5. At a school fair, the spinner represented in the accompanying diagram is spun twice. What is the probability that it will land in section G the first time and then in section B the second time? a. ᎏ 1 2 ᎏ b. ᎏ 1 4 ᎏ c. ᎏ 1 8 ᎏ d. ᎏ 1 1 6 ᎏ e. ᎏ 3 8 ᎏ 6. If a and b are integers, which equation is always true? a. ᎏ a b ᎏ = ᎏ a b ᎏ b. a + 2b = b + 2a c. a – b = b – a d. a + b = b + a e. a – b 7. If x ≠ 0, the expression ᎏ x 2 + x 2x ᎏ is equivalent to a. x + 2. b. 2. c. 3x. d. 4. e. 5. 8. Given the statement: “If two sides of a triangle are congruent, then the angles opposite these sides are congruent.” Given the converse of the statement: “If two angles of a triangle are congruent, then the sides opposite these angles are congruent.” What is true about this statement and its converse? a. Both the statement and its converse are true. b. Neither the statement nor its converse is true. c. The statement is true, but its converse is false. d. The statement is false, but its converse is true. e. There is not enough information given to determine an answer. 9. Which equation could represent the relationship between the x and y values shown below? xy 02 13 26 311 418 a. y = x + 2 b. y = x 2 + 2 c. y = x 2 d. y = 2 x e. y 2 10. If bx – 2 = K, then x equals a. ᎏ K b ᎏ + 2. b. ᎏ K b –2 ᎏ . c. ᎏ 2– b K ᎏ . d. ᎏ K b +2 ᎏ . e. k – 2. RG B –THE SAT MATH SECTION– 152 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 152 11. What is the slope of line l in the following diagram? a. – ᎏ 3 2 ᎏ b. – ᎏ 2 3 ᎏ c. ᎏ 2 3 ᎏ d. ᎏ 3 2 ᎏ e. 2 ᎏ 2 3 ᎏ 12. From January 3 to January 7, Buffalo recorded the following daily high temperatures: 5°, 7°, 6°, 5°, 7°. Which statement about the temperatures is true? a. mean = median b. mean = mode c. median = mode d. mean < median e. median < mode 13. In which of the following figures are segments XY and YZ perpendicular? a. Figure 1 only b. Figure 2 only c. both Figure 1 and Figure 2 d. neither Figure 1 nor Figure 2 e. not enough information given to determine an answer 14. Let x and y be numbers such that 0 < x < y < 1, and let d = x – y. Which graph could represent the location of d on the number line? 15. A car travels 110 miles in 2 hours. At the same rate of speed, how far will the car travel in h hours? a. 55h b. 220h c. ᎏ 5 h 5 ᎏ d. ᎏ 2 h 20 ᎏ e. 10h 16. In the set of positive integers, what is the solution set of the inequality 2x – 3 < 5? a. {0, 1, 2, 3} b. {1, 2, 3} c. {0, 1, 2, 3, 4} d. {1, 2, 3, 4} e. {0} 17. Which is a rational number? a. ͙8 ෆ b. π c. 5͙9 ෆ d. 6͙2 ෆ e. 2π a. b. c. d. e. −110 0 0 0 0 xy d −11xy −11xy −11xy −11x y d d d d Y ZX Figure 1 10 8 6 Y ZX Figure 2 10 65° 25° l y x –THE SAT MATH SECTION– 153 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 153 18. Which polynomial is the quotient of ᎏ 6x 3 +9 3 x x 2 +3x ᎏ ? a. 2x 2 + 3x + 1 b. 2x 2 + 3x c. 2x + 3 d. 6x 2 + 9x e. 2x – 3 19. If the length of a rectangular prism is doubled, its width is tripled, and its height remains the same, what is the volume of the new rectangular prism? a. double the original volume b. triple the original volume c. six times the original volume d. nine times the original volume e. four times the original volume 20. A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. An association gives a dinner and charges $3 a plate but invites four nonpaying guests. If each person has one plate, how many paying persons must attend for the association to collect the exact amount needed to pay the hotel? a. 60 b. 44 c. 40 d. 20 e. 50 21. One root of the equation 2x 2 – x – 15 = 0 is a. ᎏ 5 2 ᎏ . b. ᎏ 3 2 ᎏ . c. 3. d. –3. e. – ᎏ 2 5 ᎏ . 22. A boy got 50% of the questions on a test correct. If he had 10 questions correct out of the first 12, and ᎏ 1 4 ᎏ of the remaining questions correct, how many questions were on the test? a. 16 b. 24 c. 26 d. 28 e. 18 23. In isosceles triangle DOG, the measure of the ver- tex angle is three times the measure of one of the base angles. Which statement about ΔDOG is true? a. ΔDOG is a scalene triangle. b. ΔDOG is an acute triangle. c. ΔDOG is a right triangle. d. ΔDOG is an obtuse triangle. e. ΔDOG is an alien triangle. 