CE Math 1010 Test Chapter 8
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1) (p + 8)2 = 17
A) 17 - 8
1)
B) -8 ±
17
17 -
C)
2) Let f(x) = (x + 9)2 . Find x so that f(x) = 36.
A) 27
B) -3
8
C) 15
D) 8 ±
17
D) -15, -3
Complete the square to find the x-intercepts of the function.
3) f(x) = x2 + 14x + 36
3)
A) (7 + 13, 0)
C) (7 + 6, 0), (7 - 6, 0)
4) f(x) = 4x2 + 48x + 92
A) (-6 + 13, 0), (-6 C) (-6 + 13, 2), (-6 -
B) (-14 + 6, 0)
D) (-7 + 13, 0), (-7 -
13, 0)
4)
13, 0)
13, 2)
B) (-6 + 11, 0), (-6 - 11, 0)
D) (6 + 13, 0), (6 - 13, 0)
Use A = P(1 + r)t to find the interest rate. Round to the nearest hundredth, if necessary.
5) $4000 grows to $4326 in 2 years. Assume that interest is compounded annually.
A) 4%
B) 0.04%
C) 1.08%
D) 1.04%
Solve.
6) 4x2 + 10x = - 3
-5 ± 13
A)
4
7)
5)
6)
B)
-10 ± 13
4
C)
-5 ± 13
8
D)
-5 ± 37
4
2
2
+
=1
x x+3
A) 2, -3
2)
7)
B) 2
C) 3
D) -2, 3
8) x2 - 4x + 20 = 0
A) 4 ± 8i
B) -2 ± 4i
C) 2 ± 4i
D) 6, -2
9) 5x(x - 5) - 90 = 4x(x - 3)
A) 18
B) 5, -18
C) -5, 18
D) -5
10) Let f(x) = 2x2 + 5x - 1. Find x so that f(x) = 0.
5 ± 17
5 ± 33
A)
B)
4
4
8)
9)
10)
C)
1
-5 ± 17
4
D)
-5 ± 33
4
Use the discriminant to determine whether the following equations have solutions that are: two different rational
solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
11) s2 - 5s - 6 = 0
11)
A) Two different rational solutions
C) Two different irrational solutions
B) Two different imaginary solutions
D) Exactly one rational solution
Write a quadratic equation having the given numbers as solutions.
12) 9, 4
A) x2 - 13x + 36 = 0
B) x2 + 36x - 13 = 0
C) x2 + 36x + 13 = 0
13) -
12)
D) x2 + 13x + 36 = 0
8
10
,5
3
13)
A) 3x2 - 50x + 80 = 0
B) 3x2 +
C) 3x2 + 80x - 50 = 0
D) 3x2 -
74
x + 16 = 0
5
74
x + 16 = 0
5
Solve the problem.
14) Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than
the other to fill the tank. How long would each pipe take to fill the tank alone?
A) 15 hr for one
B) 12.5 hr for one
30 hr for the other
25 hr for the other
C) 10 hr for one
D) 25 hr for one
20 hr for the other
50 hr for the other
15) Amy travels 450 miles at a certain speed. If the car had gone 15 mph faster, the trip would have
taken 1 hour less. Find Amy's speed.
A) 72 mph
B) 75 mph
C) 68 mph
D) 78 mph
Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
16) v2 = 2as for v
A) v =
2a
s
2a
B) v =
s
C) v =
2as
14)
15)
16)
D) v = 2a s
Answer the question. You will need to use the formula 4.9t2 + vot = s.
17) A ball is thrown downward at a speed of 40 meters per second from an altitude of 719 meters.
Approximately how long does it take to reach the ground?
A) 11.24 seconds
B) 13.92 seconds
C) 7.13 seconds
D) 8.70 seconds
17)
18) 5t-2 - 11t-1 - 12 = 0
5 1
A) , 4 3
18)
Solve.
5 1
B) - ,
4 3
4
C) - , 3
5
4
D) , -3
5
19) (p - 4)2/3 + 6(p - 4)1/3 + 5 = 0
A) -1, -5
19)
B)
3
-1,
3
C) 3, -121
-5
2
D) -3, -121
20) -38 - x 2 - 12 -38 - x + 14 = 0
A) 1936 + 88 22
C) 1936 - 88 22
20)
B) No solution
D) 1936 - 88 22 , 1936 + 88 22
Find the x-intercepts of the graph of the function.
x2 - 1 2
x2 - 1
- 20
+ 100
21) f(x) =
x
x
21)
B) (10 ± 2 26, 0), (10 ± i 10, 0)
D) (5 ± 26 , 0), (5 ± 26 , 0)
A) (10, 0)
C) (10, 0), (-10, 0)
Without graphing, find the vertex.
22) f(x) = - 10(x + 4)2 - 9
A) (4, 9)
B) (-4, -9)
C) (4, -9)
Without graphing, find the maximum value or minimum value.
23) f(x) = -(x + 9)2 - 2
A) 8
B) -2
C) 9
D) (-4, 9)
D) 10
Complete the square to write the function in the form f(x) = a(x - h)2 + k.
24) f(x) = -x2 - 6x - 5
A) f(x) = -(x - 3)2 - 4
C) f(x) = -(x - (-3))2 + 4
22)
23)
24)
B) f(x) = -(x - (-3))2 - 4
D) f(x) = -(x - 3)2 + 4
Find the vertex.
25) f(x) = 2x2 + 16x + 30
A) (-4, -2)
Find the line of symmetry.
26) f(x) = 3x2 - 18x + 25
A) x = -2
B) (4, 2)
C) (2, 4)
B) x = -3
C) x = 3
3
D) (-2, -4)
D) x = 2
25)
26)
Graph.
27) f(x) = x2 + 3x - 9
27)
A)
B)
C)
D)
Find the x- and y-intercepts. If no x-intercepts exist, state so.
28) f(x) = x2 - 3
A) x-intercepts (0, 3) and (0, - 3); y-intercept (0,-3)
B) x-intercepts ( 3, 0) and (- 3, 0); y-intercept (0,-3)
C) x-intercepts ( 3, 0) and (- 3, 0); y-intercept (0,3)
D) x-intercepts (0, 3) and (0, - 3); y-intercept (0,3)
4
28)
Solve.
29) A gardener is fencing off a rectangular area with a fixed perimeter of 32 ft. What is the maximum
area?
A) 8 ft2
B) 2 ft2
C) 64 ft2
D) 256 ft2
29)
30) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by
c = 4x2 - 232x + 84, where c is the cost in dollars, and x is the number of watches repaired. How
30)
many watches must he repair to have the lowest cost?
A) 42 watches
B) 29 watches
C) 40 watches
5
D) 84 watches
Answer Key
Testname: TEST 8
1) B
2) D
3) D
4) A
5) A
6) A
7) D
8) C
9) C
10) D
11) A
12) A
13) B
14) A
15) B
16) C
17) D
18) B
19) C
20) B
21) D
22) B
23) B
24) C
25) A
26) C
27) B
28) B
29) C
30) B
6