Practice Test: Elementary Mathematics (68)

Use the diagram below to answer the question that follows.

Five rectangles are shown in a row. The fill color of the rectangles alternates as follows: black, white, black, white, black. A key shows that a black rectangle represents the digit 1, a white rectangle represents the digit zero, and a striped rectangle represents the digit 2.

A teacher is using cards to model the digits in base-3 numbers. Which of the following is the number shown in the diagram written in base 10?

1. 91
2. 93
3. 271
4. 273

Use the information below to answer the question that follows.

Which of the numbers listed above has the greatest value?

1. − negative 2.1
2. − negative 2.4
3. − negative 2 ¹ / ₅  1 fifth 
4. − negative 2 ⁴ / ₅  4 fifths 

The edge length of a cube may be found from its volume, and the volume of the cube may be found from its edge length. Which of the following statements best explains the relationship between these two procedures?

1. All the edges of a cube are equal in length.
2. Multiplying by 3 and dividing by 3 are inverse operations.
3. The volume of a rectangular prism is length times width times height.
4. Exponentiating to the power of 3 and finding a cube root are inverse operations.

An event organizer is asked to arrange a set of folding chairs as follows:

• Make equal rows of chairs.
• The number of rows should be less than the number of chairs in a row.
• The number of rows should be greater than 1.

The event organizer realized that there was only one way to arrange the chairs in this manner. How many chairs could have been in this set?

1. 30
2. 35
3. 36
4. 37

Use the number line below to answer the question that follows.

A number line is shown with tick marks in intervals of 1 from 0 to 4. A point x is located slightly less than halfway between 3 and 4.

Point X represents an irrational number. Which of the following expressions could represent the same number?

1. ³⁸ / ₁₁  38 elevenths 
2. √ 7  radical 7 
3. 3.46
4. √ 12  radical 12 

Use the diagram below to answer the question that follows.

A rectangle is shown with a dimensions 5 units tall by 14 units wide. A vertical line divides the rectangle into two smaller rectangles with areas of 8 times 5 square units and 6 times 5 square units, respectively.

Student A says that the area of the large rectangle can be found using 5 × 14.

Student B says that the area of the large rectangle can be found using 5 × 8 +plus 5 × 6.

Which of the following statements best evaluates the claims of the students?

1. Only Student A is correct because area is length times width.
2. Only Student B is correct because the whole is the sum of the parts.
3. They are both correct because multiplication is repeated addition.
4. They are both correct because multiplication distributes over addition.

Which of the following equations best illustrates the concept of the additive inverse?

1. 4 + 0 = 4 − minus  0
2. 3 + (− negative 3) = 0
3. 4 + (− negative 1) = (− negative 1) + 4
4. 3 + ¹ / ₃  1 third  = ¹ / ₃  1 third  + 3

Which of the following diagrams exhibits a one-to-one correspondence?

1. One book is shown with three rays pointing away from the book. There is one crayon at the end of each ray.


2. Three books are shown, each with a ray pointing to the same singular crayon.


3. Three books are shown. Three rays connect each individual book with one unique crayon.


4. A column of three books is shown beside a column of three crayons. A ray connects the top book to the top crayon. A second ray connects the top crayon to the second book. A third ray connects the second book to the second crayon. A fourth ray connects the second crayon to the third book. A fifth ray connects the third book to the third crayon.

The average distance from Earth to the Moon is about 2.4 × times  10⁵ 10 to the fifth power  miles. The shortest distance from Earth to Mars in 2018 is about 3.6 × times  10⁷ 10 to the seventh power  miles. If the distance from Earth to Mars is n times the distance from Earth to the Moon, which of the following expressions is the best approximation for n?

1. 1.5 × times  10⁻² 10 to the negative second power 
2. 15
3. 150
4. 15 × times  10² 10 squared 

There are x students in an art class. On y occasions, a teacher gives each one of them a sheet of stickers. On each sheet, there are z stickers. The total number of stickers on all the sheets is 1,125. How many of the numbers x, y, and z must be odd?

1. exactly one
2. exactly two
3. one or three, but not two
4. all three

Given that a, b, and c are integers and that a ≤ is less than or equal to  b and b > is greater than  c, which of the following number lists could represent a, b, and c, respectively?

1. 1, 1, 2
2. − negative 3, − negative 2, 1
3. − negative 1, − negative 2, 3
4. − negative 2, − negative 1, − negative 2

Use the table and number line below to answer the question that follows.

A number line is shown with the points e, f, g, and h appearing in that order from left to right. Point E is located at 0.25, and point H is located to the left of 0.26.

The thicknesses of four different metal sheets are listed in the table and are represented by points on the number line. Which sheet is best represented by point G on the number line?

1. Sheet 1
2. Sheet 2
3. Sheet 3
4. Sheet 4

A decimal is written with nonzero digits to the thousandths place and another decimal is written with nonzero digits to the hundredths place. What is the smallest possible place value that can contain a nonzero digit in the product of these two numbers?

1. thousandths
2. ten-thousandths
3. hundred-thousandths
4. millionths

Use the table below to answer the question that follows.

Which of the following statements accurately describes the mathematical steps shown in the division problem?

1. The identity property of addition was used to write 426 ÷ divided by  20 as (400 + 20 + 6) ÷ 20. The quantity 400 plus 20 plus 6 divided by 20 
2. The distributive property was used to write (400 + 20 + 6) ÷ 20 as 20 + 1 + ⁶ / ₂₀ .  6 twentieths 
3. The commutative property was used to write 20 + 1 + ⁶ / ₂₀  6 twentieths  as 21 ⁶ / ₂₀ .  6 twentieths 
4. The associative property was used to write 21 ⁶ / ₂₀ .  6 twentieths  as 21 ³ / ₁₀ .  3 tenths 

A clothing store has a sale where a customer who buys one shirt at the regular price may buy a second identical shirt at a discount of half-off the regular price. If a customer buys these two shirts, what percent discount, to the nearest whole, does the customer receive on the entire purchase?

