Celina High School
Math Department:
Pre-AP Algebra 2
Summer Review Packet
DUE THE FIRST DAY OF
SCHOOL!
This packet will count as part of your first marking
period grade.
The problems in this packet are designed to help you review
topics from previous mathematics courses that are important
for your success in Algebra 2.
Directions: Show all of your work in order to receive full credit.
You may use your notes from previous mathematics courses to
help you. Additional copies of this packet may be obtained from
the guidance office at the high school or printed from the schools
website: www.celinaisd.com
Helpful website:
http://www.khanacademy.org/
http://www.projectsharetexas.org
Enjoy your summer. We are looking forward to meeting you! Name:
_______________________________
Algebra 2, page 1
BIG Ideas Entering Algebra 2
You should be able to:
A. Simplify and evaluate expressions using order of operations.
B. Simplify using rules of exponents.
C. Evaluate functions.
D. Solve, graph and write linear equations and inequalities.
E. Solve Systems of Equations.
F. Factor basic polynomials.
G. Solve literal equations.
H. Solve quadratic equations using the Quadratic Formula.
Algebra II, page 2
A. Evaluating Expressions
B. Simplify using Rules of Exponents
1. am × an = am+n
am
2. n = a m -n
a
3. (am )n = amn
1
4. a -n = n
a
5. a0 =1
C. Evaluating Functions
Evaluate the following functions.
 Substitute the value of x into the given function. 
 Simplify the function. 

f(x) = 6x2-8
Evaluate f(-2)=
f(-2) = 6(-2)2-8
f(-2) = 6(4)-8
f(-2) = 24-8
f(-2) = 16
Algebra 2, page 3
Evaluate f(5a)=
f(5a)=6(5a)2 - 8
f(5a) = 6(25a2) - 8
f(5a) = 150a2 – 8
D. Solving Linear Equations
1. Distribute if there are parentheses.
2. Combine like terms.
3. Isolate the variables.
4. Solve for the variable indicated.
Example:
3 1
4
- n=
4 2
5
Find a common denominator20
3 1
4
20( - n) = 20( )
4 2
5
Multiply both sides of the equation by the LCD.
15 -10n =16
Fractions are cleared from the equation. Subtract 15
from both sides.
-10n =1
Divide by -10 to isolate n.
n=-
1
10
Slopes of Lines
The slope of a non-vertical line passing through the points ( x1, y1) and ( x 2 , y 2 ) is defined
by:
The slope of a horizontal line is 0.
The slope of a vertical line is undefined.
Lines are parallel if and only if they have the exact same slope.
Lines are perpendicular if the two lines have opposite reciprocal slopes.
Writing Equations of Lines
Types of Linear Equations:
1. Slope-Intercept Form
2. Standard Form
Algebra 2, page 4
y = mx + b (m = slope, b = y-intercept)
Ax + By = C (A, B, C are integers)
Equations of Vertical and Horizontal Lines
1. The equation for a horizontal line through the point (a, b) is y = b.
2. The equation for a vertical line through the point (a, b) is x = a.
Example: Write an equation for the line passing through the points (-2, -3) and (2, 5).
Step 1: Find the slope
m=
5 - (-3) 8
= =2
2 - (-2) 4
Step 2: Choose either point and use slope intercept form to write the equation of the line.
If you chose (-2, -3):
m = 2; so y = mx+b
-3 = (2)(-2) + b
-3 = -4 + b
+4 +4
1=b
Therefore, the equation for the line is y = 2x + 1
If you chose (2, 5):
m = 2; so y = mx + b
5 = (2)(2) + b
5=4+b
-4 -4
1=b
Therefore, the equation for the line is y = 2x + 1.
Graphing Linear Equations
E. Solve Systems of Linear Equations
1. Substitution Method
2. Elimination Method
3. Graphing Method
F. Polynomials and Factoring
Key Terms: polynomial, terms, coefficients, degree, monomial, binomial, trinomial,
factor, constant. If you are not already familiar with these terms, you should look them up.
Special Products
1. ca + cb = c(a + b)
2. a2 – b2 = (a + b)(a - b)
3. a2 + 2ab + b2 = (a + b)2
4. a2 – 2ab + b2 = (a - b)2
Algebra 2, page 5
G. Geometric Formulas
Literal Equations – Solve for the indicated variable.