24. Which equation illustrates the distributive prop- erty for real numbers? a. ᎏ 1 3 ᎏ + ᎏ 1 2 ᎏ = ᎏ 1 2 ᎏ + ᎏ 1 3 ᎏ b. ͙3 ෆ + 0 = ͙3 ෆ c. (1.3 × 0.07) × 0.63 = 1.3 × (0.07 × 0.63) d. –3(5 + 7) = (–3)(5) + (–3)(7) e. 3x + 4y = 12 25. Factor completely: 3x 2 – 27 = a. 3(x – 3) 2 b. 3(x 2 – 27) c. 3(x + 3)(x – 3) d. (3x + 3)(x – 9) e. 3x – 9 –THE SAT MATH SECTION– 154 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 154 26. A woman has a ladder that is 13 feet long. If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house? a. 8 b. 9 c. 11 d. 12 e. 14 27. At a school costume party, seven girls wore masks and nine boys did not. If there were 15 boys at the party and 20 students did not wear masks, what was the total number of students at the party? a. 30 b. 33 c. 35 d. 42 e. 50 28. If one-half of a number is 8 less than two-thirds of the number, what is the number? a. 24 b. 32 c. 48 d. 54 e. 22 29. If a is an odd number, b an even number, and c an odd number, which expression will always be equivalent to an odd number? a. a(bc) b. acb 0 c. acb 1 d. acb 2 e. a 2 b 30. Which statement is NOT always true about a parallelogram? a. The diagonals are congruent. b. The opposite sides are congruent. c. The opposite angles are congruent. d. The opposite sides are parallel. e. The lines that form opposite sides will never intersect. 31. Of the numbers listed, which choice is NOT equivalent to the others? a. 52% b. ᎏ 1 2 3 5 ᎏ c. 52 × 10 –2 d. .052 e. none of the above 32. On Amanda’s tests, she scored 90, 95, 90, 80, 85, 95, 100, 100, and 95. Which statement is true? I. The mean and median are 95. II. The median and the mode are 95. III. The mean and the mode are 95. IV. The mode is 92.22. a. statements I and IV b. statement III c. statement II d. statement I e. All of the statements are true. 33. Which figure can contain an obtuse angle? a. right triangle b. square c. rectangle d. isosceles triangle e. cube –THE SAT MATH SECTION– 155 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 155 34. If 5% of a number is 20, what would 50% of that number be? a. 250 b. 100 c. 200 d. 400 e. 500 35. Use the pattern below to determine which state- ment(s) are correct. xy 12 411 720 12 35 I. The pattern is 3x – 1. II. The pattern is 2x + 1. III. The pattern is 3x + 1. IV. Of the first 100 terms, half will be even numbers. a. statement I only b. statement II only c. statement III only d. statements I and IV e. All of the above statements are correct. 36. The pie graph below is a representation of the allocation of funds for a small Internet business last year. Suppose this year’s budget was $225,198. Accord- ing to the graph, what was the dollar amount of profit made? a. $13,511.88 b. $18,015.84 c. $20,267.82 d. $22,519.80 e. $202,678.20 37. What type of number solves the equation x 2 – 1 = 36? a. a prime number b. irrational number c. rational number d. an integer e. There is no solution. 38. Points A and B lie on the graph of the linear function y = 2x + 5. The x-coordinate of B is 4 greater than the x-coordinate of A. What can you conclude about the y-coordinates of A and B? a. The y-coordinate of B is 5 greater than the y-coordinate of A. b. The y-coordinate of B is 7 greater than the y-coordinate of A. c. The y-coordinate of B is 8 greater than the y-coordinate of A. d. The y-coordinate of B is 10 greater than the y-coordinate of A. e. The y-coordinate of B is 20 greater than the y-coordinate of A. 30% Rent 20% Utilities 25% Employee Wages 6% Taxes 9% Profit 10% Insurance –THE SAT MATH SECTION– 156 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 156 39. Marguerite is remodeling her bathroom floor. Each imported tile measures 1 ᎏ 2 7 ᎏ inch by 1 ᎏ 4 5 ᎏ inch. What is the area of each tile? a. 1 ᎏ 3 8 5 ᎏ square inches b. 1 ᎏ 1 3 1 5 ᎏ square inches c. 2 ᎏ 1 3 1 5 ᎏ square inches d. 3 ᎏ 3 3 5 ᎏ square inches e. 4 ᎏ 3 1 2 ᎏ square inches 40. If Deirdre walks from Point A to Point B to Point C at a constant rate of 2 mph without stopping, what is the total time she takes? a. (x + y) × 2 b. 2x + 2y c. xy Ϭ 2 d. (x + y) Ϭ 2 e. xy 2 A BC x miles y miles –THE SAT MATH SECTION– 157 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 157 . 3x + 4y = 12 25. Factor completely: 3x 2 – 27 = a. 3( x – 3) 2 b. 3( x 2 – 27) c. 3( x + 3) (x – 3) d. (3x + 3) (x – 9) e. 3x – 9 THE SAT MATH SECTION 154 5658 SAT2 006[04](fin).qx 11/21/05 6:44 PM. 2 10 65° 25° l y x THE SAT MATH SECTION 1 53 5658 SAT2 006[04](fin).qx 11/21/05 6:44 PM Page 1 53 18. Which polynomial is the quotient of ᎏ 6x 3 +9 3 x x 2 +3x ᎏ ? a. 2x 2 + 3x + 1 b. 2x 2 + 3x c. 2x + 3 d the distributive prop- erty for real numbers? a. ᎏ 1 3 ᎏ + ᎏ 1 2 ᎏ = ᎏ 1 2 ᎏ + ᎏ 1 3 ᎏ b. 3 ෆ + 0 = 3 ෆ c. (1 .3 × 0.07) × 0. 63 = 1 .3 × (0.07 × 0. 63) d. 3( 5 + 7) = ( 3) (5) + ( 3) (7) e. 3x