1. 25%
2. 33%
3. 50%
4. 75%

On Monday, a construction supervisor accurately reports that 5% of an original supply of concrete was used that day. On Tuesday, another supervisor accurately reports that ¹ / ₅  1 fifth  of the original supply of concrete was used that day. What part of the original supply of concrete, written in decimal form, was used on these two days?

1. 0.07
2. 0.10
3. 0.20
4. 0.25

Use the diagram below to answer the question that follows.

A square that is divided into 100 square units (10 rows and 10 columns) is shown with a shaded gray region that contains the first 5 columns and 6 of the units in the sixth column. There is a minus symbol, followed by a congruent square that is evenly divided into 10 vertical columns, the first two of which are shaded.

The model above represents subtraction of decimals. What is the value represented by the model?

1. 0.24
2. 0.36
3. 0.42
4. 0.54

Use the number line below to answer the question that follows.

A number line is shown that has tick marks in intervals of 0.25 from 0 to 1. Point P is slightly to the left of 0.50, and point Q is slightly to the right of 0.75.

Points P and Q on the number line above represent two numbers. Which of the following set of equations expresses possible values of both numbers?

1. P = 0.18, Q = 0.31
2. P = 0.40, Q = 0.70
3. P = 0.42, Q = 0.77
4. P = 0.48, Q = 0.92

Let n represent a whole number from 1 to 10. Which of the following numbers can be used to represent ⁿ / ₁₁  N divided by 11  as a decimal in the form 0.ab Zero point a b repeating 

1. any values of n that are prime
2. any values of n that are odd
3. any values of n that are even
4. any of the possible values for n

Students are simplifying fractions that are less than one and then writing them as decimals. Which of the following statements would be a correct conclusion for the students to make about each of the simplified fractions that produces a terminating decimal?

1. The denominator is not divisible by any prime number other than 2 or 5.
2. The numerator is not divisible by any prime number other than 2 or 5.
3. The denominator must be an even number.
4. The numerator must be an even number.

A shopper finds a refrigerator with a list price of $755 755 dollars  offered for sale at a 20% discount. To estimate the sale price of the refrigerator, the shopper correctly rounds the list price to the nearest hundred dollars and then applies the discount. What is the difference between the shopper's estimate and the actual sale price?

1. $9.00 9 dollars 
2. $11.00 11 dollars 
3. $36.00 36 dollars 
4. $44.00 44 dollars 

In a particular adult skeleton, the length of the humerus is 36.46 centimeters. The length of the hand is 18.9 centimeters. How much longer is the length of the humerus than the length of the hand?

1. 17.56 centimeters
2. 18.37 centimeters
3. 27.44 centimeters
4. 55.36 centimeters

In a certain recipe for pancakes, 42% percent  of the pancake batter is flour. A person doubles the recipe to create 600 grams of pancake batter. How many grams of flour are used to make the pancake batter?

1. 84 grams
2. 126 grams
3. 252 grams
4. 504 grams

A retailer puts out-of-season clothing on sale for 40% percent  off the regular price, r. Each subsequent week, the retailer reduces the sale price by an additional 10% percent . Which of the following expressions represents the sale price during the third week of the sale?

1. 0.324r
2. 0.486r
3. 0.514r
4. 0.996r

Two boxes of flavored granola bars each contained the same number of bars. After 21 of the honey bars and 32 of the raisin bars were eaten, there were twice as many honey bars as raisin bars left over. Which of the following tape diagrams best illustrates this situation?

1. A rectangle that represents 21 is used to indicate the number of raisin bars. The rectangle that represents the number of honey bars is two times as long.
2. A rectangle that represents the value of 11 is used to indicate the number of honey bars. The rectangle that represents the raisin bars is two times as long.
3. For the honey bars, a large rectangle is divided such that two smaller, equal rectangles are shaded, and the unshaded portion of the diagram is labeled 21. For the Raisin bars, a large rectangle is divided such that one smaller rectangle is shaded, and the unshaded portion of the diagram is labeled 32.
4. For the Honey bars, a large rectangle is divided such that one smaller rectangle is shaded, and the unshaded portion of the diagram is labeled 32. For the Raisin bars, a large rectangle is divided such that two smaller, equal rectangles are shaded, and the unshaded portion of the diagram is labeled 21.

Use the number sentence below to answer the question that follows.

11 ÷ divided by  4 = 2 remainder 3

The remainder shown above can be represented by which of the following?

1. ³ / ₂  3 halves 
2. ³ / ₄  3 fourths 
3. ² / ₃  2 thirds 
4. ⁴ / ₃  4 thirds 

The fractions ^x / ₄  x over 4  and ⁶ / _y  6 over y  are equivalent. The value of the product of x and y must be equal to which of the following values?

1. 10
2. 12
3. 24
4. 25

A group of 30 students is eating pizza for lunch. Each student will eat 2 slices of pizza and each pizza is divided into 8 slices. One-third of the students will eat the cheese pizza and the remaining students will eat pepperoni pizza. Which of the following expressions illustrates the total number of pepperoni pizzas that should be purchased?

1. ^{(30 × 2)} / ₈ × ² / ₃  The quantity 30 times 2 divided by 8 times the fraction 2 thirds 
2. ^{(30 × 2)} / _{8 × ¹ / 3}   The quantity 30 times 2 divided by the quantity 8 times 1 third 
3. ^{(30 × 2)} / ₈ × ¹ / ₃  The quantity 30 times 2 divided by 8 times the fraction 1 third 
4. ^{(30 × 2)} / _{8 × ² / 3}   The quantity 30 times 2 divided by the quantity 8 times 2 thirds 

An artist created three pieces of art. The first piece weighs 9 pounds, the second piece weighs ⁵ / ₆  5 sixths  as much as the first piece, and the third piece weighs ⁴ / ₅  4 fifths  as much as the second piece. What is the total combined weight of the three art pieces?

1. 22 ¹ / ₂  and 1 half  pounds
2. 23 ⁷ / ₁₀  and 7 tenths  pounds
3. 27 ⁹ / ₁₁  and 9 elevenths  pounds
4. 28 ¹⁹ / ₃₀  and 19 thirtieths  pounds

Use the diagram below to answer the question that follows.