Sometimes you do not know values for the variable in a formula, so you cannot substitute.
To solve a formula or a literal equation for one of the variables in it, use properties of
equality.
Example:
Solve
Divide each side by 2.
Subtract l from each side.
So,
P = 2(l + w) for w.
P
= l+w
2
P
-l =w
2
w=
P
-l
2
H. Solve quadratic equations by factoring and using the Quadratic Formula.
-b ± b 2 - 4ac
Quadratic Formula: y =
2a
Algebra 2, page 6
Print pages: 7-13
Name:
________________________________
Solve each problem.
Bring this packet with you to the first day of class.
Refer to video tutorials at http://www.khanacademy.org/
3
1
Evaluate each expression if a = , b = -8, c = -2, d = 3 and e = .
4
3
2.
ae
+ d2
c
4.
a2c 3 - be 2
6.
2x 7 × 4x 9
7.
47
42
8.
(34 ) 5
9.
(x 7 ) 3
10.
5 -2
11. 60 × x 2 × x 3
12.
(2-3 ) 2
1. ab2 - c
3.
d(b - c)
de
Evaluate each expression using exponent rules.
5. 34 × 35
Algebra 2, page 7
Evaluate the function for the given value.
f (x) = 4x - 3
x2 - 4
g(x) =
x -2
h(x) = x - 4
2
f (9a) =
13. f (-4) =
14.
15. h(-7a) =
16. h(x +1) =
17. g(0) =
18. g(-6) =
Solve each equation.
19. -6x + 7 = 4
21.
5
1
7
b- b=
3
2
9
23.
-(12 - 6x) = 6(x - 2)
Algebra 2, page 8
20.
3m + 9m =10(11+ 3m) - 9(6 + 2m)
22.
5 x -6
=
6 x +1
Find the slopes.
24. Find the slope of the line that passes through the two given points.
a. (-3, 2) and (1, -6)
b. (8,-1) and (8,-3)
25. What is the slope of the line parallel to y = 4x - 7 ?
26. What is the slope of the line perpendicular to y = - 3 x + 2 ?
4
Write the equation of the line.
27. Write an equation in slope-intercept form of the line passing through the points (4, 8)
and (-3, -6).
28. Write an equation in slope-intercept form of the line passing through the points (6, -2)
and (4,-1).
29. Write an equation of the line that is:
5
a. parallel to y = - x + 5 and passes through the point(-2, 6).
6
5
b. perpendicular to y = - x + 5 and passes through the point (-2, 6).
6
30. Write an equation of a vertical line that passes through the point (3, 0).
31. Write an equation of a horizontal line that passes through (-2, 2).
Algebra 2, page 9
Graph the following equations. (Hint: Make a table of values or determine the
y- intercept & slope)
32. y = -2x -1
33. 3x + 4y =12
34.
x=3
Graph the following inequalities.
36. -2y £ 4x + 6
Algebra 2, page 10
35.
y = -4
1
2
37. -y ³ x - 4
Solve the following systems of linear equations using the substitution method.
38. x + 3y = 3
39. 2x - 3y = 3
2x - 4y = 6
-2x + y = -4
Solve the following systems of linear equations using the elimination method.
40. 5x - y = -9
41. -5x +12y = 20
2x + y = 2
x - 2y = -6
Solve the following system of linear equations by graphing.
42.
4x + y = 8
2x - 3y =18
Algebra 2, page 11
Factor completely.
43. x 2 - 64
44.
x 2 - 2x - 3
45.
x 2 + 4x - 21
46. x 2 +13x + 36
47.
3x 2 -15x +18
48.
2x 2 - 50
Solve the formula for the indicated variable.
1
5
49. A = bh, for h.
50. C = (F - 32), for F.
2
9
Algebra 2, page 12
Solve the following quadratic equations by factoring.
51.
52. x 2 - 9x + 20 = 0
x 2 - 3x -18 = 0
Solve the following quadratic equations using the Quadratic Formula.
53.
54. x 2 - 6x + 7 = 0
x 2 + 3x = 2
Algebra 2, page 13