Name: ____________________________________________________________________________________
All students enrolled in Pre-AP Algebra II at El Campo High School
Going into Pre-AP Algebra II there are certain skills that have been taught to you over the previous years that we assume you have. If you do not have these skills, you will find that you will consistently get problems incorrect next year, even though you understand the concepts. It is frustrating for students when they are tripped up by the basic algebra skills. This summer packet is intended for you to brush up and possibly relearn these topics.
We assume you have basic skills in algebra like being able to solve equations, work with algebraic expressions, and basic factoring. If not, you would not be going on to Pre-AP
Algebra II. The topics covered in the packet are skills that are used continually in Pre-AP
Algebra II.
You should have this packet complete for the first day of school. Bring the packet to class on the first day of school. This assignment will be checked for completeness , not accuracy. All problems should be done or attempted. Show work on every problem in the space provided.
Write neatly and circle final answers.
You will be assessed on the topics presented in this packet during the first week of school. You will be given an opportunity to ask some questions in class in the days prior to the assessment, but if you have significant trouble completing this packet you should contact your guidance counselor to reconsider your course placement.
Don’t fake your way through these problems. As stated, students are notoriously weak in them, even students who have achieved well prior to Pre-AP Algebra II. You should not work together with other students nor receive extensive help from a tutor.
If you have any questions regarding this packet, please email dhamman@ecisd.org
. Have a good summer and see you in the fall.

Below are listed topics in the review. You can certainly do Google searches for any of these topics. But we have given you several sites that will cover pretty much all of these topics.
Here are good sites for most algebra topics: http://www.purplemath.com/modules/index.htm
http://www.sosmath.com
http://www.freemathhelp.com
Beginning Algebra topics
Exponents
Negative and fractional exponents
Intermediate Algebra topics
Domain
Solving inequalities: absolute value
Solving inequalities: quadratic
Special Factoring formulas
Function transformation
Factor theorem ( p over q method)
Even and odd functions
Solving quadratic equations and quadratic formula
Advanced Algebra topics
Asymptotes
Complex fractions
Composition of functions
Solving Rational (fractional) equations

Use the following formulas:
Distance Formula: d

 x
2
 x
1
  y
2
 y
1

2
Midpoint Formula: ( x , y )


 x
1
 x
2 ,
2 y
1
 y
2
2


Slope Formula: m
 y
2 x
2
 y
1
 x
1
Quadratic Formula: x

 b
 b
2 
4 ac
2 a
Standard form of a line: A x + B y = C
Quadratic Standard form: A x 2 + B x + C = 0
Slope Intercept form:
Point-slope form: y = m 𝑦 − 𝑦 x
1
+ b
= 𝑚(𝑥 − 𝑥
1
)
Pythagorean Theorem: a
2  b
2  c
2
Applications involving distance (d), speed/rate (r), and time (t). d
 rt

PATTERNS
1.
This table contains data that was gathered by Mrs. Baron's geometry students. They cut squares out of grid paper. The length, l , of the sides of the squares varied from student to student. They counted the number of grids in each square they cut out to determine the area, A , of the square.
Write an equation that best fits the table.
Length of side
( l )
8
10
7
5
9
Enclosed Area
( A )
64
100
49
25
81
2.
Ross used identical square tiles to design the four figures shown below.
Figure 1 Figure 2 Figure 3 Figure 4
Write an expression that can be used to determine the number of square tiles used in each figure if n represents the number assigned to the figure?

3.
The first four terms of a pattern involving algebraic expressions is shown below. What would be the 6 th term of this pattern?
2 3 4 x x x x
5
, , , ,....
4 8 16 32
INDEPENDENT and DEPENDENT
4.
Erin received a statement from her bank listing the balance in her savings account for the past four years.
Year Balance
0 $2000
1 $2140
What is the dependent quantity in this table?
2 $2290
3 $2450
4 $2622
5.
To find c , the total cost of an order of DVDs from a certain website, the equation c = 19.99
n + 4.99 can be used, where n represents the number of DVDs ordered. If c is a function of n, identify the independent and dependent quantities.
ATTRIBUTES OF FUNCTIONS
6.
State whether the following graphs are functions or not.