An array model for multiplication is shown with the horizontal axis label "payment" and the vertical axis label "number of monthly payments." Both the payment and the number of monthly payments are expressed in standard form, but the only digit that is known is a "5" in the ones place for the payment. The table is divided into four quadrants, with the top row containing 600 and 150 from left to right. The bottom row has a 120 in the first column and the second column is blank.

A college student buys a sofa and pays for it in equal monthly installments. The partially filled area model above represents the product of the number of monthly payments with the monthly payment in dollars. How many monthly payments does the college student have to make?

1. 25
2. 26
3. 35
4. 36

A large university marching band has a drum line with 46 members. The band director is considering purchasing new snare drums for all members at a cost of $237 237 dollars  each. The director rounds both numbers to the nearest ten to estimate the total cost. What is the correct estimate using this method?

1. $9,200 9,200 dollars 
2. $9,600 9,600 dollars 
3. $11,500 11,500 dollars 
4. $12,000 12,000 dollars 

A student uses estimation to add four piles of money. The student rounds up each pile of money to the nearest tenths place and then adds the rounded values. What is the greatest possible difference between the value computed by the student and the actual amount of money?

1. $0.10 10 cents 
2. $0.12 12 cents 
3. $0.15 15 cents 
4. $0.18 18 cents 

A confectioner makes a tray of fudge that is 12 inches wide, 15 inches long, and 1 inch deep. A cubic inch of fudge weighs about ¹ / ₂₀  1 twentieth  pound. The confectioner cuts the fudge into pieces that weigh ¹ / ₁₆  1 sixteenth  pound. How many pieces does the tray produce?

1. 140
2. 144
3. 180
4. 225

What is the value of the expression − negative  ³ / ₂  3 halves  ÷ divided by  (−5)² the quantity negative 5 squared ?

1. − negative  ⁹ / ₁₀₀  9 hundredths 
2. − negative  ³ / ₅₀  3 fiftieths 
3. ³ / ₅₀  3 fiftieths 
4. ⁹ / ₁₀₀  9 hundredths 

Use the number line below to answer the question that follows.

A number line is shown that has tick marks in increments of 1 from b to a. The labels on the tick marks, from left to right, are b, negative 1, 0, 1, and a. A line segment of length d is shown above the number line that spans the length from b to a.

Which of the following expressions represents the length of line segment d?

1. |a + b| The absolute value of the quantity a plus b 
2. |a| + |b| The absolute value of a plus the absolute value of b 
3. a + ba plus b
4. |a| − |b| The absolute value of a minus the absolute value of b 

Use the expression below to answer the question that follows.

2 ¹ / ₂ × ¹ / ₄  2 and one half times 1 fourth 

Which of the following problems can be solved using the operation above?

1. A person has 2 ¹ / ₂  2 and one half  gallons of paint and uses ¹ / ₄  1 fourth  of it to paint a wall. How much paint was used?
2. A bicyclist travels 2 ¹ / ₂  2 and one half  miles in ¹ / ₄  1 fourth  of an hour. How many miles per hour is the bicyclist traveling?
3. A rectangle has a length of 2 ¹ / ₂  2 and one half  inches. If the width of the rectangle is ¹ / ₄  1 fourth  of the length, what is the area of the rectangle?
4. A bag contains 2 ¹ / ₂  2 and one half  cups of chocolate chips. If one batch of a recipe calls for ¹ / ₄  1 fourth  cup of chocolate chips, how many batches can be made?

Which of the following equations represents a valid algorithm?

1. 2 ³ / ₄ + 3 ¹ / ₃ = (2 + 3) + ³ / ₄ + ¹ / ₃  2 and 3 fourths plus 3 and 1 third equals the quantity 2 plus 3 plus the quantity 3 fourths plus 1 third 
2. 2 ³ / ₄ × 3 ¹ / ₃ = (2 × 3) + ³ / ₄ × ¹ / ₃  2 and 3 fourths times 3 and 1 third equals the quantity two times 3 plus the quantity 3 fourths times 1 third 
3. 2 ³ / ₄ ÷ 3 ¹ / ₃ = (2 ÷ 3) + ³ / ₄ ÷ ¹ / ₃  2 and 3 fourths divided by 3 and 1 third equals the quantity 2 divided by 3 plus the quantity 3 fourths divided by 1 third 
4. 2 ³ / ₄ − 3 ¹ / ₃ = (2 − 3) − ³ / ₄ − ¹ / ₃  2 and 3 fourths minus 3 and 1 third equals the quantity 2 minus 3 minus the quantity 3 fourths minus 1 third 

Use the graph below to answer the question that follows.

A graph is shown in the first quadrant with a vertical axis label of perimeter, in feet, and a horizontal axis label of area, in square feet. Both axes increase in increments of one unit from 0 to 10. A continuous graph is shown that starts at the origin. The graph increases at a progressively decreasing rate, passing through the point 4, 8.

A rancher wants to build a square enclosure with area x square feet and will need y feet of fencing. The graph above models the relationship between x and y. Which of the following equations represents the same relationship?

1. y = 2x
2. y = √ x radical x  + 6
3. y = x² − 8 x squared minus 8 
4. y = 4√ x 4 radical x 

Use the table below to answer the question that follows.

The table above shows how the intensity of light changes with increased distance from the point of the light source. Which of the following functions best models the relationship between the distance from the light source, x, and the intensity of the light, f(x)?

1. f(x) f of x  = ¹ / _√ x  1 divided by the square root of x 
2. f(x) f of x  = ^x / _√ x  x divided by the square root of x 
3. f(x) f of x  = ^x2 / ₁  x squared divided by 1 
4. f(x) f of x  = ¹ / _x²  1 divided by x squared 

Use the diagram below to answer the question that follows.

A function machine is shown where an input goes into the machine. The input is subtracted by 2, and that result is squared to get the output.

Which of the following graphs models the input and output of the function machine shown in the diagram?

1. The graph of a parabola that opens up is shown with a vertex at a positive value on the x axis. The x axis is labeled input and the y axis is labeled output.
2. The graph of a function is shown that increases at a progressively decreasing rate. The x axis is labeled input and the y axis is labeled output.
3. The graph of a cubic function is shown with the inflection point in the first quadrant. The x axis is labeled input and the y axis is labeled output.
4. The graph of a parabola that opens down is shown, with a vertex in the first quadrant. The x axis is labeled input and the y axis is labeled output.

