Math Test—Calculator
38 Questions
Turn to Section 4 of your answer sheet to answer the questions in this section.
Directions
For questions 1 through 30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31 through 38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 31 on how to enter your answers in the grid. You may use scratch paper for scratch work.
Notes
1. The use of a calculator is permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which _{ } f of x is a real number.
Reference
Begin skippable figure descriptions.
The figure presents information for your reference in solving some of the problems.
Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.
A equals pi times the square of r.
C equals 2 pi r.
Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.
A equals ℓ w.
Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.
A equals onehalf b h.
Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.
c squared equals a squared plus b squared.
Special Right Triangles
Reference figure 5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.
Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.
Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.
V equals ℓ w h.
Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.
V equals pi times the square of r times h.
Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.
V equals fourthirds pi times the cube of r.
Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.
V equals onethird times pi times the square of r times h.
Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.
V equals onethird ℓ w h.
End skippable figure descriptions.
Additional Reference Information
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2 pi.
The sum of the measures in degrees of the angles of a triangle is 180.
Question 1.
A musician has a new song available for downloading or streaming. The musician earns $0.09 each time the song is downloaded and $0.002 each time the song is streamed. Which of the following expressions represents the amount, in dollars, that the musician earns if the song is downloaded d times and streamed s times?
A. 0.002 d, plus 0.09 s
B. 0.002 d, minus 0.09 s
C. 0.09 d, plus 0.002 s
D. 0.09 d, minus 0.002 s
Explanation for question 1.
Question 2.
A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate, how many lightbulbs will be inspected if the factory produces 20,000 lightbulbs?
A. 300
B. 350
C. 400
D. 450
Explanation for question 2.
Question 3 refers to the following equation.
l equals 24 plus 3.5 m
Question 3.
One end of a spring is attached to a ceiling. When an object of mass m kilograms is attached to the other end of the spring, the spring stretches to a length of l centimeters as shown in the preceding equation. What is m when l is 73 ?
A. 14
B. 27.7
C. 73
D. 279.5
Explanation for question 3.
Questions 4 and 5 refer to the following information.
The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns $120 at a performance where 8 people attend.
Question 4.
How much money will the performer earn when 20 people attend a performance?
A. $960
B. $480
C. $300
D. $240
Explanation for question 4.
Question 5.
The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performer’s profit. What is the profit the performer makes at a performance where 8 people attend?
A. $51.60
B. $57.00
C. $68.40
D. $77.00
Explanation for question 5.
Question 6.
_{When 4 times the number}_{ }_{x}_{ }_{is added to 12, the result is 8. What number results when 2 times}_{ }_{x}_{ }_{is added to 7 ?}
A. negative 1
B. 5
C. 8
D. 9
Explanation for question 6.
Question 7 is based on the following equation.
y equals x squared, minus 6 x plus 8
Question 7.
The preceding equation represents a parabola in the x yplane. Which of the following equivalent forms of the equation displays the xintercepts of the parabola as constants or coefficients?
A. y minus 8, equals, x squared, minus 6 x
B. y plus 1, equals, parenthesis, x minus 3, close parenthesis, squared
C. y equals, x, parenthesis, x minus 6, close parenthesis, plus 8
D. y equals, parenthesis, x minus 2, close parenthesis, times, parenthesis, x minus 4, close parenthesis
Explanation for question 7.
Question 8.
In a video game, each player starts the game with k points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points, what is the value of k ?
A. 0
B. 150
C. 250
D. 400
Explanation for question 8.
Question 9.
A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40pound boxes and y be the number of 65pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship?
A. open bracket, 40 x plus 65 y is less than or equal to 2,400; and, x plus y is less than or equal to 45.
B. open bracket, the fraction x over 40, plus, the fraction y over 65, is less than or equal to 2,400; and, x plus y is less than or equal to 45.
C. open bracket 40 x plus 65 y is less than or equal to 45; and, x plus y is less than or equal to 2,400.
D. open bracket, x plus y is less than or equal to 2,400; and 40 x plus 65 y is less than or equal to 2,400.
Explanation for question 9.
Question 10.
A function f satisfies f of 2 equals 3 and f of 3 equals 5. A function g satisfies g of 3 equals 2 and g of 5 equals 6. What is the value of f of, g of 3?
A. 2
B. 3
C. 5
D. 6
Explanation for question 10.
Question 11 refers to the following table.
Number of hours Tony plans to read the novel per day

