–THE SAT SECTION– 102 45˚ 45˚ s s 2s Ί ¯¯¯¯¯ 3x 60˚ 30˚ x 2x h b A = 1 2 bh l w h l w r A = πr 2 C = 2πr r V = πr 2 h h Special Right Triangles V = lwh A = lw • The sum of the interior angles of a triangle is 180 ˚ . • The measure of a straight angle is 180 ˚ . • There are 360 degrees of arc in a circle. Ί REFERENCE SHEET 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 102 Five-Choice Questions Solve each problem. Then, decide which of the answer choices is best, and fill in the corresponding oval on your answer sheet. 1. By how much does the product of 8 and 25 exceed the product of 15 and 10? a. 25 b. 50 c. 75 d. 100 e. 125 2. If k – 1 is a multiple of 4, what is the next larger multiple of 4? a. k + 1 b. 4k c. k – 5 d. k + 3 e. 4(k – 1) 3. If 2 x + 1 = 32, then (x + 1) 2 = a. 5 b. 4 c. 16 d. 25 e. 31 4. If (x + 7)(x – 3) = 0, then x = a. 7 or 3 b. 7 or –3 c. –7 or 3 d. –7 or –3 e. –4 or –3 5. Which of the following expressions represents the phrase “3 less than 2 times x”? a. 3 – 2x b. 2 – 3x c. 3x – 2 d. 2x – 3 e. 2(3 – x) 6. A recipe for 4 servings requires salt and pepper to be added in the ratio of 2:3. If the recipe is adjusted to make 8 servings, what is the ratio of the salt and pepper that must now be added? a. 4:3 b. 2:6 c. 2:3 d. 3:2 e. 8:4 –THE SAT MATH SECTION– 103 Math Pretest ■ All numbers in the problems are real numbers. ■ You may use a calculator. ■ Figures that accompany questions are intended to provide information useful in answering the questions. Unless otherwise indicated, all figures lie in a plane. Unless a note states that a figure is drawn to scale, you should NOT solve these problems by estimating or by measurement, but by using your knowledge of mathematics. 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 103 7. In a triangle in which the lengths of two sides are 5 and 9, the length of the third side is represented by x. Which statement is always true? a. x > 5 b. x < 9 c. 5 ≤ x ≤ 9 d. 4 < x < 14 e. 5 ≤ x < 14 8. What is the area of a circle with a circumference of 10π? a. ͙10π ෆ b. 5π c. 25π d. 100π e. 100π 2 9. An ice cream parlor makes a sundae using one of six different flavors of ice cream, one of three dif- ferent flavors of syrup, and one of four different toppings. What is the total number of different sundaes that this ice cream parlor can make? a. 72 b. 36 c. 30 d. 26 e. 13 10. a 1 , a 2 , a 3 , a 4 , a 5 , a n In the sequence of positive integers above, a 1 = a 2 = 1, a 3 = 2, a 4 = 3, and a 5 = 5. If each term after the second is obtained by adding the two terms that come before it and if a n = 55, what is the value of n? a. 12 b. 10 c. 9 d. 8 e. 5 11. Consider this sequence: 9,45,225, What will the eighth term of the sequence be? a. 45,000 b. 78,125 c. 390,625 d. 703,125 e. 1,953,125 12. Alex wore a blindfold and shot an arrow at the tar- get shown below. Judging by the noise made on impact, he can tell that he hit the target. What is the probability that he hit the shaded region shown? a. 1 out of 4 b. 1 out of 8 c. 1 out of 16 d. 1 out of 32 e. 1 out of 64 2 8 –THE SAT MATH SECTION– 104 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 104 13. Given the following: Set A is the set of prime integers. Set B is the set of positive odd integers. Set C is the set of positive even integers. Which of the following are true? I. Set A | Set C yields Ø. II. Set A | Set B contains more elements than Set A | Set C. III. Set B | Set C yields Ø. a. I only b. II and III only c. II only d. III only e. I and III only 14. Line l has the equation 3x – y = 8. What is the y-intercept of line l? a. (8,0) b. (0,8) c. (–8,–8) d. (0,–8) e. (–8,0) 15. In the triangle below, what is the length of the hypotenuse, h? a. 12.5͙3 ෆ b. c. 25 d. 25͙3 ෆ e. 25͙3 ෆ ᎏ 3 12.5͙3 ෆ ᎏ 3 30 o 12.5 h –THE SAT MATH SECTION– 105 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 105 Grid-in Questions For the next 15 questions, solve the problem and enter your solution into the grid by