Dear Rising Algebra I Students and Parents,

This Summer Packet has been designed to provide you with a comprehensive review of the basic

skills and concepts that you worked on In 7^^ grade math class and/orenrichment. It is intended to keepyour skill level fresh and to make us aware of whether there any areas that may require additional

instruction in the fall.

Please do not try to do this packet in one sitting. A page or two a day is sufficient to get this

sixteen page packet done and still enjoy your summer! As you work, we would appreciate ifyou used

the checklist provided (separately) to give us feedback in each skill area.

This packet will be collected and reviewed, specificallyto see how you show your work which

helps us understand your thinking process. Although an answer key Is provided, please check your work

for accuracy before you refer to the answer key as your goal is to strive for accuracy. You must show all

your work when calculations are necessary to receive credit.

Algebra I is a foundatlonal math course that Introduces you to skills and concepts that you will

be using throughout your high school and college math and science courses, and even into your line of

work as you grow up. We like to think it is a very Important class as it provides the foundation for all

future courses.

We are looking forward to supporting you as you work through the course. This is a fast paced,

rigorous course, so communication between parents, students, and teachers is essential for a positive

experience next year.

Sincerely,

Your Algebra I teacher

Dear RisingAlgebra IStudents,

As you work through the summer packet please use this separate checklist to let us know how strong

you feel in each skill area. Your feedback will help us plan our instruction as we begin the school year.

Your answers WILL NOT affect your placement in Algebra I, so please be as honest as you can about your

level of comfort with each page.

Thank you,

8 '̂' gradeAlgebra ITeachers

Easy Med Slightlydifficult

Difficult

Evaluating expressions (page 1 & 2)

Writing expressions in exponential form (page 1)

Check whether a number is a solution to an equation/inequality (page 2)

Write an algebraic equation/inequality from a given sentence (page 3)

Order numbers (page 3)

Absolute value (page 3)

Basic Integer operations (page 4 & 5)

Distributive Property (page 5)

One step equations (page 5)

Converting rational numbers from fraction/percent/decimal (page 6)

Two step equations (page 7)

Fraction operations (page 7 & 8)

Percent of a number (page 9)

Solving problems using percent (page 9)

More challenging integer operations (page 10 & 11)

Solving equations 1(page 12)

Solving equations II (page 12)

Solvingequations III (page 13)

Equations with variables on both sides (page 14)

Graphing inequalities (page 15)

Problem solving (page 16)

Evaluate the expression.

1) 12;cwhenx = 5

2) 1 -y wheny = 22

Show

your

work!

3) Write an expression for the perimeter of the figure, and thenuse it to find the perimeter.

4) 2x^ when x = 3

5) -3x-\-y when x = ~2 and y = -5

Section 1.2

Write each expressionin exponential form:

6) x*x*x*x*x*x*x 'x'x

7) z to the seventh power

8) (-4)(-m)(-m)(-m)

9) 2ix){x)

Section 1.3

Evaluate the expression.

10) 3"^ when Xis 5

11) 4xVhenA:is2

Evaluate the expression.

11) 10-30^6 + 7

12) [(9-3)^3]-7

Section 1.4

Checkwhetherthe given number is a solution to the equation.

13) 2x2 + 5 = 37, whenA: = -4

13) 7;c-3a: = 45-4jc, whenj: = 3

2.

Show

your

work!

Check whether the given number is a solution to the inequality.

- 3 >10, when x--l

Section 1.5

Write the algebraicequation or inequality for the given sentence.

15) Four less than a number, divided by six is nine.

16) Eleven more than a number is greater than or equal to twenty.

Rewrite the following numbers in order from least to greatest.

17) 0.46,-4.06,-0.45,4.6,0

10X mm^ 5'5'3 2'2'S

Evaluate each absolute value expression.

19) 1-21.51

3

Show

your

work!

Section 2.2 and 2.3

Simplify.

21) -9+ -17+ 16

23) -4-6

25) 3-9 -8

22) -11+-5+ 18

24) 8-(-2)

'i

Show

your

workl

Sections 2.5 and 2.7

Simplify.