3

Number of parts in the novel

8

Number of chapters in the novel

239

Number of words Tony reads per minute

250

Number of pages in the novel

1,078

Number of words in the novel

349,168

Question 11.
Tony is planning to read a novel. The preceding table shows information about the novel, Tony’s reading speed, and the amount of time he plans to spend reading the novel each day. If Tony reads at the rates given in the table, which of the following is closest to the number of days it would take Tony to read the entire novel?
A. 6
B. 8
C. 23
D. 324
Explanation for question 11.
Question 12.
On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?
A. 325,000 minus 7,500, is less than or equal to y
B. 325,000 is less than or equal to 7,500 y
C. 150,000 is greater than or equal to 7,500 y
D. 175,000 plus 7,500 y, is greater than or equal to 325,000
Explanation for question 12.
Question 13.
A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sportswatching preferences of all people in the town?
A. Sample size
B. Population size
C. The number of people who refused to respond
D. Where the survey was given
Explanation for question 13.
Question 14 refers to the following figure.
Begin skippable figure description.
The figure, titled “Miles Traveled by Air Passengers in Country X, 1960 to 2005,” shows a graph of a scatterplot with the line of best fit. The horizontal axis is labeled “Year” and the years appearing on it from left to right are from 1960 through 2010, in increments of 10 years. There are vertical gridlines at every 5 years. The vertical axis is labeled “Number of miles traveled, in billions,” and the numbers appearing on it from bottom to top are from 0 to 600, in increments of 100 billion miles. There are horizontal gridlines at every 50 billion miles. The scatterplot shows a cluster of data points that begins in the year 1960 at 30 billion miles, extends upward and to the right, showing a pattern of line, and ends in 2005 at 590 billion miles. The line of best fit extends in the pattern that the cluster shows. It starts from about 1961 at 0 miles and slants upward to the right, ending in 2010 at about 620 billion miles.
End skippable figure description.
Question 14.
According to the line of best fit in the preceding scatterplot, which of the following best approximates the year in which the number of miles traveled by air passengers in Country X was estimated to be 550 billion?
A. 1997
B. 2000
C. 2003
D. 2008
Explanation for question 14.
Question 15.
The distance traveled by Earth in one orbit around the Sun is about 580,000,000 miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun?
A. 66,000
B. 93,000
C. 210,000
D. 420,000
Explanation for question 15.
Question 16 refers to the following table.
Results on the Bar Exam of Law School Graduates
Question 16.
The preceding table summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did NOT take the review course?
A. 18 over 25
B. 7 over 25
C. 25 over 200
D. 7 over 200
Explanation for question 16.
Question 17.
The atomic weight of an unknown element, in atomic mass units (a m u), is approximately 20% less than that of calcium. The atomic weight of calcium is 40 a m u. Which of the following best approximates the atomic weight, in a m u, of the unknown element?
A. 8
B. 20
C. 32
D. 48
Explanation for question 17.
Question 18.
A survey was taken of the value of homes in a county, and it was found that the mean home value was $165,000 and the median home value was $125,000. Which of the following situations could explain the difference between the mean and median home values in the county?
A. The homes have values that are close to each other.
B. There are a few homes that are valued much less than the rest.
C. There are a few homes that are valued much more than the rest.
D. Many of the homes have values between $125,000 and $165,000.
Explanation for question 18.
Questions 19 and 20 refer to the following information.
A sociologist chose 300 students at random from each of two schools and asked each student how many siblings he or she has. The results are shown in the following table.
Students’ Sibling Survey
Number of siblings

