There is no penalty for wrong answers, so it makes sense to give the best answer you can to every question, even if it is just your best guess.
The time is up. You have completed all sections of the SAT.
Math – Calculator Tests
Mathematics Test—Calculator 2
38 Questions. 55 Minutes to Complete.
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 (x) is a real number.
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.
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1. Turn to Section 4 of your answer sheet to answer the questions in this section.
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.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f (x) is a real number.
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 refers to the following figure.
Begin skippable figure description.
The figure presents a graph titled “Marilyn’s Hike” in a coordinate plane. The horizontal axis has 4 equally spaced tick marks labeled, from left to right, 12 P.M., 1 P.M., 2 P.M., and 3 P.M., and there are vertical gridlines at those tick marks. The vertical axis is labeled “Distance from campsite, in miles,” and the numbers 0, to 2.0, in increments of 0.5, appear along the vertical axis. There are horizontal gridlines at those numbers. In the figure, a curve starts off at 12 P.M. at 0 mile, moves upward and to the right while it fluctuates, passing 1 P.M. at a distance of 1.25 miles, until it stops fluctuating at a time that is one sixth of the hour past 1 P.M. Then it moves horizontally until a time that is two thirds of the hour past 1 P.M. The curve starts moving upward and to the right, until it crosses 2 P.M. at about 1.6 miles. The curve then fluctuates down and to the right until it stops at 3 P.M. at 0 mile.
End skippable figure description.
The preceding graph shows Marilyn’s distance from her campsite during a 3hour hike. She stopped for 30 minutes during her hike to have lunch. Based on the graph, which of the following is closest to the time she finished lunch and continued her hike?
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2. Question 2 refers to the following figure.
The figure presents a table with age and gender distributions. The table has 4 columns: the first column heading is Gender. The second and third column headings are ages: Under 40, and, 40 or older, both under the heading Age. The fourth column heading is Total. According to the table, the three rows of data are as follows.
Row 1, male, 12 are under age 40, and 2 are age 40 or older, making a total of 14.
Row 2, female, 8 are under age 40, and 3 are age 40 or older, making a total of 11.
Row 3, total, 20 are under age 40, and 5 are age 40 or older, making a total of 25.
The preceding table shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40 or a male age 40 or older?
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3. Question 3 refers to the following figure.
The figure presents a line graph titled “Annual Music Album Sales.” The horizontal axis is labeled “Years since 1997” and years 0 through 12 appear along the axis. The vertical axis is labeled “Sales, in millions of music albums,” and numbers 0 to 1,000, in increments of 200, appear along the axis. There are horizontal gridlines at every 50. According to the graph, the annual sales over the 13 year period can be summarized as follows. The annual sales in year 0 are 650 million; the sales go up each year until year 3. Then the sales start going down each year for three years, and after one year of a slight increase the sales go down every year until year 12 with the annual sales of about 355 million.
Based on the preceding graph, which of the following best describes the general trend in music album sales from 1997 through 2009?
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4. Question 4 refers to the following figure.
The figure presents a table with 2 rows and 4 columns of values. From top to bottom, the row heading of the first row is, n, and the row heading of the second row is, f of n. From left to right, the values of the first row are, 1, 2, 3, and 4; the values of the second row are, negative 2, 1, 4, and 7.
The preceding table shows some values of the linear function f. Which of the following defines f?
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5. At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled seniors were inducted into the National Honor Society last year. If there were 562 juniors and 602 seniors enrolled at Lincoln High School last year, which of the following is closest to the total number of juniors and seniors at Lincoln High School last year who were inducted into the National Honor Society?
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6. Question 6 refers to the following polynomials.
Which of the following is the sum of the preceding two polynomials?
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7. If what is the value of w?
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8. The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?
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9. Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, which of the following is closest to the distance he will walk in 4 minutes?
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10. Question 10 and 11 refer to the following information.
