Download Math 96 - Packet A.tst

Math 96 - Final Exam Sample Packet A
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1) Find the volume of the circular cylinder below whose diameter is 12 m and height is 8 m.
1)
12 m
8m
A) 108π m 3
B) 648π m 3
C) 54π m 3
D) 288π m3
2) The sum of two numbers is -2. Three times the first number equals 4 times the second number.
Find the two numbers.
A)
8
6
and
7
7
B) -2 and 12
C) -8 and -6
D) -
8
6
and 7
7
3) A boat moves 5 kilometers upstream in the same amount of time it moves 20 kilometers
downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still
water.
2
A) 6 km/hr
B) 9 km/hr
C) 3 km/hr
D) 15 km/hr
3
4)
3
4x - 2 =
3
x +6
A) 2
2)
3)
4)
8
B)
3
4
C)
3
4
D)
5
5) The amount of water in a leaky bucket is given by the linear function f(t) = 125 - 7t, where f(t) is
in ounces and t is in minutes. Find the amount of water in the bucket after 4 minutes.
A) 28 oz
B) 118 oz
C) 153 oz
D) 97 oz
5)
6) x4 + 36 = 37x2
A) -1, 1, -6, 6
6)
7)
4x + 6 - 3 = 0
3
A)
4
B) 1, 36
C) -i, i, -6i, 6i
D) -1, 1, -6i, 6i
7)
B)
4
3
C) 12
1
D) ∅
Graph the piecewise defined function.
8)
-4
if x ≤ -1
f(x) =
-2 + x if x > -1
8)
A)
B)
y
-4
y
4
4
2
2
-2
2
4
6x
-4
-2
2
-2
-2
-4
-4
C)
6x
4
D)
y
y
6
4
4
2
-4
-2
2
2
4
6x
-6
-4
-2
2
4
6
x
-2
-2
-4
-4
-6
Solve the equation.
9) (4x + 2)2 = 36
A) 10, -10
9)
B) 0, 1
C) 1, 2
D) 1, -2
C) (-2, -19)
D) (2, -61)
Find the vertex of the graph of the quadratic function.
10) f(x) = -7x2 - 14x - 5
A) (1, -26)
Solve for x.
11) log
3/5
A)
10)
B) (-1, 2)
x=2
9
25
11)
B) 23/5
C)
2
9
5
D)
3
5
Graph the function. Find the vertex.
12) f(x) = -5x2
12)
A) vertex: (0, 0)
B) vertex: (0, 0)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C) vertex: (0, 0)
10 x
5
10 x
D) vertex: (0, -5)
y
-10
5
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
13) x2 + 1 x + _______
13)
3
1 2
A) x2 + 1 x + 1 = x +
B) x2 + 1 x + 36 = (x +6)2
3
3
9
3
1 2
1 2
C) x2 + 1 x + 1 = x +
D) x2 + 1 x + 1 = x +
6
3
3
36
3
6
3
Graph the exponential function.
14) f(x) = 4x + 1
14)
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Find the power of i.
15
15) i
A) 1
15)
B) -i
C) i
D) -1
B) 7, -5
C) 7, 5
D) -7, 5
Solve the equation.
16) x2 + 2x - 35 = 0
A) -7, 1
17)
11 = 6 - 1
x
x
A)
18)
16)
11
6
17)
B) 2
C) 1
D)
3
5
1 + 2 =
-3
x + 6 x + 3 x2 + 9x + 18
A) -6
18)
B) 0
C) 3
4
D) no solution
( 3x - 5 )
19) 4
= 256
19)
A) 128
B) 3
20) log (x + 2) - log x = 2
9
9
1
A)
40
C)
1
64
D) -3
20)
B) 40
C) 9
D)
2
81
Solve the proportion.
4 = 5
21)
y-6 y+6
21)
A) 54
B) 12
C) - 54
D) -
4
3
Graph the function.
22) f(x) = -|x + 1| - 7
22)
A)
B)
y
y
10
10
-10
10
x
-10
-10
10
x
10
x
-10
C)
D)
y
y
10
10
-10
10
x
-10
-10
-10
5
23) f(x) =
A)
x- 4
23)
B)
y
-10
y
10
10
5
5
-5
10 x
5
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
10 x
5
-10
-5
-5
-5
-10
-10
Rationalize the denominator and simplify.
24)
33+
4
4
A) -7 - 2
24)
12
B) 7 + 2
12
C) 2
Write the series with summation notation.
25) 14 + 20 + 26 + 32
4
4
A) ∑ (6i + 2)
B) ∑ (6i + 8)
i=1
12 - 7
-3 - i
8
C)
i=1
C)
3-i
8
7 , -3 + i
8
7 , -3 + i
8
12
25)
4
∑
(i + 13)
i=1
D)
4
∑
14i
i=1
Use the quadratic formula to solve the equation.
26) 4x2 + 1 = 3x
A)
D) 7 - 2
26)
7
7
6
B)
-3 - i
8
D)
3-i
8
7 , 3 +i 7
8
7 , 3 +i 7
8
Evaluate.
27)
27)
7 0 0
6 3 9
6 2 8
A) -42
B) 294
C) 47
D) 42
Write the first five terms of the sequence whose general term is given.
28) an = n2 - n
A) 2, 6, 12, 20, 30
B) 1, 4, 9, 16, 25
C) 0, 2, 6, 12, 20
28)
D) 0, 3, 8, 15, 24
Find an equation of the line.
29) Through (-2, 4); perpendicular to y = 2x - 2
A) y= -2x + 3
29)
B) y = 2x + 3
C) y =
1
x+ 3
2
Write the function in the form y = a(x - h)2 + k.
30) f(x) = -2x2 + 4x - 9
D) y= -
1
x+ 3
2
30)
A) y = -2(x + 1)2 - 15
C) y = -2(x - 1)2 - 7
B) y = -2(x + 2)2 - 25
D) y = -2(x - 2)2 - 13
7
Answer Key
Testname: MATH 96 - PACKET A
1) D
2) D
3) D
4) B
5) D
6) A
7) A
8) A
9) D
10) B
11) A
12) C
13) C
14) C
15) B
16) D
17) B
18) D
19) B
20) A
21) A
22) A
23) C
24) C
25) B
26) D
27) D
28) C
29) D
30) C
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