Download MAC 1105 Spring 2011 Mini-Term A Exam #4

MAC 1105 Spring 2011 Mini-Term A Exam #4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
1) x2 - 5x ≥ -4
1)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A) [4, ∞)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
B) (-∞, 1]
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C) (-∞, 1] ∪ [4, ∞)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
D) [1, 4]
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
2) (x - 3)(x - 4)(x - 6) < 0
2)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
A) (3, 4) ∪ (6, ∞)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
B) (-∞, 3) ∪ (4, 6)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
C) (6, ∞)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
D) (-∞, 4)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
1A
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
x
3)
≥ 2
3)
x + 3
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
A) (-∞, -6] or (-3, ∞)
B) (-3, 6]
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
C) (-∞, -3) or [0, ∞)
D) [-6, -3)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
4) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(x - 1)(3 - x)
≤ 0
(x - 2)2
-12 -10 -8
-6
4)
-4
-2
0
2
4
6
8
10
12
A) (-∞, -3] ∪ (-2, -1) ∪ [1, ∞)
-12 -10 -8
-6
-4
-2
0
2
4
6
8
10 12
-4
-2
0
2
4
6
8
10 12
-4
-2
0
2
4
6
8
10 12
-2
0
2
4
6
8
10 12
B) (-∞, 1) ∪ (3, ∞)
-12 -10 -8
-6
C) (-∞, 1] ∪ [3, ∞)
-12 -10 -8
-6
D) (-∞, -3) ∪ (-1, ∞)
-12 -10 -8
-6
-4
2A
Graph the function by making a table of coordinates.
5) f(x) = 3 x
6
5)
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
A)
B)
6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
y
2
4
6 x
2
4
6 x
D)
6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
Write the equation in its equivalent exponential form.
6) log 216 = x
6
A) 216 6 = x
B) x6 = 216
y
6)
C) 6 x = 216
D) 216 x = 6
C) logb 1000 = 3
D) log1000 b = 3
Write the equation in its equivalent logarithmic form.
7) b3 = 1000
A) log3 1000 = b
7)
B) logb 3 = 1000
3A
Evaluate the expression without using a calculator.
8) log 125
5
1
A) 3
B)
3
9) log
8)
C) 15
D) 1
1
4 64
9)
B) -3
A) 3
C)
1
3
D) 12
10) log 2
8
10)
A) 3
B) 1
C)
1
3
D) 6
Graph the function.
11) Use the graph of log x to obtain the graph of f(x) = -2 + log x.
2
2
11)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
4A
10
x
C)
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
5A
10
x
12) Use the graph of f(x) = ln x to obtain the graph of g(x) = 3 - ln x.
12)
y
5
-5
5
x
-5
A)
B)
y
y
5
5
-5
5
x
-5
-5
5
x
5
x
-5
C)
D)
y
y
5
-5
5
5
x
-5
-5
-5
Find the domain of the logarithmic function.
13) f(x) = log (x - 4)
3
A) (4, ∞)
B) (-4, ∞)
13)
C) (-∞, 0) or (0, ∞)
6A
D) (-∞, 4) or (4, ∞)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
16
14) log2 14)
x - 1
A) 4 - log2 x - 1
1
B) 4log2 2 - log2 (x - 1)
2
1
C) 4 - log2 (x - 1)
2
D) log2 16 - log2 x - 1
15) loga 3
x4 x + 5
(x -2)2
15)
1
A) 4 loga x + loga (x + 5) - 2 loga (x - 2)
3
B) 4 loga x - 3 loga (x + 5) - 2 loga ( x - 2)
C) loga x4 + loga (x + 5)1/3 - loga (x - 2)2
D) loga x4 + loga (x + 5)-3 - loga (x - 2)2
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
16) log 6 - log 2
16)
3
3
A) 1
B) log 4
C) log 6 1/2
D) log 12
3
3
3
17)
1
(log8 x + log8 y) - 2 log8 (x + 4)
5
5
5
x + y
A) log8 (x + 4)2
17)
5
5
x + y
B) log8 (x + 4)2
xy
C) log8 2(x + 4)
5
D) log8 (x + 4)2
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
18) log 21
9
A) 1.3856
B) 2.2765
C) 0.7217
D) 0.3680
If y varies directly as x, find the direct variation equation for the situation.
19) y = 9 when x = 63
1
C) y = 7x
A) y = x + 54
B) y = x
7
Solve the problem.
20) If y varies directly as x, and y = 5 when x = 7, find y when x = 49.
5
7
343
A)
B)
C)
7
5
5
9
x
B) y = 1
x
729
C) y = 7A
1
9x
18)
19)
1
D) y = x
9
20)
D) 35
If y varies inversely as x, find the inverse variation equation for the situation.
1
21) y = when x = 81
9
A) y = xy
21)
D) y = x
9
Solve the problem.
22) x varies inversely as y 2 , and x = 4 when y = 6. Find x when y = 2.
A) x = 3
B) x = 48
C) x = 16
22)
D) x = 36
Write an equation that expresses the relationship. Use k for the constant of proportionality.
23) P varies directly as the square of R and inversely as S.
A) P = k + R2 - S2
B) P = kS
C) P = kR2 S
R2
Find the variation equation for the variation statement.
24) z varies jointly as y and the cube of x; z = 64 when x = 2 and y = -4
A) y = 2xy3
B) y = 2x3 y
C) y = -2x3 y
D) P = 23)
kR2
S
24)
D) y = -2xy3
Write an equation that expresses the relationship. Use k for the constant of proportionality.
25) P varies jointly as R and S and inversely as the square root of a.
kRS
k(R + S)
RS
kR
B) P = C) P = D) P = A) P = a
a
k a
S a
8A
25)
Answer Key
Testname: EXAM4A
1) C
2) B
3) D
4) C
5) B
6) C
7) C
8) A
9) B
10) C
11) B
12) B
13) A
14) C
15) A
16) A
17) D
18) A
19) B
20) D
21) A
22) D
23) D
24) C
25) B
9A