Acceleration due to gravity
The preceding chart shows approximations of the acceleration due to gravity in meters per second squared for the eight planets in our solar system. The weight of an object on a given planet can be found by using the formula W = mg where W is the weight of the object measured in newtons, m is the mass of the object measured in kilograms, and g is the acceleration due to gravity on the planet measured in
What is the weight, in newtons, of an object on Mercury with a mass of 90 kilograms?
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11. An object on Earth has a weight of 150 newtons. On which planet would the same object have an approximate weight of 170 newtons?
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12. If the function f has five distinct zeros, which of the following could represent the complete graph of f in the x yplane?
Each option is a graph of a smooth curve in the x y-plane. All the graphs show the same curve that is placed in a different vertical position. The starting and ending points are above the x axis with one on either side of the y axis.
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13. Question 13 is based on the following equation.
The preceding equation gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. Which of the following gives v in terms of h, t, and k?
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14. The cost of using a telephone in a hotel meeting room is $0.20 per minute. Which of the following equations represents the total cost c, in dollars, for h hours of phone use?
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15. In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?
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16. Question 16 refers to the following figure.
The figure presents a graph of two curves in the x y-plane. The horizontal axis is labeled x, and the vertical axis is labeled y. There are evenly spaced horizontal and vertical gridlines along the axes. The first vertical gridline to the right of the y axis is one unit from the y axis, and the second horizontal gridline above the x axis is 2 units from the x axis.
The two curves in the graph look like parabolas; one opens up and another opens down. The curve that opens up has its lowest point 4 units directly below the highest point of another curve that opens down. Both curves are symmetric with respect to the vertical gridline that is 2 units to the left of the y axis, and they intersect at two points below the x axis.
The curve that opens up is labeled, y equals f of x, and another is labeled, y equals g of x. From left to right, the curve labeled f of x goes down and the curve labeled g of x goes up, crossing each other at the point that is 1 unit below the x axis and 3 units to the left of the y axis. Then the curve f of x reaches its lowest point that is 2 units below the y axis and 2 units to the left of the y axis, and the curve g of x reaches its highest point that is 2 units above the y axis and 2 units to the left of the y axis. The curve f of x turns to go up while the curve g of x turns to go down, crossing each other again at the point that is one unit below the x axis and 1 unit to the left of the y axis. Finally, the curve f of x extends upward crossing the y axis 2 units above the x axis, and the curve g of x extends downward, crossing the y axis 9 units below the x axis.
Graphs of the functions f and g are shown in the preceding xyplane. For which of the following values of x does f(x) + g(x) = 0?
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17. Questions 17 and 18 refer to the following information.
D(P) = 220 – P
The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The preceding functions are the estimated supply and demand functions for a certain product. The function S(P) gives the quantity of the product supplied to the market when the price is P dollars, and the function D(P) gives the quantity of the product demanded by the market when the price is P dollars.
How will the quantity of the product supplied to the market change if the price of the product is increased by $10?
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18. At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market?
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19. Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately acres, about how many acres could 48 ounces of graphene cover?
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20. Question 20 refers to the following figure.
The figure presents a graph of scatterplot with the line of best fit, titled “Swimming Time versus Heart Rate.” The horizontal axis is labeled “Swimming time, in minutes” and the numbers appearing on it from left to right are from 33 to 37, in increments of 0.5. There are vertical gridlines at every 0.25 minutes. The vertical axis is labeled “Heart rate, in beats per minute” and the numbers appearing on it from bottom to top are from 120 to 160, in increments of 10. There are horizontal gridlines at every two beats per minute. The scatterplot shows a cluster of data points that begin at data point 34 minutes and 148 beats per minute, spread over a wide area from heart rates 124 to 152 beats per minute and time 34 to 36 minutes, ending at almost 36 minutes and 149 beats per minute.
The line of best fit passes through the point at 33 minutes and 160 beats per minute and the point at 37 minutes and 120 beats per minute.
