Math 098 Final Exam Review
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List a factor of:
1) 7x2 + 34x - 5
A) (x - 1)
2) 20x2 + 23x + 6
A) (20x -3)
3) 12a 4b - 75b3
A) (2a - 5b)
B) (7x - 5)
C) (7x - 1)
D) (x - 5)
B) (5x + 2)
C) (4x - 3)
D) prime
B) (2a 2 + 5b)
Factor completely.
4) 512x3 - 1
A) (512x - 1)(x2 + 8x + 1)
C) (8x - 1)(64x2 + 8x + 1)
Solve the equation.
5) t2 + 2t - 80 = 0
A) -10, 1
6) 81x2 = 16
4
A)
9
Solve.
1)
2)
3)
C) (4a + 15b)
D) (2a + 5b)
4)
B) (8x + 1)(64x2 - 8x + 1)
D) (8x - 1)(64x2 + 1)
B) 10, -8
C) 10, 8
D) -10, 8
4
4
B) , - , 0
9
9
4 4
C) ,9 9
4
D) 9
5)
6)
7) The width of a rectangle is 6 kilometers less than twice its length. If its area is 108 square
kilometers, find the dimensions of the rectangle.
A) width = 9 km, length = 12 km
B) length = 9 km, width = 12 km
C) length = 6 km, width = 6 km
D) length = 3 km, width = 36 km
7)
Perform the indicated operation and simplify if possible.
y2 - 6y + 8 y + 4
·
8)
3y + 12
4y - 8
A)
9)
y-4
12
B)
(y - 4)(y - 2)
12(y + 2)
8)
C)
y-2
12
D)
y+4
12
x2 - 4
x2 + 7x + 1
÷
3x + 18
x2 - 2x
9)
A)
(x + 2)(x2 + 7x + 1)
3x(x + 6)
B)
(x - 2)(x2 + 7x + 1)
3x(x + 6)
C)
3(x + 2)(x + 6)
x(x2 + 7x + 1)
D)
3(x - 2)(x + 6)
x(x2 + 7x + 1)
Revised 2012FL (11/19/2012)
1
10)
12
6
+
2
x
+1
x -1
A)
11)
6
B)
x2 - 1
7a
a 2 - 2a - 8
A)
10)
-
6
x+1
C)
6(x + 3)
x2 - 1
D)
6
x-1
2
a+2
5a - 8
(a + 4)(a + 2)
11)
B)
5a - 8
(a - 4)(a + 2)
C)
5a + 8
(a - 4)(a + 2)
D)
5a + 8
(a + 4)(a + 2)
Solve the equation.
12
1
3
=
12)
x2 - 16 x + 4 x - 4
A) no solution
12)
B) 28
C) 14
D) -14
Simplify the complex fraction.
13)
3
2
+
y y2
13)
9
4
y2 y
A)
1
3 - 2y
B)
3y + 2
9 - 4y
C)
1
3y - 2
D)
3y2 + 2
9 - 4y
Find the domain.
4
14) y =
x + 11
A) x
11
C) all real numbers
Solve.
14)
B) x
-11
D) x - 4
15) Mark and Rachel both work for Smith Landscaping Company. Mark can finish a planting job in 2
hours, while it takes Rachel 3 hours to finish the same job. If Mark and Rachel will work together
on the job, and the cost of labor is $55 per hour, what should the labor estimate be? (Round to the
nearest cent, if necessary.)
A) $45.83
B) $66.00
C) $137.50
D) $132.00
Determine whether the relation is also a function.
16) {(-3, -2), (2, -3), (6, 5), (8, 3), (12, -2)}
A) yes
Revised 2012FL (11/19/2012)
15)
16)
B) no
2
Determine whether the graph is the graph of a function.
17)
A) yes
17)
B) no
Find an equation of the line with the given slope and containing the given point.
18) Slope -4; through (-3, 3)
A) f(x) - 3 = mx + 3
B) f(x) - 3 = x + 3
C) f(x) = -4x + 9
D) f(x) = -4x - 9
Solve.
18)
19) The distance that an object falls when it is dropped is directly proportional to the square of the
amount of time since it was dropped. An object falls 288 feet in 3 seconds. Find the distance the
object falls in 5 seconds.
A) 480 feet
B) 160 feet
C) 15 feet
D) 800 feet
19)
Solve the compound inequality.
20) -5x + 1 11 or 6x + 3 -21
A) [-4, -2]
Solve the equation or inequality.
21) |4x + 8| + 9 = 11
3
5
A) - , 4
4
22) |3t + 2| = -8
10
A) - 2,
3
5
1 9
A) - ,
2 2
20)
B) [-4, )
C) (- , )
D) [-2, )
B)
3
5
C) - , 2
2
3 5
D) ,
2 2
C) 3, - 5
10
D) 2, 3
B)
23) |2x - 4|
C)
9
,
2
Revised 2012FL (11/19/2012)
B) -
21)
22)
23)
1 9
,
2 2
D) - , -
1
2
9
,
2
3
24) |x + 7| - 1 < 2
A) (-10, -4)
B)
C) (-10, 2)
25) |5k + 1| > -3
4 2
A) - ,
5 5
B)
25)
2
,
5
D) - , -
C) (- , )
24)
D) [-10, -4]
4
5
2
,
5
Use radical notation to write the expression. Simplify if possible.
