Algebra Final Exam Review
How to use this study guide: Complete all Practice problems in this packet. Check with the
answer key. If you need more work on a topic, see the Extra practice sections and select odd
numbered problems. Check answers at the end of the Selected Answers section of your book.
Solving Equations (Chapter 3; sections 3.3-3.5):
Important skills: Solve multi-step linear equations, equations with variables on both sides, and proportions.
Extra practice: pg. 940, sections 3.3-3.5
Practice problems:
1)
Solve
x  1 3x  6

4
7
2)
Solve
27  3x  3  6  2 x 
Graphing Linear Equations and Functions (Chapter 4; sections 4.1-4.7):
Important skills: Identify solutions of linear equations and write equations of horizontal and vertical lines,
Calculate the x and y intercepts for a linear equation, calculate slope by using the slope formula, graph using
slope and y-intercept, evaluate a function with f(x) notation
Extra practice: pg. 941 sections 4.2-4.7
Practice Problems:
3)
What is the slope of the line that passes through the points
 2, 4 and  3, 7  ?
through the points (-3,6)
and (-3,2)?
4)
What are the x and y intercepts of these equations? 5 x  4 y  12 and 3x  2 y  12 ?
5)
Which of these equations represent direct variation? A) 2 x  3 y
6)
What is the constant of variation in the equation 5 x  3 y  0 ?
7)
How do you recognize the graph of a direct variation equation?
8)
What is the value of
B) 12 x  3  4 y
5
f  3 if f  x    x  4 ?
2
Writing Linear Equations (Chapter 5; sections 5.1-5.7):
Important Skills: Write the equation of a line: slope intercept form, point slope form, and standard form (“A” is
an integer!); write equations of parallel and perpendicular lines, write an equation for a line of best fit for a set
of points
Extra practice: pg. 942 sections 5.1-5.7
Practice Problems:
9)
Write the equation of the line that passes through the points
 2, 1 and  7, 4
a. in Point-Slope form
b. in Slope-Intercept form
c. in Standard form
10)
Write the equations of the vertical and horizontal lines that pass through the point
11)
How do you recognize the equations of parallel lines?
12)
How do you recognize the equations of perpendicular lines?
 6, 2
?
13)
On page 296, do problems # 11, 13, 17 and 19.
14)
Write the equation of the line through (2, 4) that is parallel to 3 x  y  12 .
15)
Write the equation of the line through (0, 1) that is perpendicular to
16)
On page 329, do problem #8.
3
x y 2.
4
Solving and Graphing Linear Inequalities (Chapter 6; sections 6.4 - 6.7):
Important skills: Find solutions to linear inequalities with two variables, graph linear inequalities with two
variables, solve compound inequalities
Extra practice: pg. 943, sections 6.4-6.7
Practice problems:
17)
Graph the linear inequality x  2 y  6
18)
Graph the linear inequality
1
x y 3
2
#17-18 Use graph paper and
don’t forget to shade!
19)
Solve
6  3n  9  21
20)
Solve
16   x  6 or 2x  5  11
#19-20 Graph your solutions on a number line.
Systems of Equations and Inequalities (Chapter 7; sections 7.1-7.6):
Important skills: Solve systems of linear equations: graphing, substitution, elimination (add/subtract) and write
a system of linear equations to represent a word problem
Extra practice: pg. 944, sections 7.1-7.6
Practice problems:
21)
A linear system can have 0, 1, or infinitely many solutions. How do you determine the number of solutions
to a system without actually solving?
22)
Solve these systems by any method of your choosing (graphing, substitution, or elimination):
a)
23)
b)
x  y  5
2 y  x  4
y  x  5
c)
x  2y  7
x  2 y  7
Which ordered pair is a solution to the system x  y  2 and 7 x  4 y  8 ?
a)
24)
x  2 y  13
( 2, 0)
b) (0, 2)
On page 440, do problem #31.
c) (2, 0)
d) (0, 2)
Exponents (Chapter 8; sections 8.1-8.4)
Important skills: apply all exponent rules to simplify an expression
Extra practice: pg. 945, sections 8.1-8.4
Practice problems:
25)
Simplify
10x 4 y 6
26)
Simplify
(5 x 2 y)3
5 2 3
27)
Simplify (2d
28)
Simplify 10b c
e )
29)
5 x3 y 4 2
Simplify (
)
2 x2 y
30)
Simplify
6a 4b5 2ab 3
( 2 2 )
ab
ab
3 5
Polynomials and Factoring (Chapter 9; sections 9.1-9.7)
Important skills: Add, subtract, and multiply polynomials, factor polynomials, use the zero product property to
solve equations in factored form
Extra practice: pg. 946, sections 9.1-9.7
Practice problems:
31)
Subtract:
32)
Add:
33)
Multiply:
36)
Factor:
12 x
12 x
2
2
 8x  6    9 x2  2 x  5
 8x  6    9 x2  2 x  5
 2 x  3
2
34)
Simplify:
35)
What are the roots of
 y  3 y  2  0
?
 2x  4 2x  4
a)
x 2  15 x  56
d)
x 2  3x  70
b)
y 2  7 y  18
e) x  4
c)
 x 2  12 x  27
f) 5 x  x  3
2
2
Quadratic Equations (Chapter 10; sections 10.3-10.6):
Important skills: Solve quadratic equations by graphing, factoring, taking square roots and using the quadratic
formula.
Extra practice: pg. 947, sections 10.3 – 10.6
b  b 2  4ac
x
2a
Practice problems:
f  x    x2  13x  36
37)
Where are the zeros on the graph of a
quadratic equation?
40)
Find the zeros of
38)
Solve 25 x  9
41)
What are the solutions of 6 x  10 x  3 x  5 ?
39)
Solve 107  5 x  18
42)
Solve 2 x  5 x  3  0
2
2
2
2
43)
Solve using the quadratic formula:
9  7 x2  2 x .
44)
On pg. 655 complete problems 7, 8, and 10.
45)
On pg. 674, complete problem 13.
Radicals (Chapter 11; sections 11.2, 11.4)
Important skills: Evaluate squares and square roots; write an expression in simple radical form; apply
Pythagorean Theorem, solve radical equations
Extra practice: pg. 948, sections 11.2, 11.4,
Practice problems:
46)
Simplify
48
50)
Solve
2 x  x4
47)
Simplify
36  2
51)
Solve
6 x  2  5  35
48)
Simplify
25 x
64
52)
On pg. 756, complete problem #29.
49)
Simplify
16
27
Chapter 12; sections 12.1, 12.3:
Important skills: Dividing polynomials; inverse variation
Extra practice: pg. 949, sections 12.1 and 12.3
Practice problems:
53)
Find the quotient:
12x
54)
Find the quotient:
(2m2  5m  12)  (2m  3) .
55)
Given that y varies inversely with
56)
On pg. 769, complete problems 3, 5, 7, 29 and 31.
4

 30 x2  72 x   6 x  ?
x , and y  12 when x  3 . What is the constant of variation ?
Statistics:
Important skills: Using the bell curve and z-score formula to interpret data.
Z-score: Z 
57)
X 

Draw and label a bell curve: If a set of data is normally distributed with a mean of 82 and a
standard deviation of 2.5, how many standard deviations away from the mean is the element 87?
58). Use the z-score formula: If the class mean on a test was 91 with a standard deviation of 2.3, what
was the test score (to the nearest integer) of a student whose z-score was -1.3 ?