The sat math section 3

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5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 152 – THE SAT MATH SECTION – 5. At a school fair, the spinner represented in the 8. Given the statement: “If two sides of a triangle accompanying diagram is spun twice. are congruent, then the angles opposite these sides are congruent.” Given the converse of the statement: “If two R G angles of a triangle are congruent, then the sides opposite these angles are congruent.” B What is true about this statement and its What is the probability that it will land in section converse? G the ﬁrst time and then in section B the second a. Both the statement and its converse are true. time? b. Neither the statement nor its converse is true. c. The statement is true, but its converse is false. 1 a. 2 d. The statement is false, but its converse is true. 1 b. e. There is not enough information given to 4 1 determine an answer. c. 8 1 d. 16 9. Which equation could represent the relationship 3 e. between the x and y values shown below? 8 x y 6. If a and b are integers, which equation is always 0 2 true? 1 3 a b a. b = a 2 6 b. a + 2b = b + 2a 3 11 c. a – b = b – a 4 18 d. a + b = b + a e. a – b a. y = x + 2 b. y = x2 + 2 x2 + 2x 7. If x ≠ 0, the expression is equivalent to c. y = x2 x a. x + 2. d. y = 2x b. 2. e. y2 c. 3x. d. 4. 10. If bx – 2 = K, then x equals K e. 5. a. b + 2. K–2 b. b. 2–K c. b. K+2 d. b. e. k – 2. 152
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 153 – THE SAT MATH SECTION – 11. What is the slope of line l in the following 14. Let x and y be numbers such that 0 < x < y < 1, diagram? and let d = x – y. Which graph could represent y the location of d on the number line? d a. −1 0 x y 1 l x d b. −1 0 x y 1 d c. −1 0 x y 1 3 d a. – d. 2 −1 0 x y 1 2 b. – 3 d e. 2 c. −1 3 0 x y 1 3 d. 2 2 e. 2 3 15. A car travels 110 miles in 2 hours. At the same rate of speed, how far will the car travel in h 12. From January 3 to January 7, Buffalo recorded hours? the following daily high temperatures: 5°, 7°, 6°, a. 55h 5°, 7°. Which statement about the temperatures b. 220h is true? h c. 55 a. mean = median h d. b. mean = mode 220 c. median = mode e. 10h d. mean < median 16. In the set of positive integers, what is the solution e. median < mode set of the inequality 2x – 3 < 5? 13. In which of the following ﬁgures are segments a. {0, 1, 2, 3} XY and YZ perpendicular? b. {1, 2, 3} c. {0, 1, 2, 3, 4} Y Y d. {1, 2, 3, 4} 8 6 25° e. {0} X Z X Z 10 10 65° 17. Which is a rational number? Figure 2 Figure 1 a. 8 a. Figure 1 only b. π b. Figure 2 only c. 5 9 c. both Figure 1 and Figure 2 d. 6 2 d. neither Figure 1 nor Figure 2 e. 2π e. not enough information given to determine an answer 153
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 154 – THE SAT MATH SECTION – 6x3 + 9x2 + 3x 18. Which polynomial is the quotient of 22. A boy got 50% of the questions on a test correct. ? 3x a. 2x2 + 3x + 1 If he had 10 questions correct out of the ﬁrst 12, 1 b. 2x2 + 3x and 4 of the remaining questions correct, how c. 2x + 3 many questions were on the test? d. 6x2 + 9x a. 16 e. 2x – 3 b. 24 c. 26 19. If the length of a rectangular prism is doubled, its d. 28 width is tripled, and its height remains the same, e. 18 what is the volume of the new rectangular prism? 23. In isosceles triangle DOG, the measure of the ver- a. double the original volume b. triple the original volume tex angle is three times the measure of one of the base angles. Which statement about ΔDOG is true? c. six times the original volume a. ΔDOG is a scalene triangle. d. nine times the original volume b. ΔDOG is an acute triangle. e. four times the original volume c. ΔDOG is a right triangle. d. ΔDOG is an obtuse triangle. 20. A hotel charges $20 for the use of its dining room e. ΔDOG is an alien triangle. and $2.50 a plate for each dinner. An association gives a dinner and charges $3 a plate but invites 24. Which equation illustrates the distributive prop- four nonpaying guests. If each person has one plate, how many paying persons must attend for erty for real numbers? 