Algebra 1 Review
Solve the following equations if possible.
1.
3x  1  5x
2.
8  2 y  21  6 y
3.
1
(14  8a)  9a
2
4.
7  6d  3(5  2d )
6.
4 x  (2 x  8)  (3x  6)
7.
5.
7(b  1)  5(b  2)
x  4( x  12)  8
Solve the equation. Round to the nearest hundredth. (you may use your calculator on these)
15 y  8  4 y  3
11.
Plot and label the ordered pairs in a coordinate plane. Indicate what Quadrant each point is in, and
if not in a quadrant, state where it is.
A(2, 4), B(2,0), C (5, 2)
9.
2(2n  11)  31  3n
7.6x  3.7  2.8 1.6x
8.
10.
12. Use a table of values to graph the following equations.
a. y  5 x  1
b.
x  2
x
13.
y
x
Find the x -intercept and the y -intercept of the line below, and graph the equation.
a. 5 x  y  5
b. 2 x  y  6
c. y  1
x-intercept: ________
x-intercept: ________
x-intercept: __________
y-intercept: ________
y-intercept: ________
y-intercept: __________
14. Write the formula for finding the slope, m , of a line passing through two given points ( x1 , y1 ) and
( x2 , y2 ) .
15.
Find the slope, m , of the line passing through the given two points.
a. (6,1),(4,1)
b. (2, 2),( 1, 4)
y
16. Write the equation for slope-intercept form. _________________________
17. Write the following equations in slope-intercept form. State the slope and y-intercept. Then, graph the
equation.
a.
x  y 1
b.
3x  2 y  6
m  ________
m  ________
y  int  _________
y  int  _________
18. Decide whether the graphs of the two equations are parallel lines. Explain your answer.
y  3x  2
a.
1
y  x4
3
b.
y  5x  1
3 y  15 x  4
What are the general equations for the three ways to write the equation of a line?
19.) ____________________________________
20.) ____________________________________
21.) ____________________________________
Write an equation of the line with the given slope and y-intercept. Write the equation in
slope-intercept form.
1
22.) m  4 , b  3 ___________________ 23.) m  , b  3 ____________________
4
Write an equation of the line that passes through the given point and has the given slope.
Write the equation in slope-intercept form, point-slope form, and standard form.
24.)
(3, 9) , m  5
Point-Slope Form: ____________________________
Slope-Intercept Form: _________________________
Standard Form: ______________________________
25.)
(1,8) , m  4
Point-Slope Form: ____________________________
Slope-Intercept Form: _________________________
Standard Form: ______________________________
Graph the line that passes through the given points. Then, write the equation of the line in
point-slope form, slope-intercept form, and standard
form.
26.)
(6, 2),(8, 4)
Point-Slope Form:
____________________________
Slope-Intercept Form:
_________________________
Standard Form:
______________________________
27.)
(5, 1),(5, 4)
Point-Slope Form:
____________________________
Slope-Intercept Form: _________________________
Standard Form:
______________________________
28.)
(1, 1),(6, 1)
Point-Slope Form:
____________________________
Slope-Intercept Form: _________________________
Standard Form:
______________________________
Write an equation of the line for the following lines. Give the equation in slope-intercept
form.
1
29.) A line parallel to the line y  x  7 , and passes through the point (1, 2) .
3
30.)
A line perpendicular to y  2 x  6 and passes through the point (4,7).
Solve the following linear systems by graphing.
y 5
31.
x  2
32.
1
x5
2
y  3x  5
y
Solve the following
linear systems using the SUBSTITUTION method.
