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Pre-Algebra
FINAL EXAM / Unit 5 Review
Name ______________________________________________
Period ________
Unit 1 Review
1. Choose the correct graphs when plotting the given irrational numbers on a number line.
7 ,  17
a)
b)
c)
d)
For #2 and #3, simplify the expressions.
2. 4  2(8  3)
a)
b)
c)
d)
30
17
45
14
3. 2  5  2
a)
b)
c)
d)
16
2744
18
2000
3
Pre-Algebra
FINAL EXAM / Unit 5 Review
For #4 and #5, evaluate the expressions for x = 2 and y = -3 .
5.  x  y
4. 9( x  2 y )
a)
b)
c)
d)
-36
24
-108
64
a)
b)
c)
d)
5
–1
–5
1
For #6 to #8, simplify the expressions.
6.
100
a)
b)
c)
d)
7.
10
100
50
1
64
a)
b)
c)
d)
8.
24
16
32
8
2 8
a)
b)
c)
d)
16
4 2
4
2 2
Unit 2 Review
Write an algebraic expression for each of the following word statements. Let n = the unknown number.
9. The sum of a number and 5
Choices for #9 to #12:
10. The product of a number and 5
a) 5  n
b) n  5
11. The difference of a number and 5
c)
n
5
d) n  5
e)
5
n
ab) 5n
12. The quotient of a number and 5
FINAL EXAM / Unit 5 Review
Pre-Algebra
Simplify the following expressions.
13. x  y  2 x  5 y
a)
b)
c)
d)
14.  4  x 
 x  6y
 6 xy
 2  5y
 2x  5 y
a)
b)
c)
d)
15. 3  4(5 x  3)
a)
b)
c)
d)
4x
4 x
4 x
 4x
Expand Each Expression.
16. 54
a)
b)
c)
d)
17. (3 x ) 5
5 5 5 5
44444
5 4
5 4  5 4  5 4  5 4
a)
b)
c)
d)
3 x  x  x  x  x
3 5 x  x  x  x  x
3x  3x  3x  3x  3x
3 5  x
Write each expression using exponents.
18. (2)(2)(2)(2)(2)(2)
19. 8  x  x  x
a)
 26
a) (8 x) 3
b)
c)
(2) 6
(2)(6)
b) 83 x 3
c) 8  3  x
d)
(2)( 6)
d) 8x 3
20x
20x  9
35x  21
35x  3
FINAL EXAM / Unit 5 Review
Pre-Algebra
Evaluate Each Expression.
20. 43
a)
b)
c)
d)
21. (1)8
12
81
36
64
a)
b)
c)
d)
22. (1)11
1
–1
8
–8
a)
b)
c)
d)
Simplify each product.
23. 10 2  10 4
a)
b)
c)
d)
1016
10 24
108
106
24. a  a 6
a)
b)
c)
d)
25.
a7
a5
a
Simplify each expression.
26.
 