Use the diagram below to answer the question that follows.

A diagram shows a board that is balanced on a fulcrum located at the midpoint of the board. A 30 gram object is resting on the far left side of the board, and an object with mass m is located on the board to the right of the fulcrum. The distance between the object on the right and the fulcrum is labeled x.

The diagram above shows a 30-gram mass at the end of a board that is at rest on a fulcrum. The mass, m, needed to balance the 30-gram mass is inversely proportional to x, its distance from the fulcrum. The board balances when m = 30 grams and x = 60 centimeters. If x = 20 centimeters, what mass, m, is needed to balance the board?

1. 10 grams
2. 40 grams
3. 90 grams
4. 120 grams

Use the figures below to answer the question that follows.

A pattern is shown where figure one is a square that is divided into four congruent triangles by the diagonals of the square. The rightmost triangle is shaded. Figure 2 contains a 2 by 2 arrangement of the square from figure 1. Figure 3 is a 3 by 3 arrangement, and figure 4 is a 4 by 4 arrangement.

The four squares in the series above contain shaded and unshaded triangles. If this pattern continues, how many unshaded triangles will there be in the seventh figure in the series?

1. 49
2. 81
3. 108
4. 147

Use the diagram below to answer the question that follows.

A cross section of a container is shown that is composed of three parts from top to bottom: a square on top of a trapezoid such that one side of the square makes up the small base of the trapezoid, on top of an inverted trapezoid such that the long base of the first trapezoid is also the long base of the inverted trapezoid.

Water is poured at a constant rate into a container with the shape shown above. Which of the following graphs best represents the height, h, of the water as a function of time, t?

1. A curve is shown that increases at an increasing rate then increases at a decreasing rate, then increases at an increasing rate. The horizontal axis is labeled t and the vertical axis is labeled h.
2. A graph is shown that increases at a decreasing rate, then increases at an increasing rate. The horizontal axis is labeled t and the vertical axis is labeled h.
3. A graph is shown that increases at an increasing rate, then decreases to a horizontal line, then increases at an increasing rate. The horizontal axis is labeled t and the vertical axis is labeled h.
4. A graph is shown that increases at a decreasing rate until the graph is horizontal, then it rapidly increases at an increasing rate. The horizontal axis is labeled t and the vertical axis is labeled h.

Use the graph below to answer the question that follows.

A graph is shown that relates time on the x axis to distance from home on the y axis. Time is indicated in increments of 20 minutes and distance from home is indicated in units of 1 mile. The graph is composed of linear segments that connect the following points: (0, 0), (10, 1), (30, 2), (60, 2), (90, 5), and (120, 0).

The graph above best represents which of the following scenarios?

1. A bicyclist leaves home and travels 1 mile during the first 10 minutes and then 2 miles in the next 10 minutes. The cyclist then stops for a 30-minute break before continuing for another 30 minutes on a 3-mile rough dirt road. Finally, the cyclist rides for 30 minutes on a 5-mile direct route home.
2. A bicyclist leaves home and travels 1 mile during the first 10 minutes and then an additional mile uphill in the next 20 minutes. The cyclist then bicycles out a short side road and returns to the main road before cycling another 30 minutes on a 2-mile rough dirt road and returning home along a direct 5-mile route.
3. A bicyclist leaves home and travels 1 mile on a paved road during the first 10 minutes and an additional mile on a rough dirt road during the next 20 minutes. The cyclist then stops for 30 minutes before continuing 3 miles down a paved road to a river. Finally, the cyclist returns home on a direct paved road, completing the trip in 2 hours.
4. A bicyclist leaves home and travels 1 mile during the first 10 minutes and then an additional 2 miles in the next 20 minutes. The cyclist then stops for a 30-minute break before continuing, traveling on a 3-mile rough dirt road for 30 minutes. Finally, the cyclist rides home on a direct route on a paved road, completing the trip in 2 hours.

What is the value of 3x⁻¹ − x³ 3 x to the negative first power minus x cubed  when x = − negative 2?

1. −9 ¹ / ₂  negative 9 and 1 half 
2. −8 ¹ / ₆  negative 8 and 1 sixth 
3. 6 ¹ / ₂  6 and 1 half 
4. 7 ⁵ / ₆  7 and 5 sixths 

An engineer describes the rate at which water passes through a pipe using a flow rate. The flow rate, Q, is directly proportional to V, the volume of water passing through the pipe, and inversely proportional to t, the amount of time that this takes. Which of the following equations correctly relates these variables?

1. QV Q times V  = t
2. Qt Q times t  = V
3. V = ^Q / _t  Q divided by t 
4. t = ¹ / _QV  1 over the product of Q and V 

Which of the following expressions is equivalent to 8x − 5(x − 1) + 3x 8 x minus 5 times the quantity x minus 1 plus 3 x ?

1. 10x − minus  1
2. 3x + 5
3. 6x − minus  1
4. 6x + 5

Which of the following equations expresses y = x + dn − minus  d when it is correctly rearranged to solve for n?

1. n = y + x − minus  2d
2. n = ^{y − d + x} / _d  the expression y minus d plus x all divided by d 
3. n = 1 + ^{y − x} / _d  the quantity y minus x divided by d 
4. n = ^{x − d} / _{y − d}  the expression x minus d divided by the expression y minus d 

Use the problem below to answer the question that follows.

The shaded area of which of the following graphs represents the solution to this problem?

1. A graph is shown in the first quadrant of the coordinate plane such that the horizontal axis represents the number of racers and the vertical axis represents the number of cruisers. The graph shows the shaded area that is defined by the inequalities x plus y is less than or equal to 24 and 2 x plus y is less than or equal to 40.
2. A graph is shown in the first quadrant of the coordinate plane such that the horizontal axis represents the number of racers and the vertical axis represents the number of cruisers. The graph shows the shaded region defined by the inequalities y is less than or equal to 20 and x plus y is less than or equal to 24.
3. A graph is shown in the first quadrant of the coordinate plane such that the horizontal axis represents the number of racers and the vertical axis represents the number of cruisers. The graph shows the shaded region defined by the inequalities x plus y is less than or equal to 24 and x is less than or equal to 12.
4. A graph is shown in the first quadrant of the coordinate plane such that the horizontal axis represents the number of racers and the vertical axis represents the number of cruisers. The graph shows the shaded region defined by the inequality x plus y is less than or equal to 24.

