Algebra I Review
______________________________
(CH. 6, 7, 8, 9, 10, & 11)
Name
(7.2 & 7.3) Solve the following linear systems by any method (elimination or
substitution).
5) y = 2x + 7
6) x + 2y = 8
4x = y – 6
3x + 2y = 6
(7.4)
8)
3x – 2y = 3
-6x + 4y = -6
7)
x + 4y = 23
-x + y = 2
9)
In early spring, you buy 6 potted tomato plants for your container garden.
The plants contained in 8-inch pots sell for $5 and the plants contained in
10-inch pots sell for $8. If you spend $36, how many of each size are you
buying?
10) A steamboat went 8 miles upstream in 1 hour. The return trip took 30
minutes. Assume that the speed of the current and the direction were
constant during both parts of the trip. Find the speed of the boat in still
water and the speed of the current.
(7.1)
Graph each linear system and determine its solution.
11) x – 3y = 6
12) 4x – 2y = -6
x–y=4
2x – y = -3
(7.6)
Graph each linear system of inequalities.
13) -x + y < 6
14) -3x + 2y < 6
x+y < 2
x – 4y > -2
2x + y < 3
Chapter 8:
(8.1) Simplify each expression.
15)
(3x 4 y 3 )( 4 x 4 y)
16)
 3ab 
17)
 2xy  4x y 
18)
 3x y  x y 
2 3
3
2 3
2
4 2
3
3
(8.3)
Simplify each expression.
(8.2)
b5c 2
19)
b 3c 8
Simplify each expression.
22)
m 2 n 3
m 4 n 2
25)
5 x 3 y 2
2 xy3

xy
x 5 y 1

20)
22a 2 b 5 c 7
 11abc 9
23)
 6 x 7 y 5
18 x 3 y 5 z 0
28)
4
24)
 2 xy 2 z 4

1
 xyz
3



2
2
 
9x




Chapter 10:
(10.1) Add or subtract the polynomials.
26) 4 x 2  7 x  2   x 2  x  2

21)
 2x3 y 4

5
 3 xy
 


 
27) 3a 3  4a 2  3  a 3  3a 2  a  4
 


 x 2  7 x  x 3  6 x 2  2 x  9  4 x 3  3x  8
(10.2) Find the product.
29) 5x 3x 3  2 x  5


32) (2x + 4)(2x – 4)
30) (x + 4)(x – 3)
33)
 x  6 2
31) (3x + 11)(5x – 2)


34) 5x  2 3x 2  x  1
(10.4) Use the zero product property to solve the equation.
2
35) (x – 8)(2x + 7) = 0
36) 2 x  1 x  5  0
(10.5) Factor the trinomial.
37) x 2  4 x  5
38)
x 2  19 x  60
39)
(10.6) Factor the trinomial.
40) 3x 2  11a 10
41)
2 x 2 5x  12
42) 18x 2  54 x  28
(10.7) Factor the binomial.
43) x 2  16
44)
9 x 2  64 y 2
45)
a 3  6a 2  4a  24
48) 5 x 3  25 x 2  30 x
(10.8) Factor the expression completely.
46) 12 x 4  3x 2
47)
2 x 2  46 x  180
6 x 2 150
(MIX) Solve the following quadratic equations using factoring.
49) 5 x 2 10 x 120
50) 12 x 4  27 x 2  0
51) 3x 3  6 x 2  5 x  10  0
Chapter 9:
(9.1) Simplify each square root.
52)
(9.2)
 49
Simplify each square root.
11
55)
16
3
8
58)
(9.4)
(9.5)
4 x 2  36
54)
56)
80
57)
148
60)
1

3
59)
3 63  12
62)
2 x 2  5  27
Solve the quadratic equations using the quadratic formula.
63)
2x 2  7 x  3  0
64)
 6 x  3x 2   1
Chapter 12:
(12.2) Simplify each radical expression.
4 5  125  45 66)
24  96  6
65)
Short answer
(ch. 7) 67). Solve the system of equations:
(10.5) 68) Solve for x:
25
36
0.04
Solve the quadratic equations using radicals.
61)

53)
4 x  y  23
x y 2
x2 + 4x – 12 = 0
3
7
(6.6) 69) Find the mean, median, mode, and range of the data below:
40
55
54
42
71
63
52
56
57
55
48
62
59
44
74
(9.2) 70) Graph the equation y = x2 – 16 on the coordinate plane on the answer sheet.
(11.1) 71) Solve for x:
(11.1) 72) Solve for x:
5
x

16 12
x2 x

10
15
(11.2) 73) 75 is what percent of 57?
(11.2) 74) 90 is 120% of what number?