Upload
others
View
7
Download
0
Embed Size (px)
Citation preview
Practice Test 4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Divide using synthetic division.
1) x4 + 3x3 + x2 + 7x + 5x + 1
1)
A) x3 + 2x2 + x + 6 +6
x + 1 B) x3 + 2x2 - x + 8 -3
x + 1
C) x3 + 2x2 + x + 8 +6
x + 1 D) x3 - 2x2 - x + 6 -3
x + 1
Answer: B
2) x5 + x2 - 4x + 3
2)
A) x4 - 3x3 + 10x2 - 30x + 90 +-274x + 3 B) x4 - 3x3 + 9x2 - 26x + 78 +
-238x + 3
C) x4 - 2x2 +2
x + 3 D) x4 - 2 +2
x + 3
Answer: B
Use synthetic division and the Remainder Theorem to find the indicated function value.3) f(x) = x4 - 4x3 - 6x2 + 4x + 4; f(3) 3)
A) -65 B) 65 C) -195 D) -146Answer: A
4) f(x) = 2x3 - 5x2 - 4x + 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) = x5 - 6x2 + 3x + 21 5)
A) ± 1, ± 17
, ± 13
, ± 121 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) = -2x3 + 3x2 - 2x + 8 6)
A) ± 12
, ± 1, ± 2, ± 4, ± 8 B) ± 12
, ± 1, ± 2, ± 4
C) ± 14
, ± 12
, ± 1, ± 2, ± 4, ± 8 D) ± 18
, ± 14
, ± 12
, ± 1, ± 2, ± 4, ± 8
Answer: A
1
Find a rational zero of the polynomial function and use it to find all the zeros of the function.7) f(x) = x3 + 2x2 - 9x - 18 7)
A) {-3, -2, 3} B) {-3} C) {-3, 2, 3} D) {-2}Answer: A
8) f(x) = x3 + 3x2 + 4x - 8 8)A) {1, -2 + 2i, -2 - 2i} B) {1, 2 + 2i, 2 - 2i}C) {1, 2 + 3, 2 - 3} D) {-1, -2 + 3, -4 - 3}
Answer: A
Find an nth degree polynomial function with real coefficients satisfying the given conditions.9) n = 3; 3 and i are zeros; f(2) = 10 9)
A) f(x) = 2x3 - 6x2 - 2x + 6 B) f(x) = -2x3 + 6x2 + 2x - 6C) f(x) = -2x3 + 6x2 - 2x + 6 D) f(x) = 2x3 - 6x2 + 2x - 6
Answer: C
10) n = 3; - 6 and i are zeros; f(-3) = 60 10)A) f(x) = 2x3 + 12x2 - 2x - 12 B) f(x) = 2x3 + 12x2 + 2x + 12C) f(x) = -2x3 - 12x2 - 2x - 12 D) f(x) = -2x3 - 12x2 + 2x + 12
Answer: B
11) n = 4; 2i, 5, and -5 are zeros; leading coefficient is 1 11)A) f(x) = x4 + 4x2 - 100 B) f(x) = x4 + 4x3 - 21x2 - 100C) f(x) = x4 - 21x2 - 100 D) f(x) = x4 + 4x2 - 5x - 100
Answer: C
Solve the problem.12) Solve the equation 2x3 - 23x2 + 71x - 30 = 0 given that 5 is a zero of f(x) = 2x3 - 23x2 + 71x - 30. 12)
A) 5, 1, 3 B) 5, -6, -12 C) 5, 6, 1
2 D) 5, -1, - 3
Answer: C
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solvethe polynomial equation.
13) 5x3 - 18x2 - 11x + 12 = 0; -1 13)
A) 45
, 3, -1 B) 35
, -4, -1 C) -35
, 4, -1 D) 35
, 4, -1
Answer: D
Write the equation in its equivalent exponential form.14) log 5 25 = 2 14)
A) 525 = 2 B) 52 = 25 C) 25 = 25 D) 252 = 5Answer: B
15) log 6 36 = x 15)
A) 36x = 6 B) 366 = x C) 6x = 36 D) x6 = 36Answer: C
2
Write the equation in its equivalent logarithmic form.
