9 th grade taks - released tests - by objective objective 1 1 functional relationshipsfunctional...

9th 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.

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.G The 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


(B) The student [gathers and records data, or] uses data sets, to determine functional (systematic) 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?

A n = 2r + 52

B n = r + 54

C n = 4r + 50

D n = 4r + 54Correct Answer - C April 2006 #25

Which equation could be used to generate this table of values?

A y = -2x

B y = 2x + 1

C y = x + 1

D y = x2 + 1


Which equation best describes the relationship between the corresponding values of x and y shown in the table?

F y = x – 10

G y = 2x – 8

H y = 3x – 6

J y = x2 – 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


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

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?

F r = (1350 – 75)m

G r = 75m + 1350

H r = 1350 – 75m

J r = 75m - 1350


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?

A 800 + 75x ≤ 2000

B 800x + 75 ≥ 2000

C 800x – 75 ≥ 2000

D 800 – 75x ≤ 2000

Correct Answer - A Spring 2003 #45


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

Which inequality best describes the graph shown below?


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)?


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

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?

A r

B p

C q

D s

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?

A The variable x is always 4 more than y.

B When the value of x is negative, the value of y is also negative.

C The variable y is always greater than x.

D As 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(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 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


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


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

Look at the graph. Which is the best interpretation of this graph?A Jorge earns $20 for each hour worked.

B For every 10 pieces of candy Stacey buys, she pays $1.

C For every 10 students at a dance, 2 teachers are needed as chaperones.

D A 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.


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


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

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?

A Negative trend

B Positive trend

C Constant trend

D No 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?

A A negative correlation

B No correlation

C A positive correlation

D A constant correlation


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.

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?

F p – 0.15p

G p + 0.15p

H p – 15p

J 0.15p

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?


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.

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?

A 2n + 1

B 2n – 1

C n + 2

D 2n


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.

Tammy drew a floor plan for her kitchen, as shown below. Which expression represents the area of Tammy’s kitchen floor in square units?

F 6x2 + 30x + 5 G 6x2 + 13x + 5

H 10x + 12 J 5x + 6

Correct Answer - G April 2006 #16

The area of a rectangle is 3x2 + 14x + 8, and the width is x + 4. Which expression best describes the rectangle’s length?

F 3x + 2

G 2x + 4

H 2x + 2

J 3x - 2


The area of a rectangle is given by the equation 2l2 – 5l = 18, in which l is the rectangle’s length. What is the length of the rectangle?

F 1.5

G 2

H 4.5

J 6

Correct Answer - H Spring 2003 #46

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 algebraic expression3(x + 3) – 2(x + 3).

F x + 3

G x – 3

H -6x2 – 54

J 6x2 + 3


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.

The table below shows various values for x and y. Which equation best describes the relationship between x and y?


A y = -3x + 5

B y = -5x – 7

C y = -x + 17

D y = 3x + 41

Which function includes the data set {(2, 4), (6, 6), (12, 9)}?


A y = 2x

B y = x/2

C y = 2x - 9

D y = 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?


A c = 6.75s

B c = 7.00s

C c = 2s - 20

D c = 15 + 6s

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

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

What is the slope of the line that contains the coordinate points (8, -3) and (-2, 7)?


A -1

B -9/11

C -5/3

D -2/5

What is the slope of the linear function shown in the graph?


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?


A W

B X

C Y

D Z


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

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?


A The van was purchased for $1,600.

B The van decreases in value by $1,600 per year.

C The van increases in value by $1,600 per year.

D The 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?


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


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

The graph of a linear function is shown 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?



(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 equation describes a line that has a y-intercept of 5 and a slope of ½?


Which linear function includes the points (-3, 1) and (-2,4)?



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

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?


F (4, 0) and (5, 0)

G (4, 0) and (0, 5)

H (0, 4) and (5, 0)

J (0, 4) and (0, 5)


(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.

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?


F $40

G $400

H $4,000

J $40,000

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.

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?

