Download Algebra I - The Steward School

Entering all sections of Algebra I
Summer Math Packet
This packet is designed for you to review all of your algebra skills and make sure you are well
prepared for the start of Algebra or Honors Algebra I in the fall. We anticipate this packet will
take about 10 hours to complete.
Please complete each problem in order on separate paper. This assignment is due on the third
day of class in the fall. At that time a short quiz will be given with problems taken directly from
this summer assignment (including the iXL sections below). A portion of the quiz grade will be
based on the completeness of your work from this packet.
In addition to the written work, you need to complete the following iXL sections to a
score of 60%. Please note that if at any point during the summer the name of the section does
not match the numbers below, go by the section name. If iXL becomes frustrating, REACH OUT
TO A TEACHER FOR HELP! This iXL assignment is meant to help you recall graphing
transformations without having to do lots of tedious hand graphing.
From the 8th tab on iXL:
Number theory
S.3 Write variable expressions: word problems
Z.4 Add and subtract polynomials
A.6 Least common multiple
A.7 GCF and LCM: word problems
J.1 Convert between percents, fractions, and decimals
A.5 Greatest common factor
V.3 Graph inequalities on number lines
** Please show all of your work as was required of you throughout the entire school year.
Remember No Work-No Credit. We are really looking forward to the upcoming school year
and hope you are too!
Questions? Email any of us at the following:
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
Entering Algebra I Summer Review Packet
I.Writing Algebraic Expressions
In algebraic expressions, letters such as x and w are called variables. A variable is
used to represent an unspecified number or value.
Practice: Write an algebraic expression for each verbal expression.
1. Four times a number decreased by twelve
2. Three more than the product of five and a number
3. The quotient of two more than a number and eight
4. Seven less than twice a number
II. Order of Operations
To evaluate numerical expressions containing more than one operation, use the
rules for order of operations. The rules are often summarized using the expression
PEMDAS
Practice: Evaluate each expression.
1. 250  [5 (3 7  4)]
2.
52 4  5 4 2
5(4)
1
26  32
2
4.
82  (2 8)  2
3.
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5.
50  (12  3 )  (6  1)
2
6.
2
2 42  8  2
(5  2) 2
III. Evaluating Algebraic Expressions
To evaluate algebraic expressions, first replace the variables with their values. Then, use order of
operations to calculate the value of the resulting numerical expression.
Practice: Evaluate each expression.
1. 5x2 y  y when x  4 and y  24
2.
3xy  4
7x
4
3. ( z  x)2  x when x  2 and z  4
5
4.
y2  2z2
x yz
-­­2-­­
when x  2 and y  3
when x  12, y  9, and z  4
Entering Algebra I Summer Review Packet
IV. The Real Number System
The Real number system is made up of two main sub-­­groups Rational numbers and
Irrational numbers.
The set of rational numbers includes several subsets: natural numbers, whole
numbers, and integers.
Real Numbers-­­ any number that can be represented on a number-­­line.
o Rational Numbers-­­ a number that can be written as the ratio of two integers
(this includes decimals that have a definite end or repeating pattern)
3 7
• Examples: 2, 5, , 2 , 0.253, 0.3
4 8
• Integers--- positive and negative whole numbers and 0
• Examples: -5, -3, 0, 8, …

Whole Numbers --- the counting numbers from 0 to infinity
• Examples: {0, 1, 2, 3, 4, ….}

Natural Numbers --- the counting numbers from 1 to infinity
• Examples: {1, 2, 3, 4, …}
o Irrational Numbers --- Non-terminating, non-repeating decimals
(including  , and the square root of any number that is not a perfect
square.)
• Examples: 2 , 3, 20, 3.21793156...
Practice: Name all the sets of which each number belongs.
1. -4.2
2. 8
3.
25
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4.
5
3
5. -0.9
6.

12
4
V. Integers
Adding Integers with the SAME SIGNS (both numbers are positive or both numbers are
negative)
"Same Sign - Find the Sum"
Add the numbers and keep the same sign.
Example: -6 + (-2) = -8
Adding Integers with DIFFERENT SIGNS (positive + negative or negative + positive)
"Different Signs - Find the Difference"
Subtract the numbers and keep the sign of the number with the highest absolute value.
Example 1: -8 + 2 = -6
Example 2: -4 + 7 = 3
Multiplying and Dividing TWO Integers with the SAME SIGNS
The answer is always POSITIVE.
Example 1: 5  4  20
36
4
Example 2: 9
Multiplying and Dividing TWO Integers with DIFFERENT SIGNS
The answer is always NEGATIVE.
Example 1: 5 6  30
Example 2: 30  (6)  5
1.
-15 + -35
2.
-13 – (-6)
3.
32 – 68
4.
45 – (-14)
5.
-143 + 31
6.
-34 + 12 – (-9) – 10
7.
(-9)(7)
8.
48  (8)
9.
70  7
10.
12  3  4
11.
 14 
3

