CLEP College Mathematics Study Questions AND ACCURATE VERIFIED ANSWERS 2023/2024

CLEP College Mathematics Study Questions AND ACCURATE VERIFIED ANSWERS 2023/2024 #1 Practice test 1 Which one of the following is equivalent to the negation of the statement "Cats are friendly and Bob has a hamster"? A. If cats are friendly, then Bob does not have a hamster. B. If Bob has a hamster, then cats are friendly. C. If cats are not friendly, then Bob has a hamster. D. If Bob does not have a hamster, then cats are not friendly. - correct answer A) When a statement is in the form "If P, then Q," the equivalent statement is in the form "Not P or Q." The negation of "Not P or Q" is the statement "P and not Q." Let P represent the statement "Cats are friendly." Let "not Q" represent the statement "Bob has a hamster." Then the given statement in the stem of this question is written in the form "P and not Q," so the negation will be in the form "If P, then Q." Note that Q represents the statement "Bob does not have a hamster." #5 Practice Test 1 Not counting the empty set, how many proper subsets are there for R = {2, 3, 4}? A. 5 B. 6 C. 7 D. 8 - correct answer (B) Given a set of n elements, the number of proper subsets is given by the expression 2ⁿ - 1. The set of proper subsets does not include the set itself. However the expression 2ⁿ - 1 does include the empty set. Thus, the answer is 2ⁿ - 2 = 2³ - 2 = 6. #6 Practice Test 1 If f(x) = 2x + 4 and g(x) = x² - 2, then (f∘g)(x), where (f∘g)(x) is a composition of functions, is: A. 2x² - 8 B. 2x² + 8 C. 2x² D. 2x³ + 4x² - 4x - 8 - correct answer (C) (f∘g) (x) = f(x) ∘ g(x) = f(g(x)) This is the definition of the composition of functions. For the functions given in this problem we have 2(g(x)) + 4 = 2(x²-2) + 4 = 2x²-4+4 = 2x² #8 Practice Test 1 Given that i = √-1 , what is the simplified expression for 3i³ - 4i² + 5i? A. -2i - 4 B. -2i + 4 C. 2i - 4 D. 2i + 4 - correct answer (D) i² = -1 and i³ = i² (i) = (-1) (i) = -i. So, 3i³ - 4i² + 5i = (3)(-i) - (4)(-1) + 5i = 5i - 3i + 4 = 2i + 4. #11 Practice Test 1 The sum of three different prime numbers is 22. One of these numbers is 2. What is the largest possible value of either of the other numbers? - correct answer The correct answer is 17. The sum of the other two numbers must be 20. The possible pairs of integers for which both numbers are prime are 7 and 13 or 3 and 17. Thus, 17 is the largest possible value. Note that 1 and 19 cannot be considered since 1 is not a prime. #12 Practice Test 1 There are six Knights of the Round Table. Given that Sir Lancelot must sit in a specific chair and that Sir Gawain must be directly on either side of him, in how many ways may the knights be seated? A. 24 B. 120 C. 48 D. 25 - correct answer (C) Since Sir Lancelot must sit in an assigned chair, and Sir Gawain on either side of him, there are 4! or 24 ways of seating the other four. For each of these arrangements, Sir Gawain can be in either of two seats, so the total number of ways of seating the knights is 24 x 2 or 48.