(-8)(-2)(-6) 27) (4)(-l)(-5)

29) - 50 -r 5

Section 2.6

Use the distributive property to simplify the expression. Show your work!

30) -5(8x-6) 31)9(? + 2)

32) -7 {x + 4) 33)x(x-4)

Section 3.1 to 3.3

Solve the following equations. Show your work!

34);c = 7-13 35) x4-25=9

36);c-13 = 12 37) 6x = 96your

work!

47)' 9 5

49) Write 0.35 as a fraction in simplest form.

0.35 =

50) Write 0.42 as a percent.

0.42 =

9,

48

38) -:c = 28^ 5

40)3(x + 7) = 51

Basic Pre-algebra Skills

42) List all the factors of 24

41)-5x-lx = 12

Fill in the blank with either the < or the > symbol:

43) -4

Evaluate:

45)9 8

46) 1+15 6

Exercises: Compute and simplify.

SHOW ALL WORK.

1) 7+7=

4) 77- =

Fraction Operations

9 2

77-7=3) Ih-I

6 5

6)^-1^ 7 6

Multiply and Divide Mixed Numbers

Exercises: Compute and simplify.

SHOW ALL WORK.

4) 4.4=

Algebra I

1 42) 57..- =

2 85) 57.7-

3) 7-.^

Find Percent of a Number

Hints/Guide:

To determine the percent of a number, we must first convert the percent into a decimal bydividing by 100 (which can be short-cut by moving the decimal point in the percentage twoplaces to theleft), then multiplying thedecimal by thenumber. For example:

4.5% of240 = 4.5% • 240 = 0.045 • 240 = 10.8

Exercises: Solve for n.

SHOW ALLWORK. Usea separate sheetof paper(if needed) and stapleto this page.

1) 305%of 450 = n 2) 7.5%of42 = n

3) 15%of54 = n 4) 0.65%of320 = n

Solve Problems Using Percents

Exercises: Solve the following items.SHOW ALL WORK. Use a separate sheet of paper (if needed) and staple to this page.

1) Susie has just bought a pair of jeans for $49.95, a sweater for $24.50, and a jacket for$85.95. The sales tax is 5%. What is her total bill?

2) Jack boughta set of golf clubs for $254.00 and received a rebate of 24%. How much wasthe rebate?

3) A construction manager calculates it will cost $2,894.50 for materials for her next project.She must add in 12.5% for scrap and extras. What will be the total cost?

Algebra I

Hints/Guide:Integers I

To add integers with the same sign (both positive orboth negative), add their absolute valuesand use the same sign. To add integers ofopposite signs, find the difference of their absolutevalues and then takethesign of the larger absolute value.

To subtract integers, add its additive inverse. For example, 6-ll = 6+ -ll=-5

Exercises: Solve the following problems.

1) (-4) +(-5) =

4) (-5) +(-8) =

6) -7.24+ (-6.28)-7.3 =

Algebra I

2) -9-(-2) =

5) 14+ (-4)-8 =

7) 29.45 - 56.009 - 78.2 =

3) 6-(-9) =

your

work!

Hints/Guide:

The rules for multiplying integers are:Positive • Positive = Positive

Positive •Negative = Negative

Integers 11

Negative •Negative = PositiveNegative •Positive = Negative

The rules for dividing integers are the same as multiplying integers

Exercises: Solve the following problems.

1)-2

3)-56

5) 8--15

-3

Algebra I

2)6±£i

8

4) "4^+7

6) -3+-12.(-5)

a cu^c II

SolvingEquations 1

Exercises: Solve the following problems showing all correct algebraic steps.