Use the table below to answer the question that follows.

An investor buys stock in three companies in the amounts shown in the table. A second investor buys a total of $2100 2,100 dollars  in stocks in the same three companies and in the same ratio. How much does the second investor put into each company?

1. $900 900 dollars  in X, $600 600 dollars  in Y, and $300 300 dollars  in Z
2. $950 950 dollars  in X, $700 700 dollars  in Y, and $450 450 dollars  in Z
3. $1050 1,050 dollars  in X, $350 350 dollars  in Y, and $700 700 dollars  in Z
4. $1050 1,050 dollars  in X, $700 700 dollars  in Y, and $350 350 dollars  in Z

Use the table below to answer the question that follows.

The table gives the prices for certain numbers of gourmet muffins sold at a bakery. The unit price is the same regardless of how many muffins a person buys. Which of the following values would complete the table?

1. $18.90 18 dollars and 90 cents 
2. $22.50 22 dollars and 50 cents 
3. $24.75 24 dollars and 75 cents 
4. $33.00 33 dollars 

At an animal shelter, 25% of the animals are cats and ² / ₃  2 thirds  of the cats are classified as kittens. If there are 12 kittens, which of the following proportions can be used to calculate the total number of animals, a, at this shelter?

1. ²⁵ / ₁₀₀  25 divided by 100  = ⁸ / _a  8 divided by a 
2. ²⁵ / ₁₀₀  25 divided by 100  = ^a / ₈  a divided by 8 
3. ²⁵ / ₁₀₀  25 divided by 100  = ¹⁸ / _a  18 divided by a 
4. ²⁵ / ₁₀₀  25 divided by 100  = ^a / ₁₈  a divided by 18 

Use the diagram below to answer the question that follows.

Two similar triangles, O M N and R P Q are shown. O M N is the smaller of the two triangles, with side O M equal to 9 units, side M N equal to 19 units, and side O N equal to 27 units. Side R Q is equal to 108 units.

In the diagram above, △ OMN triangle O M N  is similar to △ RPQ triangle R P Q . Which of the following proportions can be used to calculate PQ?

1. ¹⁰⁸ / _PQ  108 divided by P Q  = ²⁷ / ₉  27 divided by 9 
2. ^PQ / ₁₉  P Q divided by 19  = ¹⁰⁸ / ₉  108 divided by 9 
3. ²⁷ / _PQ  27 divided by P Q  = ¹⁹ / ₁₀₈  19 divided by 108 
4. ^PQ / ₁₀₈  P Q divided by 108  = ¹⁹ / ₂₇  19 divided by 27 

In which of the following equations does the dependent variable vary directly with the independent variable?

1. yx y times x  = 2
2. y = 3x + 9
3. yx y times x  = x + 1
4. y = 7x

If r, s, t, and u are variables, which of the following equations makes the relationship ^r / _s  r divided by s  = ^t / _u  t divided by u  a proportion?

1. r + u = t + s
2. ur u times r  = st s times t 
3. r + t = u + s
4. tr t times r  = su s times u 

A real estate company is selling building lots of various dimensions in a new development. The price of each lot is directly proportional to its area. If a 200-foot by 200-foot parcel costs $24,000 24,000 dollars , what is the cost of a 260-foot by 200-foot lot?

1. $31,200 31,200 dollars 
2. $40,000 40,000 dollars 
3. $40,560 40,560 dollars 
4. $52,000 52,000 dollars 

Use the table below to answer the question that follows.

A traveler steps onto a moving walkway in an airport and stands still while riding it. The table shows the traveler's distance in feet from the end of the walkway after having ridden for the given number of minutes. How fast is the walkway moving?

1. 120 feet per minute
2. 130 feet per minute
3. 320 feet per minute
4. 380 feet per minute

A machine in a factory, working at a constant rate, produces 36 pies in 2 hours. After some maintenance work, the machine produces 240 pies in 8 hours. By how much did the machine's rate of production improve?

1. 12 pies per hour
2. 18 pies per hour
3. 30 pies per hour
4. 34 pies per hour

At which of the following values does the graph of 3x + 2y = 12 cross the x-axis?

1. 2
2. 3
3. 4
4. 6

A company models the demand for its product with the equation d = − negative 17,500p + 78,750, where p is the price for the product in dollars per unit and d is the demand for the product in units. If the company increases the price by $0.50 50 cents , what is the predicted effect on demand for this product?

1. Demand will increase by 70,000 units.
2. Demand will decrease by 70,000 units.
3. Demand will increase by 8,750 units.
4. Demand will decrease by 8,750 units.

Use the graph below to answer the question that follows.

The graph titled cost of renting trucks shows the relationship between the driving distance in intervals of 20 miles on the x axis and the cost in dollars in intervals of 20 dollars on the y axis. A solid line passing through the points 0, 20 and 160, 100 represents the relationship for a 12 foot truck, and a dotted line passing through the points 0, 40 and 160, 80 represents the relationship for a 20 foot truck.

In the graph above, analysis of which of the following characteristics of the lines would allow the comparison of the driving costs per mile for a 12-foot versus a 20-foot truck?

1. the x-intercepts
2. the slopes
3. the y-intercepts
4. the intersection

Use the equation below to answer the question that follows.

48x = 12y − 17 − 3x  12 y minus 17 minus 3 x 

What is the x-intercept of the graph of this equation?

1. − negative 3
2. − ¹ / ₃  negative 1 third 
3. ¹⁷ / ₄₅  17 forty fifths 
4. ¹⁷ / ₁₂  17 twelfths 

Use the figure below to answer the question that follows.

Cardboard boxes are arranged on the floor of a warehouse, as shown in the figure. Each box is a cube and has a volume of 8 cubic feet. How much floor space do the boxes occupy?