Lincoln School

Washington School

0

120

140

1

80

110

2

60

30

3

30

10

4

10

10

There are a total of 2,400 students at Lincoln School and 3,300 students at Washington School.
Question 19.
What is the median number of siblings for all the students surveyed?
A. 0
B. 1
C. 2
D. 3
Explanation for question 19.
Question 20.
Based on the survey data, which of the following most accurately compares the expected total number of students with 4 siblings at the two schools?
A. The total number of students with 4 siblings is expected to be equal at the two schools.
B. The total number of students with 4 siblings at Lincoln School is expected to be 30 more than at Washington School.
C. The total number of students with 4 siblings at Washington School is expected to be 30 more than at Lincoln School.
D. The total number of students with 4 siblings at Washington School is expected to be 900 more than at Lincoln School.
Explanation for question 20.
Question 21.
A project manager estimates that a project will take x hours to complete, where x is greater than 100. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time?
A. x plus y is less than 10
B. y is greater than x plus 10
C. y is less than x minus 10
D. negative 10 is less than y minus x, which is less than 10
Explanation for question 21.
Questions 22 and 23 refer to the following information.
I, equals the fraction P over, 4 pi r squared, end fraction
At a large distance r from a radio antenna, the intensity of the radio signal I is related to the power of the signal P by the preceding formula.
Question 22.
Which of the following expresses the square of the distance from the radio antenna in terms of the intensity of the radio signal and the power of the signal?
A. r squared, equals, the fraction I P over 4 pi
B. r squared, equals, the fraction P over 4 pi, I
C. r squared, equals, the fraction 4 pi, I, over P
D. r squared, equals, the fraction I over 4 pi, P
Explanation for question 22.
Question 23.
For the same signal emitted by a radio antenna, Observer A measures its intensity to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
A. 1 over 4
B. 1 over 16
C. 1 over 64
D. 1 over 256
Explanation for question 23.
Question 24 is based on the following equation.
x squared plus y squared, plus 4 x minus 2 y, equals negative 1
Question 24.
The preceding is the equation of a circle in the x yplane. What is the radius of the circle?
A. 2
B. 3
C. 4
D. 9
Explanation for question 24.
Question 25.
The graph of the linear function f has intercepts at the points with coordinates a, comma 0, and 0 comma b, in the x yplane. If a, plus b equals 0 and a, does not equal b, which of the following is true about the slope of the graph of f ?
A. It is positive.
B. It is negative.
C. It equals zero.
D. It is undefined.
Explanation for question 25.
Question 26 refers to the following figure.
Begin skippable figure description.
The figure presents the graph of the function f in the x yplane. The graph is labeled y equals f of x. The horizontal axis is labeled x, the vertical axis is labeled y, and the origin is labeled O. There are evenly spaced horizontal and vertical gridlines, in increments of 1 unit, along each axis. The graph consists of 4 connected line segments. The first line segment slants upward and to the right. It starts at the point that is 4 units to the left of the yaxis and 1 unit above the xaxis, and it ends on the yaxis, 3 units above the xaxis. The second line segment slants downward and to the right. It starts where the first line segment ends, and ends at the point that is 1 unit to the right of the yaxis and 1 unit above the xaxis. The third line segment moves horizontally. It starts where the second line segment ends, and ends at the point that is 3 units to the right of the yaxis and 1 unit above the xaxis. The fourth line segment slants downward and to the right. It starts where the third line segment ends, and ends at the point that is 4 units to the right of the yaxis and 1 unit below the xaxis.
End skippable figure description. Question 26.
The complete graph of the function f is shown in the preceding x yplane. Which of the following are equal to 1 ?
I. f of negative 4
I I. f of three halves
I I I. f of 3
A. I I I only
B. I and I I I only
C. I I and I I I only
D. I, I I, and I I I
Explanation for question 26.
Question 27 refers to the following figure.
Begin skippable figure description.
The figure presents a graph. The horizontal axis is labeled “Time, in minutes.” The vertical axis is labeled “Temperature, in degrees Celsius.” Numbers from 0 to 70, in increments of 10, appear along both axes with gridlines extending from each number. Sixteen points are plotted on the graph with eight circles and eight squares. A key indicates that a square means “insulated” and a circle means “noninsulated.” Each 10minute interval has a pair of points plotted for insulated and noninsulated as follows.
0 minutes: insulated, 60 degrees; noninsulated, 60 degrees.
10 minutes: insulated, 52 degrees; noninsulated 42 degrees.
20 minutes: insulated, 47 degrees; noninsulated 34 degrees.
30 minutes: insulated, 41 degrees; noninsulated 30 degrees.
40 minutes: insulated, 38 degrees; noninsulated 29 degrees.
50 minutes: insulated, 36 degrees; noninsulated 28 degrees.
60 minutes: insulated, 33 degrees; noninsulated 28 degrees.
70 minutes: insulated, 31 degrees; noninsulated 28 degrees.
End skippable figure description. Question 27.
Two samples of water of equal mass are heated to 60 degrees Celsius parenthesis, degrees C, close parenthesis. One sample is poured into an insulated container, and the other sample is poured into a noninsulated container. The samples are then left for 70 minutes to cool in a room having a temperature of 25 degrees Celsius. The preceding graph shows the temperature of each sample at 10minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change?
A. In every 10minute interval, the magnitude of the rate of change of temperature of the insulated sample is greater than that of the noninsulated sample.
B. In every 10minute interval, the magnitude of the rate of change of temperature of the noninsulated sample is greater than that of the insulated sample.
C. In the intervals from 0 to 10 minutes and from 10 to 20 minutes, the rates of change of temperature of the insulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the noninsulated sample are of greater magnitude.