x  5y
33.
2 x  3 y  13
5 x  8 y  17
3x  5  y
Use the LINEAR COMBINATION method to solve the following linear systems.
35.
2 x  3 y  7
3x  y  5
Graph the following linear inequality.
y  2x  3
37.
36.
38.
4 x  3 y  31
y  2x  7
3x  y  7
34.
Graph the following systems of linear inequalities.
2x  y  4
39.
3 x  y  3
y  4
Use the method of your choice to solve the linear system and tell how many solutions the system has.
40.
6 x  6 y  12
2 x  2 y   4
41.
2x  y  7
4 x  2 y  10
Solve the inequality and graph its solution.
42.
x  7  11 ______________
43.
4x  12 ________
44.
x
 6 __________
3
45.
7  4x  13 _______
46.
2x  3  6x 1________
47.
6 x  3  3( x  2) __________
48.
3x-2  7 x 10 ________
49.
15  5x  20 _________
50.
3  4x  5  7 _________
51.
8x 11  5 or 4x  7  13 _____________
Solve the following absolute value equations.
52.
53.
2 x  6  20
x  6  8  10
Solve and graph the following inequalities:
54.
x  8  12
55.
x  7  28
Is each ordered pair a solution to the inequality?
x  24
56.
(33, 2) ___________
(1,7) ___________
y  2x  5
57.
(6,3) _____________
(3, 8) ____________
Find the Mean, Median and Mode of the collection of numbers.
58.
99,100,110,35,75, 24,88,95
Mean: ______________________
Median: _____________________
Mode: ______________________
59.
7,8,8,3, 2, 2,1,7,9,10,11
Mean: ______________________
Median: _____________________
Mode: ______________________
Add or subtract the following.
60.
( x 2  4 x  1)  (5 x 2  2)
61.
(5x 2  9 x  1)  (8x  13)
62.
(7 x3  2 x 2  x  4)  (4 x3  3x 2  8)
63.
( x 4  6 x 2  7)  (2 x 4  3x 2  1)
Find the product.
64.
( x  3)(2 x  3)
65.
(9 x  1)(7 x  4)
66.
(5x3  2)(4 x 2  8x  7)
67.
( x  12)2
68.
(7 x  2)2
69.
(8 x  3)(8 x  3)
Solve the equation using the zero-product property.
70.
(6 x  5)( x  2)  0
71.
( x  8)2  0
Factor the following trinomials.
72.
x 2  x  12
73.
x2  4 x  4
74.
x 2  10 x  21
75.
x 2  8 x  12
76.
x 2  10 x  16
77.
x 2  4 x  21
Solve the equation by factoring. (Solving for x.)
78.
x2  5x  6  0
80.
x 2  x  12  0
79.
81.
x 2  12 x  13  0
x 2  2 x  35  0
82. Fill in the table below.
Polynomial
2 x 2  3x
2  x3  9 x 4
x3
8
Degree
Classification by
Degree
Classification By Number
of Terms
Leading
Coefficient
2 x  1  3x 2  3x3  4 x 4
Simplify the expression. The simplified expression should have no negative exponents.
83.
x3  x 4
84.
a0  a4
85.
b 2  b 5
86.
5y 4
87.
( x3 )7
88.
(a 2 )3
89.
n3
n5
90.
(2b)3 (b4 )
91.
(mn)2  n4
92.
3a 5  5a 2  a 3
93.
 x3   y 
 4  
 xy   x 
94.
a 1b 2 a 2b3

ab b 2
96.
4 3
98.
5
 
2
5
Evaluate the expression.
95.
5 4  5 1
97.
 425ab
99.
3  35
34
1
xy

2 0
2
100. Write the number in decimal form.
4.27 105 _________________________________
6.283 109 _______________________________
4.56 1010 ________________________________
.
5 1012
_________________________________
101. Write the number in scientific notation.
9,875,000 _______________________________
0.00125
_______________________________
6,557,000,000 ___________________________
.
0.0000000317 ____________________________
102. Evaluate the expression. Write the result in scientific notation and decimal form.
(4 102 )(3 106 )
Scientific Notation: ________________________
Decimal Form: ___________________________
.
1.8 10 4
6  102
Scientific Notation: ________________________
Decimal Form: ___________________________Evaluate the expressions.
Simplify the expression.
103.
12
 ____________
25
104.
9
 _____________
16
105.
288  _____________
106.
5  30  _____________