F 21s + 9 < 58

G 9s + 21 ≤ 58

H 30s < 58

J 9s – 21 ≤ 58


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?

A 9245 = 85 + 475t

B 9245 = 85(t + 475)

C 9245 = 475 + 85t

D 9245 = (475 + 85)t


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?

F r = g – 2

G g = r – 2

H g = 2r

J r = g + 2


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?

F m = 3 + 2c

G c = 3 + 2m

H m = 2 + 3c

J c = 2 + 3m



(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.

If (x, -3.2) is a solution to the equation 4x = 5y – 17, what is the value of x?

F 0.84

G 0.25

H -5.96

J -8.25


If (x, -4) is a solution to the equation 4x – 5y = 8, what is the value of x?

A -4.8

B -3

C 1.6

D 7


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?

F 4

G 5

H 9

J 10


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?

F 6 h

G 5 h

H 4 h

J 3 h



(C) For given contexts, the student interprets and determines 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?

A 5

B 4

C 6

D 3


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 carnationsII. 6 roses and 10 carnationsIII. 10 roses and 8 carnationsIV. 5 roses and 14 carnations

F I and II only

G II and III only

H III and IV only

J I and IV only


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?

A 750 lb

B 175 lb

C 500 lb

D 1500 lb


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?

F 1

G 2

H 3

J 7


A(c)(4) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

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

The 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?

F 2l + 2w = 90l = 5 – 4w

G 2l + 2w = 90l = 5w – 4

H 2l + 2w = 90l = 4 – 5w

J 2l + 2w = 90l = 4w – 5


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?

A 2s + 3b = 156s = b + 8

B 2b + 3s = 156s + b = 8

C 2s + 3b = 8s = b + 156

D 2s + 3b = 156b – s = 8


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?

A l + t = 108t = 3l + 6

B l + t = 108t = 3l -6

C l + t = 108l = 3t – 6

D l + t = 108l = 3t + 6


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.

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

The graph of a function is shown below. If the graph is translated 7 units down, which of the following best represents the resulting graph?


The graph of the function y = x2 – 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?

F y = x2 + 5

G y = x2 + 2

H y = x2 – 2

J y = x2 – 8


How would the graph of the function y = x2 + 4 be affected if the function were changed to y = x2 + 1?

F The graph would shift 3 units up.

G The graph would shift 3 units down.

H The graph would shift 3 units to the right.

J The graph would shift 3 units to the left.


Which graph shows a function y = x2 + c when c < -1?


In the graph of the function y = x2 + 5, which describes the shift in the vertex of the parabola if, in the function, 5 is changed to -2?

A 3 units up

B 7 units up

C 3 units down

D 7 units down


When graphed, which function would appear to be shifted 2 units up from the graph of f(x) = x2 + 1?

F g(x) = x2 – 1

G g(x) = x2 + 3

H g(x) = x2 – 2

J g(x) = x2 + 2


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.

Which expression represents the area of a rectangle with sides measuring 2x2y4z units and 5xy4z3 units?

F 7x2y8z3 units2

G 7x3y8z4 units2

H 10x3y8z4 units2

J 10x2y8z3 units2


What is the simplified form of ?


Which expression is equivalent to

A 4x9

B 4x2

C 2x8

D 2x4


If y = x3, what is equivalent to x12?

F y36

G y15

H y9

J y4


Which expression describes the area in square units of a rectangle that has a width of 4x3y2 and a length of 3x2y3?

F 12x6y6

G 12y5x5

H 7x6y6

J 7x5y5


The area of a rectangle is 30m11n5 square units. If the length of the rectangle is 6m4n2 units, how many units wide is the rectangle? (m ≠ 0 and n ≠ 0)

A 5m7n3 units

B 24m7n3 units

C 36m15n7 units

D 180m15n7 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;

∆AHP ~ ∆ENK as shown below. Which scale factor was used to transform ∆AHP to ∆ENK?


∆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’?


