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 3

38 Questions. 55 Minutes to Complete.

Directions

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 (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. 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.

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 refers to the following graph.

Begin skippable figure description.

The figure presents a line graph titled “Number of 3D Movies Released by Year.” The horizontal axis is labeled “Year,” and the years 2003 through 2011 are indicated. The vertical axis is labeled “Number of 3D movies released,” and the numbers 0 through 50, in increments of 10, are indicated. The data, represented by 9 points on the graph, are as follows. Note that all values are approximate.

2003, 2 movies.

2004, 2 movies.

2005, 6 movies.

2006, 8 movies.

2007, 6 movies.

2008, 8 movies.

2009, 20 movies.

2010, 26 movies.

2011, 46 movies.

End skippable figure description.

Question 1.

According to the preceding line graph, between which two consecutive years was there the greatest change in the number of 3D movies released?

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2. Question 2 refers to the following table.

x

f (x)

1

5

3

13

21

Question 2.

Some values of the linear function f are shown in the preceding table. Which of the following defines f ?

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3. To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound equals 16 ounces.)

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4. If 3(c+d) = 5, what is the value of c + d?

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5. The weight of an object on Venus is approximately of its weight on Earth. The weight of an object on Jupiter is approximately of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

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6. An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

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7. The Downtown Business Association (D B A) in a certain city plans to increase its membership by a total of n businesses per year. There were b businesses in the D B A at the beginning of this year. Which function best models the total number of businesses, y, the D B A plans to have as members x years from now?

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8. Which of the following is an equivalent form of ?

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9. In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)

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10. The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?

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11. Question 11 refers to the following equation.

-2x + 3y = 6

Question 11.

In the xyplane, the graph of which of the following equations is perpendicular to the graph of the preceding equation?

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12. Question 12 refers to the following system of equations.

Question 12.

The preceding system of equations has solution (x, y). What is the value of x?

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13. Question 13 refers to the following system of inequalities.

y ≤ 3x + 1

x – y > 1

Question 13.

Which of the following ordered pairs (x, y) satisfies the preceding system of inequalities?

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14. Question 14 refers to the following table.

The figure presents a 4-column table, with 3 rows of data. The heading for column 1 is “Type of surgeon.” The heading for columns 2 and 3 is “Major professional activity.” The subheading for column 2 is “Teaching,” and the subheading for column 3 is “Research.” The heading for column 4 is “Total.” The data are as follows.

Row 1. Type of surgeon, General. Major professional activity, teaching, 258. Major professional activity, research, 156. Total, 414.

Row 2. Type of surgeon, Orthopedic. Major professional activity, teaching, 119. Major professional activity, research, 74. Total, 193.

Row 3. Type of surgeon, Total. Major professional activity, teaching, 377. Major professional activity, research, 230. Total, 607.

Question 14.

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the preceding table. If one of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated professional activity is research?

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15. A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

1. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.

2. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

3. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

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16. Questions 16 through 18 refer to the following information.

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The following table gives the growth factors for eight species of trees.

Species of tree

Growth factor

Red maple

4.5

River birch

3.5

Cottonwood

2.0

Black walnut

White birch

5.0

American elm

4.0

Pin oak

3.0

Shagbark hickory

7.5

Question 16.

According to the information in the preceding table, what is the approximate age of an American elm tree with a diameter of 12 inches?

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17. Question 17 refers to the following graph.

The figure presents the graph of a scatterplot, titled “Tree Diameter versus Age.” The horizontal axis is labeled “Tree diameter, in inches,” and the numbers 10 through 16 are indicated. The vertical axis is labeled “Age, in years,” and the numbers 70 through 130, in increments of 10, are indicated.

There are 26 data points in the scatterplot. The leftmost data point is at approximately 10.7 inches and 73 years. The points are clustered, and trend upward and to the right. The rightmost data point is at approximately 16.5 inches and 120 years.

Question 17.

The preceding scatterplot gives the tree diameter plotted against age for 26 trees of a single species. The growth factor of this species is closest to that of which of the following species of tree?

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18. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot equals 12 inches.)

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19. Question 19 refers to the following figure.

The figure presents triangle A B C, where side AC is horizontal and point B is above side AC. Point D lies on side AC, and line segment BD is drawn, forming right angle BDC. Side B C is labeled 12. Angle A B D is labeled 30 degrees, and angle BCD is labeled 60 degrees.

Question 19.

In preceding triangle ABC, what is the length of segment AD?

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20. Question 20 refers to the following figure.

The figure presents a diagram and a graph. The diagram, on the left, is a circle that represents a wheel. The circle lies on a horizontal line. A point is shown in the center of the circle and another point is shown at the top of the circle directly above the center. Four rightward pointing arrows are shown, to the left of the circle, curved around the top of the circle, and to the right of the circle, indicating the movement of the wheel.