26) 6x3/7
A)
7
6x3
B)
3
6x7
C)
26)
7
216x3
D) 6
7
x3
Simplify. Leave all exponents positive in your final answer.
x3/2 · x1/3
27)
x 1/5
A)
1
61/30
x
B) x49/30
27)
C) x61/30
D)
1
49/30
x
Perform the indicated operations. Assume that all variables represent positive numbers.
3
28) -27a 9b3
A) 27a 3b
29)
30)
B) 3a 3 b
C) 3a 12b6
252x3 - 9 28x3
A) -12 7x 3
B) -9 224x3
C) 24x 7x
D) -12x 7x
7( 28 + 14)
A) 14 + 49 2
B) 14 + 7 2
C) 28
D) 196 + 7 2
B) 9
C) 3
D) 12 - 2 3
31) ( 12 + 3)( 12 - 3)
A) 21
28)
D) -3a 3b
29)
30)
31)
Rationalize the denominator. Assume that all variables represent positive numbers.
x+9
32)
x-9
A) -1
x + 18 x + 81
x - 81
B) 18 x
C)
B) -4
C) -3
32)
D)
x + 81
x - 81
Solve.
33) x = 12x - 12 - 2
A) 6
Revised 2012FL (11/19/2012)
33)
D) 4
4
Perform the indicated operation and simplify. Write the result in the form a + bi.
34) (8 - 3i) - (8 - i)
A) 16 - 2i
B) 16 - 4i
C) 0 - 2i
35) (4 + 3i)(4 - 3i)
A) 16 - 9i2
36)
34)
D) 0 - 4i
35)
B) 7 + 0i
C) 16 - 9i
D) 25 + 0i
2 + 2i
4 - 3i
36)
A) 2 - 2i
B)
2
- 2i
7
C)
14
2
i
25 25
D)
2
14
+
i
25 25
Solve the equation.
37) m 2 + m + 1 = 0
37)
A)
1- 3 1+ 3
,
2
2
B)
1-i 3 1+i 3
,
2
2
C)
-1 - 3 -1 + 3
,
2
2
D)
-1 - i 3 -1 + i 3
,
2
2
Use the quadratic formula to solve the equation.
38) 16x2 + 1 = 3x
38)
A)
3 - i 55 -3 + i 55
,
32
32
B)
-3 - i 55 3 + i 55
,
32
32
C)
-3 - i 55 -3 + i 55
,
32
32
D)
3 - i 55 3 + i 55
,
32
32
Solve the inequality. Write the solution set in interval notation.
39) x2 + 2x 3
A) [-3, 1]
Solve.
40) x4 - 10x2 + 9 = 0
A) -1, 1, -3, 3
B) (- , -3]
B) -i, i, -3i, 3i
41) 3x2/3 - 10x1/3 - 8 = 0
A) 64
B) 64, -
8
27
C) [1, )
C) 1, 9
C) -
8
27
D) (- , -3]
[1, )
D) -1, 1, -3i, 3i
D) 64,
Revised 2012FL (11/19/2012)
C) 64 ft
40)
41)
8
27
42) An arrow is fired into the air with an initial velocity of 128 feet per second. The height in feet of the
arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 128t. Find the
maximum height of the arrow.
A) 768 ft
B) 256 ft
39)
D) 448 ft
5
42)
Graph the function. Find the vertex, y-intercept, and x-intercepts (if any).
43) F(x) = 2x2 - 8x + 10
43)
A) vertex: (2, 2)
x-intercept: none, y-intercept: (0, 10)
B) vertex: (2, 2)
x-intercept: none, y-intercept: (0, 10)
C) vertex: (2, 2)
x-intercept: (10, 0), y-intercept: none
D) vertex: (2, 2)
x-intercept: (0, 0), y-intercept: (0, 10)
For the given functions f and g, find the requested function.
44) If f(x) = x2 + 6x and g(x) = x + 2, find (g f)(4).
A) 44
B) 72
45) If f(x) = 6x + 8 and g(x) = 2x + 1, find (f · g)(x).
A) (f · g)(x) = 12x2 + 22x + 8
C) (f · g)(x) = 12x2 + 8
Revised 2012FL (11/19/2012)
C) 42
44)
D) 240
45)
B) (f · g)(x) = 12x2 + 17x + 8
D) (f · g)(x) = 8x2 + 22x + 9
6
Answer Key
Testname: MATH 098 FINAL EXAM REVIEW RD
1) C
2) B
3) B
4) C
5) D
6) C
7) B
8) A
9) C
10) D
11) C
12) D
13) B
14) B
15) B
16) A
17) B
18) D
19) D
20) C
21) C
22) B
23) D
24) A
25) C
26) D
27) B
28) D
29) D
30) B
31) C
32) C
33) D
34) C
35) D
36) D
37) D
38) D
39) D
40) A
41) B
42) B
43) A
44) C
45) A
Revised 2012FL
7