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Intermediate Algebra Final Exam Review Guide
Name___________________________________
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
Find the value of the algebraic expression at the given replacement value.
1) 4x + y when x = 3 and y = -1
2) ab when a =
1
3
and b =
7
8
3) The algebraic expression 2.7x gives the total weight in pounds of x tents of a certain type. Find the total weight
of 4 tents.
Add or subtract as indicated.
4) 5 - 12
5) -1 - 4
6) -12 - (-9)
7)
2
1
- 3
6
Multiply or divide as indicated.
8) (-6)(-3)(3)
14
2
·
18
7
9) -
10)
25
0
11)
5
5
÷6
12
Evaluate.
12) (-7)2
Find the indicated root.
1
13)
64
14)
25
Amphitheater District Final Review 2015
1
Simplify the expression.
|-9| + |-3 + 5|
15)
6
16) 2[-6+3(-5+4)]
Find the value of the algebraic expression at the given replacement value.
17) 5(x + 2) + 23
when x = -11
Simplify the expression.
18) 5x +7 +2x +8
19) -14 - (6y - 4)
Solve the equation.
20) 3x -4 = 23
21) 7x + 5 = 2x + 45
22) 2x -7 = 3(x -4)
23)
x x
- =6
3 4
24) 7x + 2 +4x +4 = 7x +4x +6
Write the solution set using interval notation.
25) 9x + 9 ≥ 6x -9
26)
-3x - 12
<-6
4
27) -9 - 3x ≤ 9
Solve.
28) A student scored 69, 76, and 99 on three algebra tests. What must he score on the fourth test in order to have an
average grade of at least 85?
Solve the compound inequality. Graph the solution set.
29) 6 < 2x ≤ 12
30) 9x - 6 < 3x or -2x ≤ -6
2
Solve the absolute value equation.
31) |x - 1| = 5
32) |6x + 5| + 5 = 14
Solve the inequality. Graph the solution set.
33) |x + 2| - 5 ≤ 1
34) |x| > 3
Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph of a
function.
35)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
36)
y
10
5
-10
-5
-5
-10
Find the indicated value.
37) Find f(-3) when f(x) = 2x2 + 4x - 1
3
38) Use the graph to find f(1).
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
Graph the inequality.
39) 5x + y > 2
y
10
5
-10
-5
-5
-10
Solve the system of equations.
40)
2x - 3y = 10
x = 4y
41)
6x + 2y = 28
2x + 2y = 36
Simplify. Write the answer with positive exponents.
42) y6 · y3
43) -7x7 · 5x3
44) (-10)0
45)
-63x5
9x2
4
46)
x9 y13
x5 y7
47)
x-6
x2
Write the number in scientific notation.
48) 0.00003197
Write the number in standard notation.
49) 7.25 × 106
Simplify. Write the answer with positive exponents.
50) (5x)3
51)
xy4 -2
x3 y
52) (x-5 y5 )-2
Perform the indicated operation. Write the answer in scientific notation.
6 × 10-5
53)
3 × 101
54) (3 × 105 ) (1.3 × 10-3 )
Perform the indicated operations.
55) (9x6 - 8x4 ) + (5x6 - 7x4 - 6)
56) (5x - 1) - (-x - 5)
Multiply.
57) (x - 10)(x - 6)
58) (-4x + 3)(2x - 1)
59) (x - 13)2
60) (x + 3)(x - 3)
Factor the polynomial completely.
61) 55x3 - 11x
62) 20x4 + 32x2
5
63) x2 - x - 56
64) 7x2 + 20x - 3
65) x2 + 6x + 9
66) 64x2 - 9
Solve the equation.
67) x2 + 2x = 24
68) x2 + 4x - 21 = 0
69) (x - 2)(x + 3) = 0
Multiply or divide as indicated. Simplify completely.
2x - 2
2x2
70)
·
5x - 5
x
71)
2x2 15
·
5
x3
72)
5x - 5
3x2
·
x
7x - 7
73)
x2 + 5x - 6
x2 - 1
÷
2
2
x + 9x + 18 x + 7x + 12
Perform the indicated operation. Simplify if possible.
20
6
74)
23x 23x
75)
8x2
-8x
+
x-1 x-1
76)
2
7
+
r r- 3
77)
3x
4
6
+
x + 1 x - 1 x2 - 1
Find the cube root.
3 1
78)
27
6
Find the root. Assume that all variables represent nonnegative real numbers.
4
79) 16
Use radical notation to write the expression. Simplify if possible.
80) 641/2
Use the product rule to multiply. Assume all variables represent positive real numbers.
81) 6 · 7
Use the quotient rule to divide and simplify.
84
82)
3
Simplify the radical expression. Assume that all variables represent positive real numbers.
140
83)
5
84)
x9
36
85)
12
86)
98
87)
63
Find the distance between the pair of points.
88) (2, -7) and (4, -3)
89) (-6, -7) and (3, -1)
Add or subtract. Assume all variables represent positive real numbers.
90) 7 5 + 6 45
91) 9
3
2-4
3
128
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
92) 7( 3 + 5)
93) ( 10 + 2)( 10 - 2)
94) ( 2 +
7)2
7
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
1
95)
5
96)
7 2
11
Solve.
97)
x+1=4
98)
3x + 2 - 9 = 0
Use the square root property to solve the equation.
99) x2 - 5 = 0
100) (x - 6)2 = 4
Use the quadratic formula to solve the equation.
101) x2 - 14x + 45 = 0
102) 6x2 = -12x - 2
Solve.
103) x =
6x + 27
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
104) f(x) = (x + 5)2 - 3
y
10
5
-10
-5
5
10
x
-5
-10
8
105) f(x) = x2 + 4
y
10
5
-10
-5
5
10
x
-5
-10
Write the function in the form y = a(x - h)2 + k.
106) f(x) = x2 - 6x - 7
107) f(x) = -4x2 + 8x - 1
9