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Accelerated Math I: SAT Practice Problems ^ 1. Which of the following is equivalent to (y + z)x ? (A) xyz (B) xy + z (C) xy + xz (D) x + yz (E) x + y + z 5. In a sequence, each term after the first is found by adding the constant k to the preceding term. The 10th term in the sequence is 23, and the 16th term is 41. What is the 7,h term in the sequence? (A) -23 (B) -22 .(C) -18 2. If 2x + 1 = -1, what is the value of x2 + 2x - 1? (D) 14 (E) 18 (A) -2 (B) -i (C) 0 (D) 2 (E) 7 3. A bookcase contains a total of 30 books, ^-/' each of which is either a hardcover book or a paperback book. If the number of hardcover books is £ the number of paperback books, how many hardcover books are in the 6. The average (arithmetic mean) weight on 8 rocks in a pile is 15 pounds. Another rock is added, and the average weight of the rocks in the pile increases to 16 pounds. What is the weight, in pounds, of the added rock? (A) 16 (B) 20 (C) 24 (D) 28 (E) 31 bookcase? (A) 5 (B) 10 (C) 15 (D) 20 (E) 25 4. If 4x - 5 =10, then x = (A) 75 (B) 95 (A) Three (B) Five (C) Seven (C) 105 (D) Ten (D) 125 (E) Twenty (E) 225 ^J 7. -Sally's class has a reading list that consists of 5 novels and 2 biographies. Sally will select one novel and one biography from the reading list to complete an assignment. How many different selections of a novel and a biography are possible? 8. The function f is defined by 12. In a certain election, 60 percent of those f(x) = xz +c, where c is a constant. What who voted were females. If 8000 males is f (7) in terms of c? voted, what was the total number of people (A) 49+ c who voted in the election? (B) 49 + 7c (A) 12,800 (C) 7 + c2 (D) 49 +c2 (E) (7 ♦ c)2 (B) 14,000 n (C) 18,600 (D) 20,000 (E) 21,000 9. At Paulie's Pizza Parlor, it costs $8.00 for a plain cheese pizza, plus $0.50 for each topping. If the function Cji) represents the 13. If 6.93 xlO"-1 is an integer between cost, in dollars, of a cheese pizza with n toppings, which of the following is true? (A) C(n) = 8.00 + 0.50 what is the value of a? 600,000 and 700,000 and a is an integer, (A) 2 (B) 3 (B) C(n) - 8.00 +0.50n (O 4 (C) C(n) = 8.00n + 0.50 (W 5 (E) 6 (D) n = 8.00 + 0.50C(n) (E) n = 8.00C(n) + 0.50 10. S, T, and U are digits such that 0 < S <T <U. Which of the following 3-digit numbers is greatest? 14. If multiplying k by 7 gives the same result as squaring k , which of the following must be true? (B) sin (A) 7 + k = k2 (B) k2 + k = 7 (C) k2 +7k =1 ce) TSU (D) 7k = 1 (D) TUS (E) 7k = k2 (A) STU r> (E) UTS 15. Mary earns $50 per week, after taxes, 11. (x +6)" =0 How many different values of x satisfy the equation above? working part-time at a hardware store. Her weekly budget allots $14 for paying back a loan, $16 for miscellaneous expenses, and the rest for savings. Based on this budget, what (A) None is the fewest number of weeks that it will (B) One take her to save $450? (C) Two (A) 9 (D) Four (B) 15 (E) More than four (C) 18 (D) 23 (E) 29 n 21. 16. If —=2, what is the value of %-? Zc 5 6c w S(L) =3£- 20.5 The function 5 defined above can be used to approximate a woman's shoe size in the United (A) 3/5 States, where L is the woman s foot length, ir (B) 3/2 inches. According to this function, which of the following best approximates the shoe sizi (C) 9/5 (D) 9/2 (E) 27/5 17. If 5 more than x is equal to 10, what is of a woman whose foot length is 9.3 inches? (A) 5 £ (B) 6 (0 6 £ (D) 7 the value of x? • (E) 7 £ (A) -15 (B)-5 (C) 2 22. For all integers n, let the function fbe (D) 5 defined by f(n) = /?2 -n. What is the value (E) 15 off(-l)? (A) -2 18. The sum of which of the following (B) -1 combinations of numbers will be odd? (C) 0 (A) (B) (C) (D) (E) One even and two odd numbers Two even numbers Three even numbers Three odd numbers Four odd numbers 19. If xy = 5, xz =10, yz = 2, and x, y, and z are positive, what is the value of xyz? (D) 1 (E) 2 23. Nir. Hampton has an 8-foot-tall oak tree in his backyard. If the tree will grow n feet in height each year, which of the following represents the height of the tree, in feet, 4 years from now? (A) 5 (A) 8 + n (B) 10 (C) 20 (B) 8 + 4n (D) 25 (C) 8(4n) (D) 8n (E) 50 (E) 4n 24. 20. If x = 3y and w = 3, what is the value of wy - x? ^ 3a + 7 = 4b - 3 Each of the following is equivalent to the equation above EXCEPT (A)0 (A) 3a = 4b + 10 (B) 1 (C) 3 (B) 3a + 10 = 4b (D) 6 (D) 10 = 4b-3a (E)9 (E) 3a - 4b = -10 (C) 3a + 3 = 4b-7 30. 8, 21, 25. The cost of a case of 12 computer adapters is $75. When purchased separately, each adapter costs $8. How many dollars would be saved by purchasing a case of adapters, rather than purchasing 12 adapters The first term of the sequence above is 8. separately? the sequence? 26. On a number line, the number x is 31. Michael ran 5.5 miles each day for the first 5 of 6 days. How many miles must he run on the sixth day so that his average (arithmetic mean) for the 6 days will be 6.0 miles per day? halfway between 2 and 3. What is the value of |l-x|? r\ Each term after the first term is 5 more than twice the term immediately preceding it. What is the sum of the first four terms of 27. A certain number n is multiplied by 12. The number that is 3 less than n is also multiplied by 12. How much greater is the first product than the second? 32. In Lewiston, 4 out of every 7 registered voters voted in the last election. If a total of 2000 votes were cast, what was the number f""^ of registered voters in Lewiston at the time of the election? 28. In dry air, the speed of sound V, in meters per second, is modeled by the function V(t) - 331.4 + 0.61, where t is the temperature in degrees Celsius. According to the model, for what value of t is the speed of sound in dry air 343.7 meters per second? 33. If 4x + 8y - 8 = 10, what is the value of x + 2y? 29. If x2 <2x , what is one possible value for x? n