1. 25 square feet
2. 100 square feet
3. 200 square feet
4. 1600 square feet

A student is painting a sign in the shape of an equilateral triangle. The student has painted from the base up to a line that is parallel to the base and halfway between the base and the vertex at the top. The amount of paint the student needs to complete the job is:

1. ¹ / ₆  1 sixth  the amount that has already been used.
2. ¹ / ₄  1 fourth  the amount that has already been used.
3. ¹ / ₃  1 third  the amount that has already been used.
4. ¹ / ₂  1 half  the amount that has already been used.

Use the diagram below to answer the question that follows.

Rectangle E F G H is divided into three triangles using congruent line segments that connect vertex E and vertex H to the midpoint of segment F G. The triangles are labeled 2, 1, 3 from top to bottom. Rectangle J K L M is divided into three triangles using congruent line segments that connect vertex m and vertex L to the midpoint of segment JK. The triangles are labeled 4, 5, and 6 from left to right.

Rectangle EFGH ≅ rectangle JKLM E F G H is congruent to rectangle J K L M . Which of the following statements comparing the areas of the numbered triangles in the diagram is true?

1. The sum of the areas of triangles 2 and 3 is equal to the area of triangle 5.
2. The sum of the areas of triangles 2 and 3 is greater than the area of triangle 5.
3. The sum of the areas of triangles 1 and 2 is less than the sum of the areas of triangles 4 and 5.
4. The sum of the areas of triangles 1 and 2 is equal to the sum of the areas of triangles 4 and 6.

Use the diagram below to answer the question that follows.

Right trapezoid W V Y U is composed of a 30 60 90 right triangle, a parallelogram, and an equilateral triangle. Right triangle W Z U shares a side with parallelogram W X Y Z which shares a side with equilateral triangle X Y V.

Which of the following statements about figure WXYZ must be true?

1. Its four sides are congruent, so it is a rhombus.
2. Opposite angles are congruent, so it is a parallelogram.
3. Adjacent angles are not congruent, so it is not a rhombus.
4. Its four sides are not congruent, so it is not a parallelogram.

Use the diagram below to answer the question that follows.

A circle is shown with a central angle measuring 60 degrees. The arc opposite the 60 degree central angle is labeled as 4 feet long.

Which of the following expressions represents the area of the circle shown?

1. 8π pie  square feet
2. ¹⁴⁴ / _π pie   144 divided by pie  square feet
3. 16π pie  square feet
4. ¹²⁰ / _π pie   120 divided by pie square feet

Use the diagram below to answer the question that follows.

A net is shown that consists of a square and 4 congruent equilateral triangles. The top of the square shares a side with one equilateral triangle, and the leftmost side of that equilateral triangle shares a side with another equilateral triangle. The right side of the square shares a side with an equilateral triangle with a vertex P that is not on the square, and the bottom right side of that equilateral triangle shares a side with another equilateral triangle.

The net shown above consists of a square and equilateral triangles. It is folded up to form a solid. A cross section of the solid passes through point P and is perpendicular to the square. What shape is the cross section?

1. a square
2. a trapezoid
3. an isosceles triangle
4. a rectangle that is not a square

Use the diagram below to answer the question that follows.

A square is inscribed in a circle with a radius of 4 inches. The area between the sides of the square and the circle is shaded.

The diagram shows a square inscribed in a circle with a radius of 4 inches. Which of the following approximations is closest to the area of the shaded region?

1. 9 square inches
2. 18 square inches
3. 28 square inches
4. 34 square inches

Use the diagram below to answer the question that follows.

A tree is supported by 2 cables attached to two posts that are located to the right and left of the tree. Each post is located 8 feet away from the tree, and each cable connects from a point that is 2 feet above the ground on a post to a location on the tree trunk that is 8 feet above the ground.

A tree is supported by two separate cables attached to posts as shown in the diagram. Each piece of cable must be 1.5 feet longer than the distance between where it attaches to the post and the tree. Assuming that the ground surface is level and that the tree is perpendicular to the ground surface, what is the total length of cable required for the project?

1. 20 feet
2. 23 feet
3. 24 feet
4. 31 feet

Use the diagram below to answer the question that follows.

The square pyramid shown has a base that is 60 feet on a side. The vertex of the pyramid is 40 feet above its base. What is the combined surface area of the triangular faces that make up the outside of the pyramid?

1. 1500 square feet
2. 4800 square feet
3. 6000 square feet
4. 9600 square feet

Use the diagram below to answer the question that follows.

The horizontal line segment A B is shown in the coordinate plane, with endpoint A located at negative 2, 1 and endpoint B located at 8, 1.

Isosceles triangle ABC A B C  has base AB A B  shown in the coordinate grid, and vertex C (not shown) in the first quadrant. Which of the following must be true of the coordinates of point C?

1. The x-coordinate is 3.
2. The x-coordinate is 4.
3. The y-coordinate is 5.
4. The y-coordinate is 11.

Use the diagram below to answer the question that follows.

Quadrilateral A B C D is shown in the coordinate plane, with vertex A located at the point negative 6, 3, vertex B located at the point negative 1, 3, vertex C located at the point 1, negative 3, and vertex D located at the point negative 5, negative 3.

Which of the following statements correctly describes figure ABCD A B C D ?

1. It is neither a trapezoid nor a parallelogram.
2. It is a trapezoid because AB A B  is parallel to DC D C .
3. It is a trapezoid because AD A D  is parallel to BC B C , AB A B  is not parallel to DC D C .
4. It is a parallelogram because both pairs of opposite sides are parallel.

Use the diagram below to answer the question that follows.

Triangle X Y Z is shown in the coordinate plane with vertex X located at the point negative 2, 0, vertex Y located at the point 2, 4, and vertex Z located at the point 5, 0.

Which of the following descriptions matches triangle XYZ X Y Z ?

1. scalene
2. isosceles, with YX Y X  = YZ Y Z 
3. isosceles, with YZ Y Z  = XZ
4. equilateral

Use the diagram below to answer the question that follows.

An isosceles triangle is shown with a point Q as the bottom right vertex for its base. The congruent legs of the triangle extend to form consecutive sides for a parallelogram. One obtuse angle in the parallelogram is 130 degrees.

