her students to look at the drawing shown below to determine the length of d. Which of the following student responses best represents the length of d?

A 8 units

B 11 units

C 14 units

D 3 units


A circle and its diameter are shown below. The value of π is the result of which of the following ratios comparing a circle’s circumference to its diameter?


Shannon has spent $850 on gasoline and repairs for her car in the last 6 months. Of this total, she spent $300 on repairs. The gasoline she purchased cost $1.29 per gallon. Which of the following can be used to determine how many gallons of gas, g, Shannon has bought within the last 6 months?

A 1.29g – 300 = 850

B 1.29g + 300 = 850

C 1.29 – 300g = 850

D 1.29 + 300g = 850


Rinaldo’s school sold all of the tickets to a band concert. The tickets cost $8 each. The auditorium where the concert was held had 39 rows, with 56 seats in each row. Which of the following is a correct method for Rinaldo to calculate the total amount of ticket sales?

F Rinaldo can multiply 56 by $8 and then add $39.

G Rinaldo can add 39 and 56 and then multiply by $8.

H Rinaldo can multiply 39 and 56 and then multiply by $8.

J Rinaldo can add 56 and $8 and then multiply by 39.


Which of the following is best represented by the data in the graph below?

F Comparing the length of a side of a square to the square’s area.

G Comparing the length of the radius of a circle to the circle’s circumference.

H Comparing the length of a side of a cube to the cube’s volume.

J Comparing the length of the diameter of a circle to the circle’s area.


(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;

Lee, Kelly, Linda, and Madison all took the same math test. Linda earned a lower score than Kelly, but she did not earn the lowest score. The highest test-scorer’s name does not begin with an L. Madison earned a higher score than Kelly. Which person earned the lowest score on the math test?

A Kelly

B Lee

C Linda

D Madison


A pattern exists for digits in the ones place of the value that results from raising 7 to the power of n, where n is an integer greater than or equal to 1. Which digit is in the ones place of the value of 750?

F 7

G 9

H 3

J 1


The table shows the first-class postage rates for different years. Which conclusion is true for the data given?

A The rate for first-class postage was above $0.18 during the 1970s.

B The rate for first-class postage remained below $0.32 during the 1990s.

C The rate for first-class postage remained below $0.29 during the 1980s.

D The rate for first-class postage increased by 4% between 1971 and 1995.


Linda owns a set of seven wrenches. The wrenches come in consecutive increments of 1/8 inch. Linda has misplaced a wrench. The sizes she has are 1/8 inch, 1/4 inch, 1/2 inch, 5/8 inch, 3/4 inch, and 7/8 inch. Which size wrench is missing from Linda’s set?

A 3/16 in.

B 3/8 in.

C 11/16 in.

D Not here


A pattern exists as a result of raising i, an imaginary number, to n, an integer greater than or equal to 1. Based on the table, which of the following best represents i raised to the 16th power?


A pattern exists among the digits in the ones place when 2 is raised to different powers, as shown in the table below. For example, in 24 = 16 the number in the ones place is 6. Which digit is in the ones place in 238?

A 2

B 4

C 6

D 8Correct Answer - B Spring 2003 #23

(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.

Stephen claims that the exterior angle for any regular polygon is either an acute angle or an obtuse angle. If each of the following polygons is regular, which one could disprove Stephen’s theory?

F Triangle

G Quadrilateral

H Pentagon

J Hexagon


Which statement about the triangles below is true?

F All the triangles are scalene.

G All the triangles are equiangular.

H All the triangles are equilateral.

J All the triangles are isosceles.


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