Michael swam 2,000 yards on each of eighteen days. The preceding scatterplot shows his swim time for and corresponding heart rate after each swim. The line of best fit for the data is also shown. For the swim that took 34 minutes, Michael’s actual heart rate was about how many beats per minutes less than the rate predicted by the line of best fit?
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21. Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?
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22. The sum of three numbers is 855. One of the numbers, x, is 50% more than the sum of the other two numbers. What is the value of x?
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23. Question 23 refers to the following figure.
The figure presents two angles, one labeled a degrees and the other labeled b degrees. Each of the angles is less than 90 degrees, and the angle labeled a degrees appears smaller than the one labeled b degrees. There is a note stating that: Figures are not drawn to scale.
The angles shown in the preceding figure are acute and sin(a°) = cos(b°). If a = 4k – 22, and b = 6k – 13, what is the value of k?
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24. Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?
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25. Question 25 refers to the following figure.
The figure presents a grain silo made up of a cylinder with height 10 feet and base radius 5 feet; and two cones, one at each base of the cylinder. Each cone has a height of 5 feet and a base radius of 5 feet.
A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the preceding figure. Of the following, which is closest to the volume of the grain silo, in cubic feet?
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26. In the xyplane, the line determined by the points, (2,k), and (k,32) passes through the origin. Which of the following could be the value of k?
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27. A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p?
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28. In planning maintenance for a city’s infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineer’s estimate of the population of the city t years from now?
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29. Question 29 refers to the following figure.
The figure presents an incomplete table with 4 rows and 3 columns. From left to right, the column heading of the first column is, Gender, and the row headings, Female, Male, and Total, are listed under it. The column headings of the second and third columns are “Left” and “Right,” both under heading “Handedness.” In the table, there are no numbers for female left, female right, male left, and male right. The numbers for the last row “Total,” are, 18 for left handedness, and, 122, for right handedness.
The preceding incomplete table summarizes the number of lefthanded students and righthanded students by gender for the eighthgrade students at Keisel Middle School. There are 5 times as many righthanded female students as there are lefthanded female students, and there are 9 times as many righthanded male students as there are lefthanded male students. If there is a total of 18 lefthanded students and 122 righthanded students in the school, which of the following is closest to the probability that a righthanded student selected at random is female? (Note: Assume that none of the eighthgrade students are both righthanded and lefthanded.)
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30. Question 30 is based on the following equations.
3x + b = 5x – 7
3y + c = 5y – 7
In the preceding equations, b and c are constants. If b is c minus 1/2, which of the following is true?
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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 must be gridded as 3.5 or 7/2. , is entered into the grid, it will be interpreted as not
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
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.
Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.
Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.
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.
Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than $14 on x student tickets and 1 adult ticket, what is one possible value of x?
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32. Question 32 refers to the following figure.
The figure presents a table titled “Ages of the First 12 United States Presidents at the Beginning of Their Terms in Office.” The ages, in years, for the 12 presidents in the table are as follows: Washington, 57. Adams, 62. Jefferson, 58. Madison, 58. Monroe, 59. Adams, 58. Jackson, 62. Van Buren, 55. Harrison, 68. Tyler, 51. Polk, 50. Taylor, 65.
The preceding table lists the ages of the first 12 United States presidents when they began their terms in office. According to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.)
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33. If the preceding expression is rewritten in the form , where a, b, and c are constants, what is the value of b?
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34. In a circle with center O, central angle AOB has a measure of radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?
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35. An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?
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36. Question 36 is based on the following set of inequalities.
In the xyplane, if a point with coordinates (a,b) lies in the solution set of the preceding system of inequalities, what is the maximum possible value of b?
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37. Questions 37 and 38 refer to the following information.
If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N equals r T. This relationship is known as Little’s law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little’s law to estimate that there are 45 shoppers in the store at any time.
Little’s law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spends an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
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38. The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)