What is the measure of angle Q in the diagram?

1. 50° 50 degrees 
2. 55° 55 degrees 
3. 60° 60 degrees 
4. 65° 65 degrees 

Use the graph below to answer the question that follows.

Two points are plotted in the coordinate plane. The point negative 4, 4 is labeled Town A. The point 8, negative 2 is labeled town b.

A company plans to build a cell tower so that it is equidistant from Town A and Town B. Which of the following points could represent the location of the cell tower?

1. (1, 1) 1, 1 
2. (2, 1) 2, 1 
3. (4, −1) 4, negative 1 
4. (8, 4) 8, 4 

Use the diagram below to answer the question that follows.

Triangle A B C is shown in the second quadrant of the coordinate plane such that B A is a horizontal line segment and A C is a vertical line segment. The congruent triangle A prime b prime c prime is shown in the first quadrant such that A prime B prime is a vertical line segment and A prime c prime is a horizontal line segment.

Which of the following transformations, when performed on △ ABC triangle A B C , will result in the image shown, △ A′B′C′ triangle A prime B prime C prime ?

1. a rotation about point A and a reflection over the y-axis
2. a rotation around the origin and a translation
3. a glide-reflection and a translation
4. a glide-reflection

Use the diagram below to answer the question that follows.

Two parallel lines, a and b, are cut by transversals c and d. Transversals c and d intersect to form a 57 degree angle. The intersection of transversal c with line a creates a 127 degree angle. The intersection of transversal d with line a creates an angle with measure n.

Lines a and b are parallel. What is the measure of angle n in the diagram above?

1. 110° 110 degrees 
2. 114° 114 degrees 
3. 123° 123 degrees 
4. 127° 127 degrees 

Use the figure below to answer the question that follows.

Two triangles that appear to be congruent are shown. One triangle is J K L, where L is a right angle and J K is the hypotenuse. The other triangle is M N O, where N is a right angle and M O is the hypotenuse.

In the figure above, the establishment of which of the following conditions demonstrates that △ JKL triangle J K L  is similar to △ MON triangle M O N ?

1. KL ≅ ON  Segment K L is congruent to segment O N 
2. ∠J + ∠K = ∠M + ∠O  Angle j plus angle k equals angle m plus angle o 
3. ∠J ≅ ∠M  Angle j is congruent to angle m 
4. JK ≅ MO  Segment J K is congruent to segment M O 

Quadrilateral ABCD  A B C D  is constructed on a set of coordinate axes with vertices at the points (2, 2), (−2, −2), (−8, 2), and (−4, 7) 2, 2, negative 2, negative 2, negative 8, 2, and negative 4, 7 . What is the area of ABCD  A B C D  ?

1. 27 square units
2. 8√ 26 8 radical 26  square units
3. 45 square units
4. 4√ 122 4 radical 122  square units

Use the diagram below to answer the question that follows.

A triangle is shown in the coordinate plane with vertices at the points (2, 0), (6, 0) and (4, 2). The point at (4, 2) is labeled as point A.

When the triangle in the diagram above is reflected across the line y = x and then across the line x = − negative 1, what will be the coordinates of the resulting point, A′ A prime ?

1. (−6, −2) negative 6, negative 2 
2. (−2, 6) negative 2, 6 
3. (−4, 4) negative 4, 4 
4. (2, −4) 2, negative 4 

The height of a refrigerator is 18 units. Which of the following units could be used for this measurement?

1. centimeters
2. decimeters
3. meters
4. kilometers

An office worker picks up a lunch order for several colleagues. The order consists of 4 drinks at $2.25 2 dollars and 25 cents  each, 3 sandwiches at $6.25 6 dollars and 25 cents  each, and 2 sandwiches at $7.50 7 dollars and 50 cents  each. The worker pays with a $50 50 dollar  bill. The cashier returns the correct change using the fewest paper bills possible using any combination of $1 1 dollar , $5 5 dollar , and $10 10 dollar  bills. How many bills are in the change?

1. 2
2. 3
3. 4
4. 7

Which of the following temperatures, in degrees Celsius, is closest to 98.6° 98.6 degrees  Fahrenheit, the average body temperature of a healthy human?

1. 35° degrees  Celsius
2. 73° degrees  Celsius
3. 120° degrees  Celsius
4. 238° degrees  Celsius

Use the diagram below to answer the question that follows.

An architect has created the scale model shown for a new building. If the front of the actual building is going to be 45 feet in width, which of the following equations can be solved to find the height, h, of the building?

1. ⁶ / _h = ¹² / ₄₅  6 divided by h equals 12 divided by 45 
2. ⁶ / ₁₂ = ^h / ₄₅  6 divided by 12 equals h divided by 45 
3. ⁶ / ₄₅ = ^h / ₁₂  6 divided by 45 equals h divided by 12 
4. ⁶ / ₁₂ = ⁴⁵ / _h  6 divided by 12 equals 45 divided by h 

Use the figure below to answer the question that follows.

A triangle is shown with side lengths 8, 3 plus 9, and 12 plus y. The triangle is divided by a line segment, labeled x, that is parallel to the side marked 8. The length of the line segments connecting the parallel line segments are 3 and y.

What is the value of y in the figure shown?

1. 3
2. 4
3. 6
4. 12

A figure, graphed on the coordinate plane, is bounded by the lines whose equations are x = 1, y = 3, and y = x − minus  4. What is the area of the figure?

1. 9 square units
2. 10 ¹ / ₂  10 and 1 half  square units
3. 13 ¹ / ₂  13 and 1 half  square units
4. 18 square units

Doubling the length of both the base and the height of a right triangle will cause the:

1. area to increase by a factor of two.
2. area to increase by a factor of four.
3. perimeter to increase by a factor of four.
4. perimeter to increase by a factor of eight.

Use the information below to answer the question that follows.

The last two people in a contest have an equal chance of winning. The winner chooses one of three identically wrapped gifts. The gifts are a book, a gift certificate, and a smartphone.

Which of the following quantities represents the size of the sample space for this scenario?