7.
What is the equation of the linear parent function?
8.
What is the equation of the quadratic parent function?
9.
Identify what type of function each of the following equations is. 𝐲 = 𝟑𝐱 𝟐 − 𝟑 𝐲 =
𝟑
− 𝟑 𝐱
𝐲 = 𝟑𝐱 − 𝟑
10.
State the domain and range of the quadratic function 𝑓(𝑥) = 4 − 𝑥 2
.
11.
Identify the domain and range represented by the function graphed below. 𝐲 = 𝟑 𝐱 − 𝟑

12.
For the relation below, determine the domain and range, if it is a function or not, and if it is discrete or continuous.
17.

2 x 2
SIMPLIFICATION
Simplify by using the distributive property and combining all like terms. Simplify as much as possible.
13.
3 m
 n

2 m


2 n ( 2 m

3 n )
14.

2 a

5
 
4 a

6
 
7

2 a

15.
3 a
2
4

2 ab
3
 ab
 a
2
16.

3


7
4 a

1
6

5
2 a
2

5 x

7
 
3 x 3  x 2 
2

18.

4 x 2 
3 x

7
 
2 x 2 
4 x


FUNCTION NOTATION
19. Given that y is a function of x , express y = 2 x + 3, using function notation.
20. A certain function is represented by 𝑓(𝑥) = −4𝑥 2 − 3𝑥 + 2 . What is the value of 𝑓(−2) ?
21. Tyler’s phone company charges $2.50 for monthly phone service plus $.30 per minute, m . The function that represents the total cost is c(m) = 2.50 + .30
m . What does the function notation c(105) = 34 mean?
LAWS OF EXPONENTS
Simplify by using the laws of exponents. Simplify as much as possible.
2
1
22.
 
2
23.
2
24.
3
5
0
25. y
3  y
4  y 26.
 x
4
3 y
2

2
27.
8 x
5 y
3
2 xy
4
28.


4 a
2 x


5 a
3 x
4

29.

16 a
3 b
2 x
4 y

48 a
4 bxy
3
30.


3 x
3 y

2
( 4 x )
3

WORKING WITH RADICALS
Simplify these radicals. Do not give decimal answers. Leave answers in simplest radical form. Rationalize the denominator when necessary.
32. 24 33. 108 31. 144
34.
 
2
8 35.
 
2
2 5 36.
2
6
37.
3
2
3
38. 4 27

8 48
BINOMIAL (& more) MULTIPLICATION
Find each product. Simplify result as much as possible.
40.
 x

5
 x

4

41.

4 n

3

3 n

4

43.

2 x

9 y

3 x
 y

44. 8


7

1

7

39. 7 6

24
42.
 a

4
  a
2 
5 a

7

45.

2 x
 y

2

EQUATIONS and MORE
46. What is the slope of the line graphed?
47. Write an equation that describes a line with a slope of −
2
3 and a y-intercept of 5?
48. Identify the slope and the equation of the line that passes through (2, −4) and (3, −1).
2
49. The original function 𝑦 = 𝑥 + 4 is graphed on the same grid as the new function 𝑦 = −
5 conclusions can you make about the two functions?
5
2 𝑥 + 4 . What

50. The graph of the line containing the points (1, -2) and (-3, 6) is shown below.
C
If the slope of this line is doubled and the y -intercept is decreased by 2, which graph below shows what the line looks like after these changes are made?
A B
D

SOLVING EQUATIONS
Solve these linear equations. Do not give decimal answers. Leave answers as simplified fractions.
51. 5 a

2 a

6

4 a

5 52. x

5

1
3

6 x

5

53.
8

5 r
6
55. y

4 y

1

3

4
3
54.

