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Intermediate Algebra
Final Exam Review
Name_________________________________________________
Chapters 3 - 9
Graph the equation.
Find the SLOPE.
1) -5x - 25y = 25
4)
2) y = 6
Decide whether the pair of lines is parallel,
perpendicular, or neither.
5) 3x - 4y = 17 and 8x + 6y = -6
Find the equation in slope-intercept form of the line
satisfying the conditions.
6) m = 4 ; y-intercept (0, 1)
5
7) Write the equation of the line through (3,
2) with m = -
Graph the inequality.
8) x + y < -6
Find the SLOPE. Does the line rise from left to right,
fall from left to right, or is it horizontal or vertical?
3) (-1, -2) and (2, -8)
1
3
.
7
MULTIPLE CHOICE.
Simplify.
16) (9x) 0
Decide whether the relation is a function, and give the
domain and range.
Simplify.
9)
-2
17) 7
4
Simplify. Write answer using only positive exponents.
x-16
18)
x-9
Simplify.
19)
A) Function; domain: (- , ); range: [2,
)
x
20) (-2r 4 + 9r 3 - 3r) - (8r 4 - 9r 3 + 6r 2 - 2r)
, )
C) Function; domain: [2, ); range: (
4
Subtract.
B) Not a function; domain: [2, ); range:
(
- 3w 5
,
21) Given: f(x) = x 2 + 4x - 3 and
)
g(x) = -9x 2 + 7x - 2, find (f + g)(x).
D) Not a function; domain: (- , );
range: [2, )
Multiply.
Solve the problem.
22) (x + 4)(x 2 - x + 8)
10) Find f(-3) when f(x) = 5x 2 - 4x + 5.
23) (4m + 7) 2
11) Find g(a + 1) when g(x) = 5x - 3.
Divide.
Solve the system by substitution or elimination.
2
4
24) 27x + 24x + 21x
12) 3x - 13 = -y
3x
2x + 9y = -8
3
2
25) 6x + 5x - 14x - 12
Solve the system by substitution or elimination.
x+3
13) x + 8y = -4
2x + 7y = 1
Factor.
26) 5x 3 + 10x
Write a system of two equations for the information.
Do NOT solve.
14) During the 2002 Little League season, the
Factor.
Tigers played 44 games. They won 24 more
games than they lost.
27) -r 3 + 2r 2 - 35r
Factor.
Simplify.
15)
28) x 3 + 7x 2 - 6x - 42
(-3x 5 y)(-4x 9 y2 )
2
Factor.
Solve the formula for G.
29) -p2 + 10p - 16
42) F =
Gm1 m 2
d2
30) 15x 2 + 19x + 6
Simplify.
31) 3x 3 + 3x 2 - 36x
43) 81/3
Factor.
Simplify.
32) 81x 2 - 16
x2
y-4
44)
33) 8x 3 + y3
SIMPLIFY.
Solve by factoring.
34) x 2 + 9x - 22 = 0
45)
Find all numbers NOT in the domain of the function.
35) f(x) = x - 1
3x - 6
Simplify.
Simplify.
Simplify.
-1/2
47) 64
y2 + 13y + 42
81
Write with radicals.
48) m 2/3
Perform the indicated operation and Simplify.
2
2
37) k + 13k + 40 · k + 8k
k2 + 16k + 64 k2 + 2k - 15
Simplify by first converting to rational exponents. Give
the answer in radical form.
49) z 14
38) (2x - 5) (x + 2) ÷ (x + 2) (3x + 5)
(x + 8) (x - 3)
39)
y2 - 3y + 2
+
2
(x 1/3)
5/3
(x 3 )
46) (-27) 2/3
2
36) y + 3y - 28
3
1/2
(x + 8) (x - 3)
7
y2 - 1
50)
6
y·
5
y2
Multiply.
51) 7 · 3
DO NOT SOLVE. List all possible numbers that would
have to be rejected if they appeared as potential
solutions.
40) 10 - 1 = 1
20x - 17 x 9x + 4
Divide.
52)
Solve.
41)
-36
4
Simplify.
6
8
6
=
m - 3 m + 3 m2 - 9
53) 175
3
66) Rationalize the denominator.
36
11
Simplify.
4
54) - 81x 6 y9
Find the missing length in the right triangle. Simplify
the answer if necessary.
Rationalize the denominator.
67) 3
4- 2
55)
b
68) If a boat uses 21 gallons of gas to go 74
6
miles, how many miles can the boat travel
on 63 gallons of gas?
4
Perform the indicated operations and simplify.
56) -3 20 + 6 125
Simplify.
3
3
57) 4 m 7 p5 - 2m 2 p mp2
Solve.
58) 5x - 5 - 3 = 0
Solve.
59) p2 - 3p + 60 = p + 4
Simplify.
60) -276
Solve.
61) -5k2 + 80 = 0
62) (8s + 7) 2 = 36
Use the quadratic formula to solve.
63) 2n2 = -8n - 3
SOLVE by completing the square.
64) a 2 - 6a - 16 = 0
Multiply.
65) (4 - 5i)(6 + 6i)
4
Answer Key
Testname: IA FE REV F15
9) A
10) 62
1) (-5, 0); (0, -1)
11)
12)
13)
14)
5a + 2
{(5, -2)}
{(4, -1)}
10 games
15) 12x 14y3
16) 1
16
17)
49
2) None; (0, 6)
18)
1
x7
19)
81w 20
x4
20) -10r 4 + 18r 3 - 6r 2 - r
21) -8x 2 + 11x - 5
22) x 3 + 3x 2 + 4x + 32
23) 16m 2 + 56m + 49
24) 9x 3 + 8x + 7
25) 3x 2 - 2x - 4
26) 5x(x 2 + 2)
27) -r(r 2 - 2r + 35)
28) (x + 7)(x 2 - 6)
29) -(p - 2)(p - 8)
30) (3x + 2)(5x + 3)
3) - 2; falls
3
4) --4/5
2
31) 3x(x - 3)(x + 4)
32) (9x + 4)(9x - 4)
33) (2x + y)(4x 2 - 2xy + y2 )
34) {-11, 2}
35) 2
y-4
36)
y+6
5) Perpendicular
4
6) y = x + 1
5
7) 3x + 7y = 23
8)
37)
k
k-3
38)
2x - 5
3x + 5
39)
10y - 11
(y - 1)(y + 1)(y - 2)
40) 0,
17
4
,- ; xx
20
9
41) { 18 }
42) G =
5
Fd2
m1 m2
0,
17
4
,20
9
Answer Key
Testname: IA FE REV F15
43) 2
44) xy2
1
45)
x 13/3
46) 9
9
47)
8
48)
3
m
2
49) z 7
30
50)
y17
51) 21
52) 3i
53) 5 7
4
54) -3xy2 x 2y
55) b = 2 5
56) 24 5
3
57) 2m 2 p mp2
14
58)
5
59) {4}
60) 2i 69
61) {4, -4}
1
13
62) - , 8
8
63)
-4 + 10 -4 - 10
,
2
2
64) 8, -2
65) 54 - 6i
66)
6 11
11
67)
12 + 3 2
14
68) 222 miles
6