16) 5-2 =125 16)
A) log 1/5 5 = -2 B) log-2
125
= 5 C) log 5125
= -2 D) log 5 -2 =125
Answer: C
17)3
64 = 4 17)
A) log 64 3 =14 B) log 64 4 =
13 C) log 4 64 = 3 D) log 4 64 =
13
Answer: B
18) 72 = 49 18)A) log 7 2 = 49 B) log 49 7 = 2 C) log 2 49 = 7 D) log 7 49 = 2
Answer: D
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
C) logbx + 2logby + 5logbz D) logbx + logby2 - logbz5
Answer: A
37) log 3x3 33 - x
4(x + 3)237)
A) log 3 + 3log x +13
log (3 - x) - log 4 - 2log (x + 3)
B) log 3 + 3log x +13
log (3 - x) - log 4 + 2log (x + 3)
C) log 3 + log x3 + log (3 - x)1/3 - log 4 - log (x + 3)2
D) log (3x3 33 - x) - log (4(x + 3)2)
Answer: A
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whosecoefficient is 1. Where possible, evaluate logarithmic expressions.
38) 6 ln x -14
ln y 38)
A) ln x64
yB) ln x6y4 C) ln x6 4
y D) ln x6
y4
Answer: A
5
39) 13
[2ln (x + 8) - ln x - ln (x2 - 9)] 39)
A) ln 3 2(x + 8)x(x2 - 9)
B) ln 3 (x + 8)2
x(x2 - 9)
C) ln 3 (x + 8)2(x2 - 9)x
D) ln 3 x(x + 8)2
(x2 - 9)
Answer: B
40) log x + log (x2 - 121) - log 9 - log (x - 11) 40)
A) log x(x - 121)(x - 11)9 B) log 2x + 11)
20 - x
C) log x(x + 11)9 D) log x(x - 121)
9(x - 11)
Answer: C
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places41) log 24 386 41)
A) 0.5336 B) 3.9668 C) 1.8741 D) 1.2064Answer: C
42) log 16 42)A) 0.7070 B) 1.7013 C) 2.4220 D) 0.4129
Answer: C
Solve the equation by expressing each side as a power of the same base and then equating exponents.43) 4(1 + 2x) = 64 43)
A) {4} B) {1} C) {-1} D) {16}Answer: B
44) 125x =15
44)
A) 16 B) -
13 C) -
16 D) {-3}
Answer: C
45) 32x = 8 45)
A) 53 B) 3
4 C) 35 D) {3}
Answer: C
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for thesolution.
46) 3 x + 6 = 8 46)A) 1.31 B) -0.35 C) 6.53 D) -4.11
Answer: D
6
47) e x + 2 = 5 47)A) -0.30 B) 1.95 C) -0.39 D) -0.05
Answer: C
48) e2x + ex - 6 = 0 48)A) 0.69, 1.10 B) 1.10, 0.14 C) 0.14 D) 0.69
Answer: D
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmicexpressions. Give the exact answer.
49) log 5 (x - 1) = 3 49)A) {126} B) {242} C) {244} D) {124}
Answer: A
50) log2
x + log2
(x - 3) = 2 50)
A) {2} B) {1, -4} C) {4} D) {-1, 4}Answer: C
51) log4
(x + 2) - log4
x = 2 51)
A) {18
} B) {152
} C) {4} D) { 215
}
Answer: D
52) log x + log (x -1) = log 30 52)
A) {-5} B) {6, -5} C) 312 D) {6}
Answer: D
53) log (x + 23) - log 3 = log (10x + 3) 53)
A) 1429 B) -
667 C) -
1429 D) 66
7
Answer: A
Graph the function by making a table of coordinates.54) f(x) = 4x 54)
7
A) B)
C) D)
Answer: A
55) f(x) =14
x55)
8
A) B)
C) D)
Answer: C
Graph the function.56) Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 4. 56)
9
A) B)
C) D)
Answer: D
57) Use the graph of log 3 x to obtain the graph of f(x) = log 3 (x - 1). 57)
10
A) B)
C) D)
Answer: B
58) Use the graph of log 5 x to obtain the graph of f(x) = -2 + log 5 x. 58)
11
A) B)
C) D)
Answer: C
12