4 a

1

10 a

3
8
Solve these equations for the indicated variable.
56. Solve for y . 4 x

2 y
 z 57. Solve for k .
8 a b
3 k

4 a
58. Solve for m . 2 m
 
3 59. Solve for all possible values of x . x

5

4

COORDINATE PLANE & GRAPHING
Graph the linear equations or inequalities
60. y
 
3 x

2 61. 3 x

2 y

10 62. y

2
Determine if these lines are parallel, perpendicular, or neither.
58. y

2 x

6 and 3 x

6 y

4 59. 4 y

10 x

3 and 5 x
  y
63. x = -5 64. y = 2 x – 6 and 3 x – 6 y = 4 65. 4 y – 10 x = 3 and 5 x = 7 + 2 y

66. 𝑦 ≥ −
2
3 𝑥 − 4 67. 2𝑥 − 4𝑦 > 8 68.
2𝑥 − 3𝑦 > 6 𝑎𝑛𝑑 𝑥 + 2𝑦 > 6
69. In the graph below, the axes and the origin are not shown. If the scale of the axes is 1 unit per box and point P has coordinates (4, 2), what are the coordinates of point Q ?
P
Q
70. Find the coordinates of the midpoint of segment AB if A (6, 0) and B (-4, 1).
71. The midpoint of segment is
3
5
. If C coordinates of D .
16
3
,

2
CD
find the

72. Find the length of and R (5,2).
PR if P (8, -2) 73. If the length of EF is 4 2 units and
E (6, -3) and F ( x , 1). Find all possible values of x .
SYSTEMS OF LINEAR EQUATIONS
Solve the system by the indicated method. State the solution as an ordered pair.
74. The graphing method.


3 x x

 y y



6
2
75. The substitution method.

 x x


3 y y


11
1
76. The elimination (linear combination) method.

9
6 x x


7
5 y y


9
15

77. Mrs. Couvillion wrote this system of equations on the board:
3 x + y = –6
6 x + 2 y = –12
She asked the class to predict the number of solutions there would be to the system. What is your prediction?
78. Kaycie’s company pays $20,000 per year plus a 5% sales commission. Kristen’s company pays $32,000 per year plus a 1% sales commission.
A. What system of equations can be used to determine the amount Kaycie and Kristen must sell, s , to receive the same pay, p ?
B. How much must Kaycie and Kristen sell to receive the same pay? How much will they get paid?
PYTHAGOREAN THEOREM
Use the Pythagorean Theorem to solve for the value of x in each right triangle.
79. 80. x
10
8
2 13 x
2 3

QUADRATICS
81. How does the graph of 𝑓(𝑥) = 3𝑥 2 + 1 differ from the graph of 𝑔(𝑥) = 𝑥 2 − 2 ?
FACTORING
Factor completely by using an appropriate factoring method.
82. 5 a
2 b
2 c

15 abc
2
83. x
2 
7 x

6

5 x

6 86. 16 m
2 
1 85. 6 x
2
84. 2 r
2 
3 r

20
87. The function f ( x ) = x
2
+ 3 x – 4 is graphed below. What are the zeros of the function?

88. What is the solution set for the equation 4 x
2
– 8 x + 3 = 0?
APPLICATIONS
Solve each problem. Show all work and any diagram necessary.
89. The length of a rectangle is 3 feet less than twice the width. If the area of the rectangle is 54 ft 2 , find the dimensions of the rectangle. Solve by using a solving a quadratic equation.
90. A rectangular field is twice as long as it is wide. A golf cart traveling at 12 miles per hour takes 7.5 minutes to travel the perimeter of the field. What is the length and width (in miles) of the field?
91. A mountain bike park has a total of 48 trails, 37.5% of which are beginner trails. The rest are divided evenly between intermediate and expert trails. How many of each kind of trail is there?

92. The perimeter P (in feet) of each of the two rectangles below is given. What are the values of c and d .
Solve by using a system of linear equations.
P = 24 ft c ft d ft
P = 42 ft
( c + 4) ft
2 d ft
93. The area of a rectangle is represented by 8𝑥 2 − 2𝑥 − 21 . If the length of the rectangle is 4 x – 7, what is the width of the rectangle?
94. The velocity of an object in a liquid can be described by the equation v = 20 – t – t
2
where v is the velocity in meters per second and t is time in seconds. At what time will v = 0?