marking the ovals, as shown below. ■ The answer sheets are scored by a machine, so regardless of what else is written on the answer sheet, you will only receive credit if you have filled in the ovals correctly. ■ Be sure to mark only one oval in each column. ■ You may find it helpful to write your answer in the boxes on top of the columns. ■ If you find that a problem has more than one correct answer, grid only one answer. ■ None of the grid-in questions will have a negative number as a solution. ■ Mixed numbers like 1 ᎏ 1 3 ᎏ must be entered as 1.3333 or ᎏ 4 3 ᎏ . (If the response is “gridded” as ᎏ 1 3 1 ᎏ , it will be read as ᎏ 1 3 1 ᎏ , not 1 ᎏ 1 3 ᎏ .) ■ If your answer is a decimal, use the most accurate value that can be entered into the grid. For example, if your solution is 0.333 ,your “gridded” answer should be .333. A less precise answer, like .3 or .33, will be scored as an incorrect response. 1 2 3 4 5 6 7 8 9 • 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 1 2 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • 1/3 .333 These are both acceptable ways to grid = 0.333. 1 3 1 2 3 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 8 9 0 • 4/3 1.47 Note: You may start your answers in any of the columns, as long as there is space. Answer: Answer: 1.47 4 3 –THE SAT MATH SECTION– 106 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 106 16. A wealthy businessperson bought charity auction tickets that were numbered consecutively, 5,027 through 5,085. How many tickets did she purchase? 17. For some value of x,5(x + 2) = y. After the value of x is increased by 3, 5(x + 2) = z. What is the value of z – y? 18. When a positive integer k is divided by 6, the remainder is 3. What is the remainder when 5k is divided by 3? 19. If (x – 1)(x – 3) = –1, what is a possible solution for x? 20. If 4 times an integer x is increased by 10, the result is always greater than 18 and less than 34. What is the least value of x? 21. A string is cut into two pieces that have lengths in the ratio 4:5. If the length of the string is 45 inches, what is the length of the longer string? 22. If x – 8 is 4 greater than y + 2, then by how much is x + 12 greater than y? 23. A brand of paint costs $14 a gallon, and 1 gallon of paint will cover an area of 150 square feet. What is the minimum cost of paint needed to cover the 4 walls of a rectangular room that is 12 feet wide, 16 feet long, and 8 feet high? 24. How many degrees does the minute hand of a clock move from 5:25 p.m. to 5:47 p.m. of the same day? 25. If the operation ∇ is defined by the equation x∇y = 3x + 3y, what is the value of 3∇4? 26. What is the value of s below? = When multiplying two 2 × 2 matrices, use the formulas: × = 27. If x 5 = 243, what is the value of x –3 ? 28. In the diagram below, AB is tangent to circle C at point B. What is the radius of circle C if AC is 20? 29. Given f(x) = 3x 2 + 2 –x + ᎏ 3 8 ᎏ , find f(3). 30. For the portion of the graph shown, for how many values of x does f(x) = 0? x y 1234567 1 2 3 4 5 –1 –2 –3 –1–2–3–4–5–6–7 A B C 16 [ a 1 b 1 + a 2 b 3 a 1 b 2 + a 2 b 4 ] a 3 b 1 + a 4 b 3 a 3 b 2 + a 4 b 4 [ b 1 b 2 ] b 3 b 4 [ a 1 a 2 ] a 3 a 4 [ qr ] st [ 1 8 ] 2 1 [ 5 8 ] 4 1 –THE SAT MATH SECTION– 107 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 107 . response. 1 2 3 4 5 6 7 8 9 • 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 1 2 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • 1 /3 .33 3 These are both acceptable ways to grid = 0 .33 3. 1 3 1 2 3 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 8 9 0 • 4 /3 1.47 Note:. or 3 b. 7 or 3 c. –7 or 3 d. –7 or 3 e. –4 or 3 5. Which of the following expressions represents the phrase 3 less than 2 times x”? a. 3 – 2x b. 2 – 3x c. 3x – 2 d. 2x – 3 e. 2 (3 – x) 6. A. 25 d. 25 3 ෆ e. 25 3 ෆ ᎏ 3 12.5 3 ෆ ᎏ 3 30 o 12.5 h THE SAT MATH SECTION– 105 5658 SAT2 006[04](fin).qx 11/21/05 6:44 PM Page 105 Grid-in Questions For the next 15 questions, solve the problem