The graph, on the right, presents the graph of a curve labeled “y equals d of t” in a t ycoordinate plane. The horizontal taxis is labeled “Time.” The curve begins on the vertical yaxis, high above the horizontal taxis. It curves downward and to the right, touches the horizontal taxis, then turns upward. It continues upward until reaching the same height at which it started, where it then turns back downward. It continues downward and to the right, touches the horizontal taxis for a second time, and then turns upward again. It continues upward until the curve ends at the same height at which it started.

Question 20.

The preceding figure on the left shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y = d(t) in the tycoordinate plane on the right could represent which of the following as a function of time from when the wheel began to roll?

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21. Question 21 refers to the following equation.

Question 21.

In the preceding equation, if a is negative and b is positive, which of the following must be true?

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22. In State X, Mr. Camp’s eighthgrade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighthgrade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighthgrade classes and there are 1,800 eighthgrade classes in the state, which of the following best estimates the number of eighthgrade students in the state who have fewer than two siblings?

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23. Question 23 and 24 refer to the following information.

The Townsend Realty Group invested in the five different properties listed in the following table. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The figure presents a 3column table with 5 rows of data that is titled “Townsend Realty Group Investments.” The heading for column 1 is “Property address.” The heading for column 2 is “Purchase price, in dollars.” The heading for column 3 is “Monthly rental price, in dollars.” The data are as follows.

Row 1, Clearwater Lane: purchase price, 128,000 dollars; monthly rental price, 950 dollars.

Row 2, Driftwood Drive: purchase price, 176,000 dollars; monthly rental price, 1,310 dollars.

Row 3, Edgemont Street: purchase price, 70,000 dollars; monthly rental price, 515 dollars.

Row 4, Glenview Street: purchase price, 140,000 dollars; monthly rental price, 1,040 dollars.

Row 5, Hamilton Circle: purchase price, 450,000 dollars; monthly rental price, 3,365 dollars.

Question 23.

The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

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24. Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

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25. A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

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26. The surface area of a cube is , where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

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27. The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

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28. Question 28 refers to the following figure.

The figure presents the graph of a line, labeled y equals f of x, in the x yplane with the origin labeled O. The number 1 is indicated on both axes. The graph begins in the second quadrant slightly above the xaxis. It moves upward and to the right, passing through the point with coordinates negative 4 comma 1. The line crosses the yaxis at the point with coordinates 0 comma 3 and ends in the first quadrant.

Question 28.

The graph of the linear function f is shown in the preceding x yplane. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point with coordinates (0, -4), what is the value of g(9)?

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29. Question 29 refers to the following equation.

Question 29.

The preceding equation defines a circle in the xyplane. What are the coordinates of the center of the circle?

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30. Question 30 refers to the following equation.

Question 30.

In the preceding equation, a is a positive constant and the graph of the equation in the x yplane is a parabola. Which of the following is an equivalent form of the equation?

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31. 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 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

Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.

Example 4

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.

Question 31.

Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?

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32. The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 1/3 the corresponding original dimension, what is the height of the reproduction, in inches?

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33. Question 33 refers to the following figure.

The figure presents line segment P S, with point P lying to the left of point S. Points Q and R lie on line segment PS, with point Q lying to the left of point R. Line segment PQ is labeled x minus 1. Line segment QR is labeled x, and line segment RS is labeled 3 x minus 7.

Question 33.

On preceding , PQ = RS. What is the length of ?

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34. In the xyplane, the point with (2, 5) lies on the graph of the function f. If , where k is a constant, what is the value of k?

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35. A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

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36. Question 36 refers to the following figure.

The figure presents a circle with center P. Points A, B, and C lie on the circle. Point A is located on the left and in the middle of the circle. Point B is located on the right and near the top of the circle. Point C is located on the right and near the bottom of the circle. Radii PB and PC are drawn forming angle BPC. Line segments AB and AC are also drawn. Angle ABP is labeled 20 degrees, angle BPC is labeled x degrees, and angle ACP is labeled 20 degrees.

Question 36.

Point P is the center of the circle in the preceding figure. What is the value of x ?

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37. Questions 37 and 38 refer to the following information.

Ms. Simon drives her car from her home to her workplace every workday morning. The following table shows the distance, in miles, and her average driving speed, in miles per hour (m p h), when there is no traffic delay, for each segment of her drive.

Ms. Simon’s Workday Morning Drive

Segment of drive

Distance (miles)

Average driving speed with no traffic delay (m p h)

From home to freeway entrance

0.6

25

From freeway entrance to freeway exit

15.4

50

From freeway exit to workplace

1.4

35

Question 37.

One morning, Ms. Simon drove directly from her home to her workplace in 24 minutes. What was her average speed, in miles per hour, during her drive that morning?

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38. If Ms. Simon starts her drive at 6:30 a. m., she can drive at her average driving speed with no traffic delay for each segment of the drive. If she starts her drive at 7:00 a. m., the travel time from the freeway entrance to the freeway exit increases by 33% due to slower traffic, but the travel time for each of the other two segments of her drive does not change. Based on the preceding table, how many more minutes does Ms. Simon take to arrive at her workplace if she starts her drive at 7:00 a. m. than if she starts her drive at 6:30 a. m.? (Round your answer to the nearest minute.)