4 2 3
3x5 4x3 
a)
b)
c)
d)
a6
27. y 5
2
a)
45
a) y 52
b)
46
b) y 7
c)
43
c) y 25
d)
48
d) y10
1
–1
11
–11
7x 8
7x15
12x 8
12x15
FINAL EXAM / Unit 5 Review
Pre-Algebra
28.
3c 4 d 6 7
a)
b)
c)
d)
21c11 d 13
21c 28 d 42
2187c11 d 13
2187c 28 d 42
Simplify each quotient.
58
29.
5
30.
h
h6
a)
1
57
b) 57
a)
1
h6
b) h 6
c)
1
58
d) 58
c)
1
h5
d) h 5
r9
31.
r3
a)
1
r6
b) r 3
c)
1
r3
d) r
6
Unit 4 Review
Solve each equation.
32.
x  5  6
a)
b)
c)
d)
-1
11
-11
1
33. n  2  6
a)
b)
c)
d)
–4
–3
–8
8
34. 5k  60
a)
b)
c)
d)
65
12
55
300
FINAL EXAM / Unit 5 Review
Pre-Algebra
35.  9 
a)
b)
c)
d)
g
2
– 4.5
18
–18
4.5
36.  3 y  16  10
a)
b)
c)
d)
3
-3
2
-2
37.
t
 10  22
4
a)
b)
c)
d)
3
18
–18
48
Unit 5 Review
Solve each equation.
38. 4 x  x  6  14
a)
b)
c)
d)
6
5
4
8
41. 4 ( x  1)  28
a)
b)
c)
d)
8
6
5
4
39. 10t  3  t  15
a)
b)
c)
d)
2
3
4
5
42. 3x  9  5( x  10)
a)
b)
c)
d)
–32.5
–29.5
–30.25
–27.25
40.  28  x  3x  84
a)
b)
c)
d)
15
12
16
14
43.  (m  6)  4m  12  9m
a)
b)
c)
d)
–3.5
–6.5
–4.5
–5.5
FINAL EXAM / Unit 5 Review
Pre-Algebra
For the given value, state whether the inequality is TRUE or FALSE.
44.  5 y  5
a)
b)
46.
y  2
x59
45.
True
False
 12
4
k
a)
b)
if
a)
b)
if x  5
True
False
47. 13  a  29
if k  2
True
False
a)
b)
if a  30
True
False
Match each statement with the correct number line.
48.
x5
49.
x5
50.
x5
51.
x5
52.
x5
53.
5 x
a)
c)
e)
5
5
5
b)
d)
5
5
FINAL EXAM / Unit 5 Review
Pre-Algebra
Solve each inequality.
54.
x  5  4
a)
b)
c)
d)
55.  12k  48
x  9
x  1
x  9
x  1
a)
b)
c)
d)
56.  2(k  2)  20
x4
x  4
x4
x  4
a)
b)
c)
d)
58
57
a)
b)
c)
d)
x  1
x  1
x  1
x  1
Write an inequality for each situation.
59
a)
b)
c)
d)
0  A  1500
A  1500
0  A  1500
A  1500
a)
b)
c)
d)
0  Y  3918
A  3918
0  Y  3918
A  3918
60
a)
b)
c)
d)
x2
x2
x2
x2
x8
x  12
x 8
x  12
FINAL EXAM / Unit 5 Review
Pre-Algebra
Find the perimeter and area of the rectangle.
Formulas: P  2b  2h or 2(b  h) and A  b h
3
7
7
61. Find the Perimeter.
a)
b)
c)
d)
10
20
15
21
62. Find the Area.
a)
b)
c)
d)
Find the perimeter and area of each square.
10
20
15
21
Formulas: P  4 s and A  s  s or A  s 2
12
63. Find the Perimeter.
a)
b)
c)
d)
144
24
48
36
a)
b)
c)
d)
Find the perimeter and area of each triangle.
12
8
64. Find the Area.
144
24
48
36
Formulas: P  add up the sides and A  12 b h
9
10
65. Find the Perimeter.
a)
b)
c)
d)
39
31
80
40
66. Find the Area.
a)
b)
c)
d)
39
31
80
40
Pre-Algebra
FINAL EXAM / Unit 5 Review
Problem Solving
67.
The perimeter of a rectangle is 40.
If the width is 5, then what is the length?
a)
b)
c)
d)
69.
15
35
20
30
The area of a square is 64.
What is the length of its side?
a)
b)
c)
d)
68. The perimeter of a square is 64.
What is the length of its side?
4
16
16
8
a)
b)
c)
d)
70.
4
6
16
8
The area of a triangle is 28.
If the base is 4, then what is its height?
a)
b)
c)
d)
9
21
7
14
FINAL EXAM / Unit 5 Review
Pre-Algebra
Operational Words:
Sum
Difference
Product
Quotient
Addition
Subtraction
Multiplication
Division
Order of Operations:
P
E
M
D
A
S
parenthesis and other grouping symbols
exponents
multiplication
Multiply and divide from left to right.
division
addition
Add and subtract from left to right.
subtraction
Some perfect squares:
4
9
16
25
36
49
64
81
100 121 144 169 196 225
Rules of Exponents:
Product of Powers:
Quotient of Powers:
a m  a n  a m n
am
n
a
am
an
 a mn

1
anm
if m  n
if n  m
Power of a Power:
a 
Power of a Product:
abn  (a n )(bn )  a nbn
Power of a Quotient:
(a) n a n
a

 n
 
n
b
(b)
b
 
m n
n
 a mn