Download Ch 9 Review

Pre-Algebra
Unit 9 Review
Name ______________________________________________
Period ________
Solve each equation.
1.
24 16  m
a)
b)
c)
d)
3.
5x  35
a)
b)
c)
d)
4.
k
 15
6
a)
b)
c)
d)
2c  4  8
a)
b)
c)
d)
7.
x
5
400
a)
b)
c)
d)
a)
b)
c)
d)
5.
2.
6.
4 ( x  1)  28
a)
b)
c)
d)
28  x  3x  84
8.
a)
b)
c)
d)
2 p  7  13  8 p
Pre-Algebra
Unit 9 Review
Use the Substitution Method to solve the systems of equations below.
9.
y  3x  9
y  11  x
a)
b)
c)
d)
10.
x  5 y
x  6 y  40
a)
b)
c)
d)
11.
x  y4
3x  9 y  36
a)
b)
c)
d)
Unit 9 Review
Pre-Algebra
12.
y  3  2x
2 x  5 y  21
a)
b)
c)
d)
Step 1: Find the slope. m 
y 2  y1
.
x 2  x1
Step 2: Use the slope ( m found in step 1) and the x 0 and y 0 coordinates from one of the points
given and substitute those values into the Point-Slope Equation , y  y 0  m ( x  x0 ) .
Step 3: Distribute the m value then add or subtract the y 0 value over.
Write an equation in slope intercept form , y  mx  b , of the line that passes through
( 3 , -3 ) and ( -11 , 4 )
13.
a)
b)
c)
d)
Unit 9 Review
Pre-Algebra
Consider the equation y   23 x  12
14. Use the equation above to find the
value of y when x = 12 .
15. Use the equation above to find the
value of x when y = 18 .
a)
b)
c)
d)
a)
b)
c)
d)
Determine whether the set of numbers in each table is models a Direct Variation.
16.
Junk E-mails
10
20
30
40
Total E-mails
15
30
45
60
17.
a) Yes
b) No
Jars
3
9
12
15
Jelly Beans
18
36
54
72
a) Yes
b) No
Determine whether each graph models a Direct Variation.
18.
6.
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
a) Yes
b) No
19.
8.
3
3
2
2
1
1
1
2
3
4
5
6
7
8
-1
-1
-2
-2
-3
-3
a) Yes
b) No
Pre-Algebra
Unit 9 Review
Step 1: Write the direct variation equation,
y  k x.
Step 2: Find the k value by either plugging in the given x and y or by using the formula
y
k 0 .
x0
Step 3: Re-write the equation from Step 1 by using the k value that you found in Step 2.
Step 4: Once you have your equation, solve each question by substituting the x or y value into the
equation and solve for the other variable.
Suppose y varies directly as x , and y = 10 when x = 2 .
20. Find the value of k .
21. Find the slope of the line.
a)
b)
c)
d)
a)
b)
c)
d)
22. Write the direct variation equation.
a)
b)
c)
d)
23. Find y when x = 3 .
24. Find x when y = 60 .
a)
b)
c)
d)
a)
b)
c)
d)
Unit 9 Review
Pre-Algebra
If f ( x)  3x  9 and g ( x)  10  2 x , find each function value.
26. f [g (6)]
25. f (12)
a)
b)
c)
d)
a)
b)
c)
d)
Graph each equation by making a table of values.
27.
5
28. y   x  4
2
y  3x  2
x
y
0
1
2
3
x
y
0
2
4
6
Unit 9 Review
Pre-Algebra
Find the slope of each table or graph.
29.
30.
x
0
5
10
15
20
y
1
11
21
31
41
Hint:
m
y
x
a)
b)
c)
d)
Hint: Use the other formula for slope.
m
rise
run
a)
b)
c)
d)
Find the slope of the line that goes through ( 1 , 9 ) and ( 8 , 44 ) .
31.
a. 5
c. 3
b. 2
d. 1
Use the formula: m 
y 2  y1
x 2  x1
y
a)
b)
c)
d)
x
Unit 9 Review
Pre-Algebra
Find the slope of each graph below.
32.
33.
y
y
x
x
a)
b)
a)
b)
Find the equation of each graph ABOVE.
34.
35.
a)
b)
a)
b)
36. Choose the correct graphs when plotting the given irrational numbers on a number line.
7 ,  17
a)
b)
c)
d)
Pre-Algebra
Unit 9 Review
For #37 and #38, evaluate the expressions.
37. 4  23 (8  3)
a)
b)
c)
d)
30
17
45
44
38.  x  y
a)
b)
c)
d)
Evaluate for x = 2 and y = -3.
5
-1
-5
1
For #39 and #40, simplify the expressions.
100
39.
a)
b)
c)
d)
40.
10
100
50
1
2 8
a)
b)
c)
d)
4
6
2
8
Simplify the following expressions.
x  y  2x  5 y
41.
a)
b)
c)
d)
 x  6y
 6 xy
 2  5y
 2x  5 y
3  4(5x  3)
42.
a)
b)
c)
d)
 20x  15
 20x  9
35x  21
35x  3
Unit 9 Review
Pre-Algebra
Simplify each expression.
43. 10 2  10 4
a)
b)
c)
d)
45.
1016
10 24
108
106
5
a)
b)
c)
d)
3y 
5 2
a)
b)
c)
d)
3x 4 x 
44.
h2
h6
46.
6 y10
6 y7
9 y7
9 y10
7x6
7x5
12x6
12x5
a)
1
h3
b) h3
c)
1
h4
d) h 4
Match each statement with the correct number line.
47.
x5
47.
x5
48.
5 x
a)
c)
e)
5
5
5
b)
d)
5
5
Unit 9 Review
Pre-Algebra
Find the perimeter and area of the rectangle.
Formulas: P  2b  2h or 2(b  h) and
Abh
3
7
49. Find the Perimeter.
a)
b)
c)
d)
10
20
15
21
50. 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
51. Find the Perimeter.
a)
b)
c)
d)
144
24
48
36
52. Find the Area.
a)
b)
c)
d)
144
24
48
36
Unit 9 Review
Pre-Algebra
Find the perimeter and area of each triangle.
12
Formulas: P  add up the sides and A  12 b h
9
8
10
5..
Find the Perimeter.
a)
b)
c)
d)
54. Find the Area.
39
31
80
40
a)
b)
c)
d)
39
31
80
40
Solve each proportion.
x 3

24 6
55.
a)
b)
c)
d)
56.
a)
b)
c)
d)
36 4

45 x
Unit 9 Review
Pre-Algebra
For each triangle in problems #55 and #56, use the Pythagorean Theorem to solve.
Pythagorean Theorem:
a2 b2  c2
x
57.
10
6
58. A right triangle has leg lengths of 21 cm and 28 cm. What is the length of the hypotenuse?
Pythagorean Theorem:
a2 b2  c2
a)
b)
c)
d)
59.
Scale Drawing
The dimensions of two scale drawings of the Statue of Liberty are given below. Find the height of the
larger drawing.
2.5 inches
???
a)
b)
c)
d)
½ inch
2 inches
Pre-Algebra
Unit 9 Review
Solve each percent problem.
60. What is 40% of 75?
a)
b)
c)
d)
62. 55 is 20% of what number?
a)
b)
c)
d)
61. 30 is what percent of 90?
a)
b)
c)
d)
Unit 9 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