1. the number of independent choices
2. the sum of the number of people and the number of prizes
3. the product of the number of people and the number of prizes
4. the product of number of people raised to the power of the number of prizes

Use the diagram below to answer the question that follows.

A smaller circle is positioned within a larger circle such that they share the same center. Two radii extend from the center to the circumference of the larger circle such that the central angle formed between them is 90 degrees. The radius of the small circle is 2, and the radius of the large circle is 4. A shaded region indicates the area inside the big circle, but not the small circle, for the region between the two radii.

A student plays a game tossing a beanbag into the circular region shown. Assuming that all locations in the circular region are equally likely, what is the probability that the beanbag lands in the shaded region for a given throw?

1. ¹ / ₁₆  1 sixteenth 
2. ¹ / ₈  1 eighth 
3. ³ / ₁₆  3 sixteenths 
4. ¹ / ₄  1 fourth 

Two hats each have 10 slips of paper in them with the numbers from 1 to 10. Two people each pick one slip at random from different hats, record the numbers, and put the slips back. This is repeated 100 times, and 20 of those times both numbers are prime. How does 20 pairs compare to the expected number of prime pairs, according to the theoretical probability?

1. This is 4 more pairs than expected.
2. This is 5 more pairs than expected.
3. This is 11 fewer pairs than expected.
4. This is 12 fewer pairs than expected.

The letter pair ea e a , found in the word heart, refers to the sequences of letters that begins with e and ends with a. How many additional arrangements can be formed from the letters h, r, t, and the letter pair ea e a ?

1. 23
2. 24
3. 119
4. 120

How many unique arrangements can be made using the letters in the word "Boston"?

1. 21
2. 120
3. 360
4. 720

Five employees have volunteered to work the first shift at a bakery for the coming week. The manager only needs two employees to work at that time. If the manager selects the employees to work the first shift randomly, what is the probability that two particular employees will work together?

1. 5% 5 percent 
2. 10% 10 percent 
3. 20% 20 percent 
4. 40% 40 percent 

Use the box plot below to answer the question that follows.

A box plot is shown that represents exam grades as a percent out of 100. The minimum is 45, the maximum is 100. Q 1 is 68, the median is 77, and q 3 is 86.

One hundred students took an exam, and the box plot above shows their collective results. Which of the following statements can be inferred from this information?

1. The mean score was 77.
2. The median score was 50.
3. Approximately 75 students scored above 68.
4. About as many students scored between 45 and 68 as scored between 77 and 100.

Use the table below to answer the question that follows.

The table shows the tips earned by a server on each of four days. How much does the server need to earn in tips on Saturday so that their five-day average is $5 5 dollars  greater than the four-day average?

1. $53 53 dollars 
2. $58 58 dollars 
3. $78 78 dollars 
4. $87 87 dollars 

Use the information below to answer the question that follows.

This survey question was sent to 4000 4,000  randomly selected e-mail addresses across the United States. Based on the results of 2500 2,500  responses, the authors of the survey concluded that people in the United States spend an average of 3.5 hours per day using a computer or cell phone for recreational purposes. Which of the following statements best describes the flaw in the survey design?

1. The survey question provides specific examples of recreational computer use.
2. The responses of sample populations should not be used to draw conclusions about entire populations.
3. The survey does not include use of other recreational electronic devices, such as tablets.
4. The survey question only polls respondents who have an e-mail address.

A scatter plot would be most useful in presenting which of the following types of data?

1. data tracking school attendance and performance on standardized tests
2. data listing the age at which children in an elementary school lost their first primary tooth
3. data recording the height of a student from kindergarten through fifth grade
4. data comparing math test scores for two sets of third-grade students

Use the information below to answer the question that follows.

The numbers in the box above represent the heights in centimeters of ten-year-old students. Based on the data provided, the student with a height of 145 centimeters is in approximately which of the following percentiles?

1. 36th
2. 55th
3. 64th
4. 70th

Use the graph below to answer the question that follows.

A scatter plot titled The Relationship Between Density of Females and Number of Offspring relates the number of females per acre on the x axis to the mean number of offspring per female on the y axis. The y intercept (when there is only 1 female per acre) is approximately 9.5. The data show a negative linear correlation between the x and y variables. The rightmost data point on the graph is 21, 1.5.

A biologist is studying the factors that limit the population size of a small mammal in a woodland area. Which of the following statements is best supported by the data in the graph?

1. Five females per acre is the density that will sustain the current population size.
2. Factors other than density had a greater effect on the number of offspring produced.
3. Approximately six offspring would be born to females in areas with a density of nine females per acre.
4. An increase in the number of females per acre causes a decrease in the mean number of offspring.

Use the information that appears in the exhibit to complete the assignment that follows.

Write an essay of approximately 150– to 300 words, or 1– to 2 pages, in which you analyze the standard provided. In your response:

• identify a related prerequisite skill and explain its relevance to the standard;
• describe an appropriate representation to model the concepts set out in the standard and explain how it supports students' understanding; and
• assess how well the situation provided aligns to the standard.

Exhibit

Standard

The Massachusetts Mathematics Curriculum Framework¹ for grade 6 provides the following content standard:

Situation

A teacher presents a lesson on area and volume formulas to the class. At the end of the lesson, the teacher asks students to find dimensions of a cube with a volume of 27 cubic units.

Use the information that appears in the exhibit to complete the assignment that follows.

Use your knowledge of mathematics to develop a response of approximately 150– to 300 words, or 1– to 2 pages, in which you:

• analyze the solution to the mathematical problem, identifying errors or misconceptions;
• provide a correct solution to the problem; and
• use an alternative method or representation to solve the problem and justify the approach.

Exhibit

Problem

A teacher presents the following diagram to students.

A pentagon is shown such that the bottom edge is horizontal and there is vertical line symmetry from the midpoint of the bottom edge through the top vertex. The bottom edge is labeled as 6 and one half feet, and the top edge to the left of the vertex is labeled 8 feet 6 inches.

The diagram shows a fence in which one section is 6 ¹ / ₂  and one half  feet long and the other four sections are 8 feet and 6 inches long. Students are tasked with determining the perimeter of this fence in yards.

Student Response