∆MNP ~ ∆RST is shown below. Which scale factor was used to transform ∆MNP to ∆RST?

A 1/3

B 1/2

C 2/7

D 5


The pentagon in the graph below is to be dilated by a scale factor of 1/3. Which graph shows this transformation?


(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.

∆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)


Triangle XYZ is translated so that X is mapped to X’. Which coordinate pair best represents Y’?


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)


(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.

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)


Which point on the grid below best represents the coordinates ?

A Point K

B Point M

C Point R

D Point U


∆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)


Which circle has a center located at coordinates (-3, 2)?


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)


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 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.


The drawing below shows a solid with hexagonal bases. Which drawing best represents the top view of this hexagonal solid?


The drawing shows a 3-dimensional solid. Which best represents the shape of the solid when viewed from the top?

F Pentagon

G Hexagon

H Heptagon

J Octagon


Match the three views of this solid to its 3-dimensional sketch.

Correct Answer

F

Spring 2003 #12


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

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?

F 112 mi

G 224 mi

H 56 mi

J 44 mi


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?

F 8.4 in.

G 18 in.

H 23.4 in.

J 486 in.


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


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?

A 192

B 96

C 48

D 14



(C) use pictures or models to demonstrate the Pythagorean Theorem.

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?

A 135 in.2

B 24 in.2

C 66 in.2

D 81 in.2


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?

A 500 yd

B 700 yd

C 1400 yd

D 2000 yd


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 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 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 ofthe cube represented by this net?

A 74 cm2

B 11 cm2

C 43 cm2

D 12 cm2

Correct Answer - AApril 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 tothe total surface areaof this cylinder?

F 4 in.2

G 11 in.2

H 14 in.2

J 25 in.2


0 1 2 3 4

0 1 2 3 4


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

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?

A 11 cm3

B 13 cm3

C 30 cm3

D 42 cm3


0 1 2


(C) estimate answers and use formulas to solve application problems involving 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?

F 19 cm3

G 97 cm3

H 192 cm3

J 513 cm3


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?

A 186 in.2

B 157 in.2

C 195 in.2

D 128 in.2


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?

F 3 h

G 2 h

H 4 min

J 1 min


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?

A 216 in.3

B 576 in.3

C 729 in.3

D 1728 in.3


(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;

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?

A 4.9 ft

B 5.3 ft

C 6.1 ft

D 6.9 ft


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?

F 6 yd

G 19 yd

H 27 yd

J 54 yd


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?

F 35 ft

G 40 ft

H 85 ft

J 110 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.

∆MNQ is similar to ∆MLP. If ML = 10 centimeters, what is the length of MN?

F 6.25 cm

G 8.3 cm

H 7.5 cm

J 4 cm


If ΔTSR is similar to ΔTNM, what is the length of x?


A 240 units

B 140 units

C 120 units

D 70 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.

F 2.4 cm

G 7.3 cm

H 16.5 cm

J 19.6 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;

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.


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?

A 1200 ft2

B 2400 ft2

C 3600 ft2

D 4800 ft2


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?

A 100 cm

B 75 cm

C 50 cm

D 150 cm


Describe the effect on the area of a circle whenthe radius is doubled.

F The area is reduced by ½.

G The area remains constant.

H The area is doubled.

J The area is increased four times.


(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.

(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.

If a wheel spins at a rate of 36 revolutions per minute, how many revolutions per hour does the wheel spin?


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


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


A watch loses 3 minutes every 24 hours. How much time till it lose in 2 hours?

A 1.6 seconds

B 5 seconds

C 15 seconds

D 22.5 seconds


(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);

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?


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?


(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?

F Red

G White

H Blue

J Yellow


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?

F 58

G 10

H 6

J 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 to describe a set of data for a particular purpose;

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?

A Mode

B Mean

C Median

D Range


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

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

The 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?


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?


Which histogram best reflects the data shown in the table?


(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.

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?


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.


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.


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 clubB The number of hours the bus was driven each dayC The number of days the bus was rentedD The total number of miles the bus was driven


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?

