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The SAT® Practice Test #6 Math Test—No Calculator 20 Questions Turn to Section 3 of your answer sheet to answer the questions in this section. Directions For questions 1 through 15, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 16 through 20, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question 16 on how to record your answers in the spaces provided. You may use scratch paper for scratch work. Notes 1. The use of a calculator is not 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. ©2016 The College Board. Page 1 Reference Begin skippable figure descriptions. The figure presents information for your reference in solving some of the problems. ©2016 The College Board. Page 2 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 one-half bh. 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 30-degree angle and a 60-degree angle. The side opposite the 30-degree angle is labeled x. The side opposite the 60-degree 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 45-degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2. ©2016 The College Board. Page 3 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 four-thirds 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 one-third 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 one-third 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. ©2016 The College Board. Page 4 Question 1. Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation T equals 15n plus 12 represents the total amount T, in dollars, Salim will pay for n tickets. What does 12 represent in the equation? A. B. C. D. The price of one ticket, in dollars The amount of the service fee, in dollars The total amount, in dollars, Salim will pay for one ticket The total amount, in dollars, Salim will pay for any number of tickets Question 2. A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B? A. 0.4x, plus, 0.6y, equals 240 B. 0.6x, plus, 0.4y, equals 240 C. D. 40x, plus, 60y, equals 240 60x, plus, 40y, equals 240 ©2016 The College Board. Page 5 Question 3. What is the sum of the complex numbers where A. 17 B. 17i C. D. 2 plus 3i and 4 plus 8i, i equals the square root of negative 1? 6 plus 11i 8 plus 24i Question 4 refers to the following equation. 4x squared minus 9, equals, open parenthesis, px plus t, close parenthesis, times, open parenthesis, px minus t, close parenthesis Question 4. In the preceding equation, p and t are constants. Which of the following could be the value of p ? A. B. C. D. 2 3 4 9 ©2016 The College Board. Page 6 Question 5. Which of the following is the graph of the equation minus 5 in the xy-plane? y equals 2x Each option presents the graph of a line in the xy-plane with the origin labeled O. The numbers negative 5 and 5 are indicated on each axis. A. Begin skippable figure description. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 5 and the y-axis at 2.5, ending in quadrant 1. End skippable figure description. ©2016 The College Board. Page 7 B. Begin skippable figure description. The line begins in quadrant 2 and moves downward and to the right. It crosses the x-axis at negative 2.5 and the y-axis at negative 5, ending in quadrant 4. End skippable figure description. C. Begin skippable figure description. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 2.5 and the y-axis at 5, ending in quadrant 1. End skippable figure description. ©2016 The College Board. Page 8 D. Begin skippable figure description. The line begins in quadrant 3 and moves upward and to the right. It crosses the y-axis at negative 5 and the x-axis at 2.5, ending in quadrant 1. End skippable figure description. Question 6. If x equals two-thirds y and y equals 18, what is the value of 2x minus 3? A. B. C. D. 21 15 12 10 ©2016 The College Board. Page 9 Question 7. A bricklayer uses the formula n equals 7 l h to estimate the number of bricks, n, needed to build a wall that is l feet long and h feet high. Which of the following correctly expresses l in terms of n and h ? A. l equals the fraction whose numerator is 7 and whose denominator is nh, end fraction B. l equals the fraction whose numerator is h and whose denominator is 7n, end fraction C. l equals the fraction whose numerator is n and whose denominator is 7h, end fraction D. l equals the fraction whose numerator is n and whose denominator is 7 plus h, end fraction ©2016 The College Board. Page 10 Question 8 refers to the following figure. Begin skippable figure description. The figure presents a 3-column table with 5 rows of data. The heading for column 1 is “x,” the heading for column 2 is “w of x,” and the heading for column 3 is “t of x.” The five rows of data are as follows. Row 1: x, 1; w of x, negative 1; t of x, negative 3. Row 2: x, 2; w of x, 3; t of x, negative 1. Row 3: x, 3; w of x, 4; t of x, 1. Row 4: x, 4; w of x, 3; t of x, 3. Row 5: x, 5; w of x, negative 1; t of x, 5. End skippable figure description. Question 8. The preceding table shows some values of the functions w and t. For which value of x is w of x plus t of x equal to x? A. B. C. D. 1 2 3 4 ©2016 The College Board. Page 11 Question 9. If the square root of x, end root, plus the square root of 9, end root, equals the square root of 64, what is the value of x ? A. the square root of 5 B. 5 C. 25 D. 55 Question 10. Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal? A. the fraction whose numerator is 240 plus 310 plus 320, and whose denominator is 3, end fraction, plus x, is greater than or equal to 280 B. 240 plus 310 plus 320, is greater than or equal to x times 280 C. the fraction 240 over 4, end fraction, plus the fraction 310 over 4, end fraction, plus the fraction 320 over 4, end fraction, plus x, is greater than or equal to 280 D. 240 plus 310 plus 320 plus x, is greater than or equal to 4 times, 280 ©2016 The College Board. Page 12 Question 11 refers to the following figure. Begin skippable figure description. The figure presents a parabola labeled, y equals ax squared plus c, in the xy-plane with the origin labeled O. The parabola opens upward and its vertex lies on the y-axis a short distance above the origin. End skippable figure description. Question 11. The vertex of the preceding parabola in the xy-plane is the point with coordinates 0 comma c. Which of the following is true about the parabola with the equation y equals negative a, times, open parenthesis, x minus b, close parenthesis, squared, plus c? A. The vertex is the point with coordinates b comma c, and the graph opens upward. B. The vertex is the point with coordinates b comma c, and the graph opens downward. C. The vertex is the point with coordinates negative b comma c, and the graph opens upward. D. The vertex is the point with coordinates negative b comma c, and the graph opens downward. ©2016 The College Board. Page 13 Question 12. Which of the following is equivalent to the fraction whose numerator is 4x squared, plus, 6x, and whose denominator is 4x plus 2, end fraction? A. x B. x plus 4 C. x minus the fraction whose numerator is 2, and whose denominator is 4x plus 2, end fraction D. x plus 1 minus the fraction whose numerator is 2, and whose denominator is 4 x plus 2, end fraction Question 13 refers to the following equation. 2x squared minus 4x equals t Question 13. In the preceding equation, t is a constant. If the equation has no real solutions, which of the following could be the value of t ? A. B. C. D. negative 3 negative 1 1 3 ©2016 The College Board. Page 14 Question 14. A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation? A. 7.35 d, plus, 6.2s, is less than or equal to 300, and, d is greater than or equal to 2s B. 7.35 d, plus, 6.2s, is less than or equal to 300, and, 2d is greater than or equal to s C. 14.7 d, plus, 6.2s, is less than or equal to 300, and, d is greater than or equal to 2s D. 14.7 d, plus, 6.2s, is less than or equal to 300, and, 2d is greater than or equal to s ©2016 The College Board. Page 15 Question 15. Which of the following is equivalent to open parenthesis, a, plus the fraction b over 2, close parenthesis, squared? A. a, squared, plus the fraction b squared over 2 B. a, squared, plus the fraction b squared over 4 C. a, squared, plus the fraction ab over 2, end fraction, plus the fraction b squared over 2 D. a, squared, plus ab, plus the fraction b squared over 4 ©2016 The College Board. Page 16 Directions For questions 16 through 20, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples. 1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help 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, indicate only one answer. 5. Mixed numbers such as seven slash two. (If three and one half must be recorded as 3.5 or three, one, slash, two, is recorded in the spaces provided on the answer sheet, 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 spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces. ©2016 The College Board. Page 17 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 seven-twelfths, 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. ©2016 The College Board. Page 18 Example 3 Begin skippable figure description. Example 3: Acceptable ways to record two-thirds are: 2 slash 3, .666, and .667. End skippable figure description. ©2016 The College Board. Page 19 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. ©2016 The College Board. Page 20 Question 16. If a, to the power of the fraction b over 4, end power, equals 16 for positive integers a and b, what is one possible value of b ? Question 17 refers to the following equation. two-thirds t equals five-halves Question 17. What value of t is the solution of the preceding equation? ©2016 The College Board. Page 21 Question 18 refers to the following figure. Begin skippable figure description. The figure presents triangle ACE, with horizontal side AC. Side AE is perpendicular to side AC such that point E is above point A. Point B lies on horizontal side AC, point D lies on hypotenuse CE, and line segment BD is drawn such that it is parallel to side AE and forms triangle CDB. Side AE is labeled 18, side BC is labeled 8, side BD is labeled 6, and a right angle symbol is at point A. End skippable figure description. Question 18. In the preceding figure, of side CE ? side BD is parallel to side AE. What is the length Question 19. How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution? ©2016 The College Board. Page 22 Question 20. Points A and B lie on a circle with radius 1, and arc AB has length pi over 3. What fraction of the circumference of the circle is the length of arc AB ? Stop. If you finish before time is called, you may check your work on this section only. Do not go on to any other section. ©2016 The College Board. Page 23