Practice Test 4 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Divide using synthetic division. 1) x 4 + 3 x 3 + x 2 + 7 x + 5 x + 1 1) A) x 3 + 2 x 2 + x + 6 + 6 x + 1 B) x 3 + 2 x 2 - x + 8 - 3 x + 1 C) x 3 + 2 x 2 + x + 8 + 6 x + 1 D) x 3 - 2 x 2 - x + 6 - 3 x + 1 Answer: B 2) x 5 + x 2 - 4 x + 3 2) A) x 4 - 3 x 3 + 10 x 2 - 30 x + 90 + - 274 x + 3 B) x 4 - 3 x 3 + 9 x 2 - 26 x + 78 + - 238 x + 3 C) x 4 - 2 x 2 + 2 x + 3 D) x 4 - 2 + 2 x + 3 Answer: B Use synthetic division and the Remainder Theorem to find the indicated function value. 3) f(x) = x 4 - 4 x 3 - 6 x 2 + 4 x + 4 ; f( 3 ) 3) A) - 65 B) 65 C) - 195 D) - 146 Answer: A 4) f(x) = 2 x 3 - 5 x 2 - 4 x + 7 ; f( - 2 ) 4) A) - 37 B) - 21 C) - 11 D) - 6 Answer: B Use the Rational Zero Theorem to list all possible rational zeros for the given function. 5) f(x) = x 5 - 6 x 2 + 3 x + 21 5) A) ± 1, ± 1 7 , ± 1 3 , ± 1 21 B) ± 1, ± 1 7 , ± 1 3 , ± 1 21 , ± 7 , ± 3 , ± 21 C) ± 1, ± 7 , ± 3 D) ± 1, ± 7 , ± 3 , ± 21 Answer: D 6) f(x) = - 2 x 3 + 3 x 2 - 2 x + 8 6) A) ± 1 2 , ± 1, ± 2, ± 4, ± 8 B) ± 1 2 , ± 1, ± 2, ± 4 C) ± 1 4 , ± 1 2 , ± 1, ± 2, ± 4, ± 8 D) ± 1 8 , ± 1 4 , ± 1 2 , ± 1, ± 2, ± 4, ± 8 Answer: A 1
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Practice Test 4 MULTIPLE CHOICE. Choose the one ...
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Practice Test 4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression without using a calculator.19) log 4 16 19)
A) 8 B) 1 C) 12 D) 2
Answer: D
20) log 3 3 20)
A) 3 B) 13 C) 1
2 D) 1
Answer: C
21) log 4116 21)
A) 2 B) -2 C) 8 D) 12
Answer: B
22) log717
22)
A) 17 B) -
17 C) 1
2 D) -12
Answer: D
23) log 5 1 23)
A) 1 B) 5 C) 15 D) 0
Answer: D
3
24) log 5 5 24)
A) 0 B) 5 C) 1 D) 15
Answer: C
Evaluate or simplify the expression without using a calculator.25) log 10,000 25)
A) 40 B) 4 C) 25 D) 1
4
Answer: B
Evaluate the expression without using a calculator.26) log 3 314 26)
A) 14 B) 3 C) log 3 14 D) 17
Answer: A
Evaluate or simplify the expression without using a calculator.
27) log 110,000 27)
A) 4 B) -4 C) 110,000 D) -
14
Answer: B
28) log 0.01 28)
A) -2 B) -12 C) 1
2 D) 2
Answer: A
29) 8 log 104.1 29)A) 328 B) 3.28 C) 11.2879 D) 32.8
Answer: D
30) 10log 4 30)A) 40 B) 0.0001 C) 10,000 D) 4
Answer: D
31) ln7
e 31)
A) 7e B) e7 C) 1
7 D) 7
Answer: C
32) ln e3 32)
A) 3 B) 1 C) e D) 13
Answer: A
4
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluatelogarithmic expressions without using a calculator.
33) log 7 (7x) 33)A) x B) 7 C) 1 + log 7 x D) 1
Answer: C
34) log x100 34)
A) log x + 2 B) 100x C) -20x D) log x - 2Answer: D
35) log 4x + 3x4 35)
A) log 4 (x + 3) - 4 log 4 x B) log 4 (x + 3) + 4 log 4 xC) log 4 (x + 3) - log 4 x D) 4 log 4 x - log 4 (x + 3)
Answer: A
36) logbxy2
z5 36)
A) logbx + 2logby - 5logbz B) logbx + logby2 + logbz5
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whosecoefficient is 1. Where possible, evaluate logarithmic expressions.