 15 
12.
3  7
  
4  8
-­­4-­­
Entering Algebra I Summer Review Packet
VI. Fractions
1.
5 1

8 2
2.
1
1
1 2
2
2
3.
3 7

2 9
4.
5
1
4 3
6
4
5.
3
2
7 5
4
3
6.
92
7.
3 7
4 9
8.
9.
5
7
8
10.
3
11.
6 3

11 4
12.
4 3

5 8
-­­5-­­
3
7
5 1
6 2
1 1
2
2 5
Entering Algebra I Summer Review Packet
VII. The Distributive Property
The Distributive Property states for any number a, b, and c:
1. a(b + c) = ab + ac or (b + c)a = ba + ca
2. a(b − c) = ab − ac or (b − c)a = ba − ca
Practice: Rewrite each expression using the distributive property.
1.
7( x  4)
2.
3(2 x  5)
3.
4(5x  9)
4.
1
(14  6 y )
2
5.
3(7 x2  3x  2)
6.
1
(16 x  12 y  4 z )
4
VIII.
Combining Like-­­Terms
Terms in algebra are numbers, variables or the product of numbers and variables.
In algebraic expressions terms are separated by addition (+) or subtraction (-­­)
symbols. Terms can be combined using addition and subtraction if they are like-­­
terms.
Like-­­terms have the same variables to the same power.
Example of like-­­terms: 5x 2 and −6x 2
Example of terms that are NOT like-­­terms: 9x 2 and 15x Although both
terms have the variable x, they are not being raised to the same power
To combine like-­­terms using addition and subtraction, add or subtract the
numerical factor
Example: Simplify the expression by combining like-­­terms
8x 2 + 9x −12x + 7x 2 = (8 + 7)x 2 + (9 −12)x
= 15x 2 + −3x
= 15x 2 − 3x
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Entering Algebra I Summer Review Packet
Practice: Simplify each expression
1. 5x − 9x + 2
2. 3q 2 + q − q 2
3. c 2 + 4d 2 − 7d 2
4. 5x 2 + 6x −12x 2 − 9x + 2
5. 2(3x − 4y) + 5(x + 3y)
6. 10x − 4(x + 2)
IX. Solving Equations with Variables on One-­­Side
Practice: Solve each equation.
1. 98 = b + 34
2. −14 + y = −2
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3. 8k = −64
4.
2
x=6
5
5. 14n − 8 = 34
6.
5  3n  38
7. 3k  7  16
8.
d
 12  7
5
9. 4m 15  21
10.
10  5n  85
12.
12 
14.
9 x  4  5x  8
11.
n
 8  12
3
13. 3( x  4)  15
-­­8-­­
x
 9
2
Entering Algebra I Summer Review Packet
X. Percent of Change
Practice: State whether each percent of change is a percent of increase or percent of
decrease. Then find each percent of change.
1. original: 50
new: 80
3. original: 27.5
new: 25
2. original: 14.5
new: 10
4. original 250:
new: 500
-­­9-­­
Entering Algebra I Summer Review Packet
XI.
Percent of Change (Continued)
Practice: Find the final price of each item. When a discount and sales tax are listed,
compute the discount price before computing the tax.
1. Two concert tickets: $28
Student discount: 28%
4. Celebrity calendar: $10.95
Sales tax: 7.5%
2. Airline ticket: $248.00
Frequent Flyer discount: 33%
5. Camera: $110.95
Discount: 20%
Sales tax: 5%
3. CD player: $142.00
Sales tax: 5.5%
6. Ipod: $89.00
Discount: 17%
Tax: 5%
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Entering Algebra I Summer Review Packet
XII.
Simplifying Exponents
Simplify.
1.
3.
34 32
2.
x3  x5  x 2
2m3  4m  3m4
4.
5y  6y
6.
6 xy 3
6 xy
8.
x y 
10.
 2m p 
8m5
5.
m3
1
x
7.
5x 
9.
9 x4 y 4
7 x2
-­­11­­
5
3 2
3
5 3
Entering Algebra I Summer Review Packet
XIII. Solving Word Problems
Practice: Write an algebraic equation to model each situation. Then solve the
equation and answer the question.
1. A video store charges a one-­­time membership fee of $11.75 plus $1.50 per
video rental. How many videos did Stewart rent if he spends $72.00?
2. Nick is 30 years less than 3 times Ray’s age. If the sum of their ages is 74, how old
are each of the men?
3. Three-­­fourths of the student body attended the pep-­­rally. If there were 1230
students at the pep rally, how many students are there in all?
4. Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37
hours, how long did Sarah and Michael each drive?
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Entering Algebra I Summer Review Packet
XIV.
Graphing Linear Equations
1. y = 3x + 4
3.
2x  y  5
-­­13­­
2.
y
1
x 3
2
4.
y
1
x2
4
Entering Algebra I Summer Review Packet
XV.
Finding Slope
Slope(m) 
rise
run
When given two ordered pairs ( x1 , y1 ) and ( x2 , y2 ) , use the slope formula of m 
Find the slope of the line through each pair of points.
1)
(4, 17), (-2, 13)
2) (-8, 5), (-12, -4)
3)
(-20, 8), (-16, 16)
4)
(-8, -12), (-7, -7)
5)
(3, 9), (3, 12)
6)
(10, -2), (-1, 5)
Determine the slope of the line in each graph.
7)
8)
-­­14­­
y2  y1
.
x2  x1