1 1 1 1 the association to collect the exact amount a. 3 + 2 = 2 + 3 needed to pay the hotel? b. 3 + 0 = 3 c. (1.3 × 0.07) × 0.63 = 1.3 × (0.07 × 0.63) a. 60 b. 44 d. –3(5 + 7) = (–3)(5) + (–3)(7) c. 40 e. 3x + 4y = 12 d. 20 e. 50 25. Factor completely: 3x2 – 27 = 21. One root of the equation 2x2 – x – 15 = 0 is a. 3(x – 3)2 5 a. 2 . b. 3(x2 – 27) 3 c. 3(x + 3)(x – 3) b. 2 . d. (3x + 3)(x – 9) c. 3. e. 3x – 9 d. –3. 2 e. – 5 . 154
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 155 – THE SAT MATH SECTION – 26. A woman has a ladder that is 13 feet long. If she 30. Which statement is NOT always true about a sets the base of the ladder on level ground 5 feet parallelogram? from the side of a house, how many feet above a. The diagonals are congruent. the ground will the top of the ladder be when it b. The opposite sides are congruent. rests against the house? c. The opposite angles are congruent. a. 8 d. The opposite sides are parallel. b. 9 e. The lines that form opposite sides will never c. 11 intersect. d. 12 31. Of the numbers listed, which choice is NOT e. 14 equivalent to the others? 27. At a school costume party, seven girls wore a. 52% 13 masks and nine boys did not. If there were 15 b. 25 boys at the party and 20 students did not wear c. 52 × 10–2 masks, what was the total number of students at d. .052 the party? e. none of the above a. 30 b. 33 32. On Amanda’s tests, she scored 90, 95, 90, 80, 85, c. 35 95, 100, 100, and 95. Which statement is true? d. 42 I. The mean and median are 95. e. 50 II. The median and the mode are 95. III. The mean and the mode are 95. 28. If one-half of a number is 8 less than two-thirds IV. The mode is 92.22. of the number, what is the number? a. 24 a. statements I and IV b. 32 b. statement III c. 48 c. statement II d. 54 d. statement I e. 22 e. All of the statements are true. 29. If a is an odd number, b an even number, and c 33. Which ﬁgure can contain an obtuse angle? an odd number, which expression will always be a. right triangle equivalent to an odd number? b. square a. a(bc) c. rectangle b. acb0 d. isosceles triangle c. acb1 e. cube d. acb2 e. a2b 155
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 156 – THE SAT MATH SECTION – 34. If 5% of a number is 20, what would 50% of that 36. The pie graph below is a representation of the number be? allocation of funds for a small Internet business a. 250 last year. b. 100 10% Insurance c. 200 9% 30% d. 400 Profit Rent e. 500 6% Taxes 35. Use the pattern below to determine which state- 25% ment(s) are correct. Employee 20% x y Wages Utilities 1 2 Suppose this year’s budget was $225,198. Accord- 4 11 ing to the graph, what was the dollar amount of 7 20 proﬁt made? 12 35 a. $13,511.88 b. $18,015.84 I. The pattern is 3x – 1. c. $20,267.82 II. The pattern is 2x + 1. d. $22,519.80 III. The pattern is 3x + 1. e. $202,678.20 IV. Of the ﬁrst 100 terms, half will be even numbers. 37. What type of number solves the equation x2 – 1 = 36? a. statement I only a. a prime number b. statement II only b. irrational number c. statement III only c. rational number d. statements I and IV d. an integer e. All of the above statements are correct. 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. 156
5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 157 – THE SAT MATH SECTION – 39. Marguerite is remodeling her bathroom ﬂoor. 40. If Deirdre walks from Point A to Point B to Point 2 4 Each imported tile measures 1 7 inch by 1 5 inch. C at a constant rate of 2 mph without stopping, What is the area of each tile? what is the total time she takes? 8 a. 1 35 square inches x miles y miles 11 b. 1 35 square inches A B C 11 a. (x + y) × 2 c. 2 35 square inches b. 2x + 2y 3 d. 3 35 square inches c. xy 2 1 e. 4 32 square inches d. (x + y) 2 e. xy2 157