College Algebra (pdf)

College Algebra1. What is the next term in the geometric sequence 16, –4, 1, – 1 4 , … ?A. – 1 8B. 0C. 116D. 1 8E. 1 22. A manufacturing company processes raw ore. The number of tons of refined materialthe company can produce during t days using Process A is A(t) = t 2 + 2t and usingProcess B is B(t) = 10t. The company has only 7 days to process ore and must choose 1of the processes. What is the maximum output of refined material, in tons, for this timeperiod?A. 8B. 10C. 51D. 63E. 703. For the 2 functions, f (x) and g(x), tables of values are shown below. What is the valueof g(f (3)) ?x f (x) x g(x)–5 7 –2 3–2 –5 1 –11 3 2 –33 2 3 –5A. –5B. –3C. –1D. 2E. 7© 2004 ACT, Inc. All rights reserved. 1

4. For positive real numbers x, y, and z, which of the following expressions is equivalent125to x2y3z 6?2 3A. 3 xyz2 5B. 6 xyz3 2 5C. 6 x yz3 4 5D. 6 x yz2 5E. 11 xyz5. If A = ⎡2 −4⎤⎢⎣6 0⎥⎦ and B = ⎡−2 4⎤⎢⎣−6 0⎥⎦ , then A – B = ?A.⎡0 0⎤⎢⎣0 0⎥⎦B. ⎡1 0⎤⎢⎣0 1⎥⎦C.D.E.⎡0−8⎤⎢⎣0 0⎥⎦⎡ −4 0⎤⎢⎣−12 0⎥⎦⎡ 4 −8⎤⎢⎣12 0⎥⎦6. Listed below are 5 functions, each denoted g(x) and each involving a real number constantc > 1. If f (x) = 2 x , which of these 5 functions yields the greatest value for f (g(x)), for allx > 1 ?A. g(x) = cxB. g(x) = c xC. g(x) = x cD. g(x) = x – cE. g(x) = log c x7. If the function f satisfies the equation f(x + y) = f(x) + f(y) for every pair of real numbers xand y, what are the possible values of f(0) ?A. Any real numberB. Any positive real numberC. 0 and 1 onlyD. 1 onlyE. 0 only© 2004 ACT, Inc. All rights reserved. 2

8. The imaginary number i is defined such that i 2 = –1. What does i + i 2 + i 3 + + i 49 equal?A. iB. –iC. –1D. 0E. 19. In an arithmetic series, the terms of the series are equally spread out. For example, in1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is3, the last term is 136, and the sum is 1,390, what are the first 3 terms?A. 3, 10, 17B. 3, 23, 43C. 3, 36 1 3 , 70D. 3, 69 1 2 , 136E. 3, 139, 1,251© 2004 ACT, Inc. All rights reserved. 3

Correct Answers for Sample College Algebra ItemsItem # Correct Answer1 C2 E3 B4 D5 E6 A7 E8 A9 A© 2004 ACT, Inc. All rights reserved. 4