A The percent markdown for the shirts

B The original price of the jeans

C The percent markdown for the jeans

D No additional information is needed


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?

F 2(x – 4) = 16

G 2x – 4 = 16

H 4 – 2x = 16

J 2(4 – x) = 16


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?

F The mean height of waves in 1955

G The range of wave heights from 1955 to 1994

H The projection of the mean height of waves for the next year

J The distance from land to where the wave measurements were taken


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?


Mr. McGregor wanted to coverthe floor in his living room withcarpet that cost $12 per squareyard. The blueprint showsthe area of the livingroom relative tothe area of the house.What information must beprovided in order to find thetotal cost of the carpet?

F The lengths and widths of the adjoining rooms in the blueprint

G The scale of yards to inches in the blueprint

H The total area of the house in the blueprint

J The thickness of the carpeting in inches



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

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?

F Determine the area of the property, multiply by 5, and then divide by the sum of 1380 and 500G Determine the perimeter of the property, multiply by 5,

add 500, and then divide by 1380H Determine the area of the property, multiply by 5, add

500, and then divide by 1380J Determine the perimeter of the property, multiply by 5,

and then divide by the sum of 1380 and 500


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 togetherG Multiply the total number of main-course choices by the

total number of side-order choices and add the product tothe total number of beverage choices

H Multiply the sum of the total number of main-coursechoices and the total number of side-order choices by thetotal number of beverage choices

J Multiply the total number of items in each of the 3categories together


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



(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?

A 34 units2

B 27 units2

C 21 units2

D 17 units2


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?

F Rosie’s Fruit Stand

G Fruits and More

H Nicky’s Fruit Store

J Freshly Picked Fruits


Jake’s square backyard covers an area of 104 square meters. How can Jake best determine the length of each side of his backyard?

F Divide the area by the number of sides

G Square the area

H Find the square root of the area

J Divide the area in half


Which of the following equations below represents the second step of the solution process?

Step 1. 5(6x + 4) + 1 = -39Step 2.Step 3. 30x + 21 = -39Step 4. 30x = -60Step 5. x = -2

A 5(6x + 1) + 4 = -39

B 5(6x + 5) = -39

C 30x + 4 + 1 = -39

D 30x + 20 + 1 = -39Correct 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 -

A volume

B surface area

C circumference

D perimeter


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


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.


Which problem is best represented by the number sentence 19 + 3(12 – x) = 40?

F Ricardo spent $19, and Lydia spent 3 times $12 less than Ricardo. Together they spent $40. How much did Lydia spend?G Gail 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?H Juan earned $19 baby-sitting and sold 3 boxes of apples for $12 each. Now he has $40. How much did he earn?J Denise 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?


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?

A The prism has the greater volume.

B The cylinder has the greater volume.

C The volumes are equivalent.

D The volumes cannot be determined.


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

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

The integers 1881, 353, 2002, and 787 are palindrome integers. Which of the following is also a palindrome integer?

F 1961

G 828

H 2525

J 783


The figure below shows a partial view of Pascal’s triangle. Which row of numbers best represents the seventh row in Pascal’s triangle?

F 1 5 10 10 5 1

G 1 6 15 20 15 6 1

H 1 7 21 35 35 21 7 1

J 1 8 28 56 70 56 28 9 1


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


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?


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 a < b and b = c, which statement must be true?

A The values of a, b, and c are positive.

B The values of a, b, and c are negative.

C The value of a is less than the value of c.

D The value of a is greater than the value of c.


Line t intersects parallel lines l1 and l2, 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


Sean is an Algebra I student who believes that xy2 = (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?

F x = 0 and y = 2

G x = 1 and y = 2

H x = 2 and y = 0

J x = 2 and y = 1


If the variables x and y are related so that x – y > x + y, which statement must be true?

F The variable x is greater than the variable y.

G The variable x is a negative number.

H The variable y is a negative number.

J The variable y is a positive number.


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