1) x+8 = -13 2) t-(-9) = 4 3) -4t = -12

4) - =24 5) y-4 = -3 6) 5-x = 6

Solving Equations II

Exercises: Solve the following problems showing all correct algebraic steps.

m

1) -4t-6 =22 2) 7^+6 =-4 3) -4r+5 = -25

4) ^+(-7) =6 5) 5g-3 =-12 6) —-6

Algebra I l2-

Hints/Guide:

Solving Equations III

When solving equations that include basic mathematical operations, we must simplify themathematics first, then solve the equations. For example:

5(4-3) + 7x = 4(9-6)5(1) +7x = 4(3)

5 +7x=12

-5 -57x = 7

7 7

x=l

Check: 5 (4-3) +7 (1) = 4(9 - 6)5+7 =4(3)

12 =12

Exercises: Solve the following problems showing all correct algebraic steps.

1) 4x + 8-6 = 2(9-2) 2) --7+31 = 8(6-4)

3) 5(t-4) = 9(7-3) 4) 6t-9-3t=8(7-4)

5) 7(6-(-8)) = —+ 2

Algebra I/3

your

work!

Equations - Variables on Each Side

Hints/Guide:

As we know, the key in equation solving is to isolate the variable. In equations with variables oneach side of the equation, we must combine the variables first by adding or subtracting theamount of one variable on each side of the equation to have a variable term on one side of theequation. Then, we must undo the addition and subtraction, then multiplication and division.Remember the golden rule ofequation solving. Examples:

8x - 6 = 4x + 5 5-6t = 24 + 4t

4x - 4x + 6t + 6t

4x - 6 = 5 5 =24+lot

+ 6 +6 -24 -24

4x = 11 -19 = lot

4 4 10 10

II

7

Exercises: Solve the following problems showingall correct algebraicsteps.

1) 4r.7 = 8r+13 2) 14 + 3t = 5t-12 3) 4x + 5 = 3x-3

4) 6y + 5 = 4y-13 5) 5x-8 = 6-2x 6) 2.9m+1.7 = 3.5 +2.3m

pOA

InequalitiesHints/Guide:

In solving inequalities, the solution process is very similar to solving equalities. The goal is stillto isolate the variable, to get the letter by itself. However, the one difference between equationsand inequalities is that when solving inequalities, when we multiply or divide by a negativenumber, we must change the direction of the inequality. Also, since an inequality as manysolutions, we can represent the solution of an inequality by a set of numbers or by the numberson a number line.

So, to solve the inequality -4x < -8 becomes i4x < ;8_4 -4

and therefore x > 2 is the solution (this is because whenever we multiply or divide an inequalityby a negative number, the direction of the inequality must change) and can be represented as:

«l I I I I I I I I I I I I 0 I I I 11 I I I ^-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Exercises: Solve the following problems:

1) 4x>9

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

2) -5t>-15

*1 I I I I 1 1 I I I I I I I II I 1 I I II 1'-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

3) 1^3

<1 I I 1 I I I I I I I I I I I I I I I I I I I'-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Algebra I ^

15

Exercises: Solve each problem.SHOW ALL WORK.

Problem Solving

1) The Acme Supply Store sells a security system for $2150.00 excluding tax. They sold 12systems. If the total profit on these sales was $4824.36, how much did each system costAcme Supply? Show your work.

2) Kristen is paid $5.60 per hour. She works 6 hours on Saturday, 3 hours on Sunday, and 5

hours on Monday. On Saturdayher hourly rate in 1— times her regular rate and she is paid

twice the regular rate on Sunday. How much did she earn in all? Show all work.

3) At the beginning of the week the value of a stock was 3214. On Monday it fell onTuesday it rose I/2, on Wednesday it rose 3, on Thursday it fell 2, and on Friday it rose 214.What was the value of the stock at the end of the week? Show all work.

4) Norma is paid $4.80 per hour. She worked 3'/2 hours on Friday, 4 hours on Saturday,and 214hours on Sunday. On Saturday, her hourly rate was 1 times her regular pay and on Sunday,it was twice the regular rate. How much did she eam in all? Show all work.

5) The formula which converts Fahrenheit degrees (F) to Celsius degrees (C) is:

C=̂ (F -32). How many degrees Celsius is 113 F?

Algebra I

U