D. In the intervals from 0 to 10 minutes and from 10 to 20 minutes, the rates of change of temperature of the noninsulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the insulated sample are of greater magnitude.
Explanation for question 27.
Question 28 refers to the following figure.
Begin skippable figure description.
The figure presents a tilted square A B C D in the x yplane. The horizontal axis is labeled x, and the vertical axis is labeled y. There are evenly spaced horizontal gridlines and evenly spaced vertical gridlines labeled negative 6 through 6, in increments of 2 units, along both axes. Vertex A is 5 units to the left of the yaxis and 2 units below the xaxis, vertex B is 1 unit to the left of the yaxis and 6 units above the xaxis, vertex C is 7 units to the right of the yaxis and 2 units above the xaxis, and vertex D is 3 units to the right of the yaxis and 6 units below the xaxis. Point E is on diagonal A C, lies on the xaxis, and is 1 unit to the right of the yaxis.
End skippable figure description.
Question 28.
In the preceding x yplane, A B C D is a square and point E is the center of the square. The coordinates of points C and E are 7 comma 2, and 1 comma 0, respectively. Which of the following is an equation of the line that passes through points B and D ?
A. y equals negative 3 x minus 1
B. y equals negative 3, parenthesis, x minus 1, close parenthesis
C. y equals negative one third x plus 4
D. y equals negative one third x minus 1
Explanation for question 28.
Question 29 is based on the following system of equations.
y equals 3
y equals a, x squared, plus b
Question 29.
In the preceding system of equations, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A. a, equals negative 2, b equals 2
B. a, equals negative 2, b equals 4
C. a, equals 2, b equals 4
D. a, equals 4, b equals 3
Explanation for question 29.
Question 30 refers to the following figure.
Begin skippable figure description.
The figure presents a polygon with six sides of equal length and six interior angles of equal measure, and a square. The polygon and the square have one side in common.
End skippable figure description. Question 30.
The preceding figure shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is 384 times the square root of 3 square inches, what is the area, in square inches, of the square?
A. 256
B. 192
C. 64 times the square root of 3
D. 16 times the square root of 3
Explanation for question 30.
Directions
For questions 31 through 38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
5. Mixed numbers such as three and one half must be gridded as 3.5 or seven slash two. (If three, one, slash, two, is entered into the grid, it will be interpreted as thirty one halves, not three and one half.)
6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.
The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.
Examples 1 and 2
Begin skippable figure description.
Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.
Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.
End skippable figure description.
Example 3
Begin skippable figure description.
Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.
End skippable figure description.
Example 4
Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.
Begin skippable figure description.
Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.
End skippable figure description.
Question 31.
A coastal geologist estimates that a certain country’s beaches are eroding at a rate of 1.5 feet per year. According to the geologist’s estimate, how long will it take, in years, for the country’s beaches to erode by 21 feet?
Explanation for question 31.
Question 32.
If h hours and 30 minutes is equal to 450 minutes, what is the value of h ?
Explanation for question 32.
Question 33.
In the x yplane, the point with coordinates 3 comma 6 lies on the graph of the function f of x equals, 3 x squared, minus b x, plus 12. What is the value of b ?
Explanation for question 33.
Question 34.
In one semester, Doug and Laura spent a combined 250 hours in the tutoring lab. If Doug spent 40 more hours in the lab than Laura did, how many hours did Laura spend in the lab?
Explanation for question 34.
Question 35 is based on the following equation.
a, equals 18 t plus 15
Question 35.
Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount to the account. The preceding equation models the amount a, in dollars, that Jane has deposited after t weekly deposits. According to the model, how many dollars was Jane’s initial deposit? (Disregard the $ sign when gridding your answer.)
Explanation for question 35.
Question 36 refers to the following figure.
Begin skippable figure description.
The figure presents a circle with center O touched by two lines, where one line touches the circle at the single point, labeled L, on the upper right part of the circle, another line touches the circle at the single point, labeled N, on the lower right part of the circle, and the two lines intersect at point M outside and to the right of the circle. Radii O L and O N are drawn, and the angle formed by line segments L M and N M is labeled 60 degrees.
End skippable figure description. Question 36.
In the preceding figure, point O is the center of the circle, line segments L M and M N are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of minor arc L N ?
Explanation for question 36.
Questions 37 and 38 refer to the following information.
A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, , N sub next year, can be estimated from the number of plants this year, , N sub this year, by the following equation.
N sub next year, equals, N sub this year, plus 0.2, parenthesis, N sub this year, close parenthesis, times, brace, 1 minus the fraction, N sub this year over K, close brace.
The constant K in this formula is the number of plants the environment is able to support.
Question 37.
According to the formula, what will be the number of plants two years from now if K equals 4000 ? (Round your answer to the nearest whole number.)
Explanation for question 37.
Question 38.
The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanist’s goal is that the number of plants will increase from 3000 this year to 3360 next year, how many plants must the modified environment support?
Explanation for question 38.
Stop.
If you finish before time is called, you may check your work on this section only. Do not turn to any other section.
Answers and explanations for questions 1 through 38 are provided in the next section of this document.
