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Accelerated Math I: SAT Practice Problems 1. Which of the following is equivalent to (y + z)x ? 5. In a sequence, each term after the first is found by adding the constant k to the (A) xyz preceding term. The 10th term in the sequence (B) xy + z is 23, and the 16th term is 41. What is the 7th (C) xy + xz term in the sequence? (D) x + yz (A) -23 (E) x + y + z (B) -22 (C) -18 2. If 2x + 1 = -1 , what is the value of 2 x + 2x – 1? (D) 14 (E) 18 (A) -2 (B) -1 6. The average (arithmetic mean) weight on 8 (C) 0 rocks in a pile is 15 pounds. Another rock is (D) 2 added, and the average weight of the rocks in (E) 7 the pile increases to 16 pounds. What is the weight, in pounds, of the added rock? 3. A bookcase contains a total of 30 books, (A) 16 each of which is either a hardcover book or a (B) 20 paperback book. If the number of hardcover (C) 24 books is ½ the number of paperback books, (D) 28 how many hardcover books are in the (E) 31 bookcase? (A) 5 7. Sally’s class has a reading list that (B) 10 consists of 5 novels and 2 biographies. Sally (C) 15 will select one novel and one biography from (D) 20 the reading list to complete an assignment. (E) 25 How many different selections of a novel and a biography are possible? 4. If x 5 10, then x = (A) 75 (B) 95 (C) 105 (D) 125 (E) 225 (A) Three (B) Five (C) Seven (D) Ten (E) Twenty 8. The function f is defined by 12. In a certain election, 60 percent of those f (x ) x c , where c is a constant. What who voted were females. If 8000 males 2 is f(7) in terms of c? (A) 49 + c (B) 49 + 7c (C) 7 + c2 (D) 49 + c2 (E) (7 + c)2 9. At Paulie’s Pizza Parlor, it costs $8.00 for a plain cheese pizza, plus $0.50 for each topping. If the function C(n) represents the cost, in dollars, of a cheese pizza with n toppings, which of the following is true? (A) C(n) = 8.00 + 0.50 (B) C(n) = 8.00 + 0.50n (C) C(n) = 8.00n + 0.50 (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? (A) STU (B) SUT (C) TSU (D) TUS (E) UTS 11. (x + 6)2 = 0 How many different values of x satisfy the equation above? (A) None (B) One (C) Two (D) Four (E) More than four voted, what was the total number of people who voted in the election? (A) 12,800 (B) 14,000 (C) 18,600 (D) 20,000 (E) 21,000 13. If 6.93 10a 1 is an integer between 600,000 and 700,000 and a is an integer, what is the value of a ? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 14. If multiplying k by 7 gives the same result as squaring k , which of the following must be true? (A) 7 + k = k2 (B) k2 + k = 7 (C) k2 + 7k = 1 (D) 7k = 1 (E) 7k = k2 15. Mary earns $50 per week, after taxes, 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 is the fewest number of weeks that it will take her to save $450? (A) 9 (B) 15 (C) 18 (D) 23 (E) 29 21. 16. If S(L) = 3L – 20.5 3b 9 9b ? , what is the value of 2c 5 6c The function S defined above can be used to (A) 3/5 States, where L is the woman’s foot length, in (B) 3/2 inches. According to this function, which of (C) 9/5 the following best approximates the shoe size (D) 9/2 of a woman whose foot length is 9.3 inches? approximate a woman’s shoe size in the United (E) 27/5 (A) 5 ½ (B) 6 17. If 5 more than x is equal to 10, what is (C) 6 ½ the value of x? (D) 7 (A) -15 (E) 7 ½ (B) -5 (C) 2 22. For all integers n, let the function f be (D) 5 defined by f (n ) n 2 n . What is the value (E) 15 off (1) ? (A) -2 18. The sum of which of the following (B) -1 combinations of numbers will be odd? (C) 0 (A) One even and two odd numbers (D) 1 (B) Two even numbers (E) 2 (C) Three even numbers (D) Three odd numbers (E) Four odd numbers 19. If xy = 5, xz = 10, yz = 2, and x, y, and z are positive, what is the value of xyz? (A) 5 23. Mr. 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) 8 + n (B) 10 (B) 8 + 4n (C) 20 (C) 8(4n) (D) 25 (D) 8n (E) 50 20. If x = 3y and w = 3, what is the value of wy – x? (A) 0 (B) 1 (C) 3 (D) 6 (E) 9 (E) 4n 24. 3a + 7 = 4b – 3 Each of the following is equivalent to the equation above EXCEPT (A) 3a = 4b + 10 (B) 3a + 10 = 4b (C) 3a + 3 = 4b – 7 (D) 10 = 4b – 3a (E) 3a – 4b = -10 30. 8, 21, . . . 25. The cost of a case of 12 computer adapters is $75. When purchased separately, The first term of the sequence above is 8. each adapter costs $8. How many dollars Each term after the first term is 5 more would be saved by purchasing a case of than twice the term immediately preceding it. adapters, rather than purchasing 12 adapters What is the sum of the first four terms of separately? the sequence? 26. On a number line, the number x is 31. Michael ran 5.5 miles each day for the halfway between 2 and 3. What is the value first 5 of 6 days. How many miles must he run of |1 - x|? on the sixth day so that his average (arithmetic mean) for the 6 days will be 6.0 miles per day? 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 32. In Lewiston, 4 out of every 7 registered first product than the second? voters voted in the last election. If a total of 2000 votes were cast, what was the number 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 + 0.6t, where t is the temperature in degrees Celsius. According to 33. If 4x + 8y – 8 = 10, what is the value of the model, for what value of t is the speed x + 2y? of sound in dry air 343.7 meters per second? 29. If x2 < 2x , what is one possible value for x?