SUMMER PACKET

PREPARING FOR ALGEBRA I

Moorestown High School

Moorestown, New Jersey

This packet will be reviewed the first day of school. All work

must be shown and final solutions should be circled.

You will be tested on the concepts covered in this packet during

the 1st

week of school. The test will be NO CALCULATORS!

Student’s Name__________________________

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HIGH SCHOOL Calculator Requirements

All High School Math courses require the use of a TI-84 Plus graphing calculator. Please purchase this calculator for use in September. Many local stores carry this calculator, including Staples, Best Buy, and Walmart. This calculator can also be purchased online (hyperlinks are included above for those stores). It costs approximately $115. You should NOT use a graphing calculator to complete this packet. This packet is reviewing skills learned in previous grade levels.

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Preparing for Algebra I

The purpose of the packet is to help you review and reinforce concepts/topics that are necessary for Algebra I.

Instructions:

Complete all sections of this packet. You will show this completed packet to your

Algebra teacher the first day of school. All work must be shown and final answers should be circled.

Students must show work that supports their understanding. Students will be tested on the concepts covered in this packet during the 1st week of

school.

It may be necessary to seek assistance on some questions/concepts...that is fine!

Websites that may be of assistance:

www.mathforum.org/dr.math Use this web site if you have a math questions that

you need answered.

www.allmath.com This website will provide you with links to games, reference, general math help and resources.

www.mathforum.com This online community includes teachers, students,

researchers, parents and educators who have an interest in math and math education. The site includes Ask Dr. Math, Problems of the Week, discussion

groups and much more.

www.AAAmath.com. Customized by grade level and topic, AAA Math features

explanations of various mathematical topics, practice problems and fun, challenging games.

www.coolmath.com This fully interactive site and allows the user to sharpen basic

math skills, play games and explore new math concepts.

www.figurethis.org Created by the National Council of Teachers of Mathematics, this site helps families enjoy mathematics outside school through a series of fun

and engaging challenges.

The more math you explore the more prepared you will be in September!

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A. Simplify Expressions

Simplify each expression. Show all your work. NO Calculator!

1. -3 + 5

2. -8 – 10 3. 18 + (-6)

4. -8 + (-5)

5. 15 + (-4) 6. -8 – 5 + 10

7. 12 + (-5) – (-19)

8. -3 + 5 + 4

9. -8 + 32 + (-12)

10. (-3)(-6)

11. (-4)(-3)(-2) 12. 8(-6)

13. 17

102

14. –88 (-11) 15.

6

150

16. (-2)4

17. (-1)9(-2)3 18. –60 10

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B. Simplify Expressions

Simplify each expression by following the order of operations. Show all your STEPS. No Calculator.

1. 3 + 5(-4) – 10

2. 18 (-2 – 1) – 3 3. 2(-5) + (-3)(-4)

4. 18 – 20(-2) + 52

5. [-3 + (-10)]5 6.

103

)2(85

7. (-15 – 13) (6 – 10)

8. 4 + (-5) – 10(2) 9. 3[5 + (-5 – 8)]

10. 16 – [(4 – 2)3]

11. 15 – 5(-2) + 6 12. 15 (-3) – (-4) + 5(-2)

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C. Simplify Expressions

Simplify each expression by combining like terms. Show all your STEPS. NO Calculator.

1. 3x – 5x – 2(3x)

2. 3(-2x) + 5x(5) 3. 4x(5) – 3x

4. 3(-2x) – 5(-3x)

5. 2x(-3) + 3(-7x) 6. 10x – 3x(-2)

7. 4x + 2y + 2x – 12y

8. -1(3x) – 4x + x

9. 2x – 5x + 2x – 8

10. 3y – 7y + 2y2

11. 5x – 2y + 8x 12. 8x + 2x – 72

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D. Simplify Expressions

Simplify each expression by using the distributive property. Show all your STEPS. NO Calculator.

1. 3(x + 2)

2. 5(x – 5) 3. 3(2x – 1)

4. -2(x + 2)

5. 3(x + 12) 6. 3(2x + 7)

7. -3(2x + 3)

8. 6(2x + 5 + x)

9. -2(4 – 2x)

10. -3(3 + 2x – 4)

11. 5(2x – 1) 12. -1(x – 4)

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E. Simplify Expressions

Simplify each expression completely; remember to do the distributive property first.

1. 2(x – 3) + 2x

2. -3(x + 3) + 6 3. 3 + 3(x + 2)

4. 4 + 2(3x + 1)

5. -8(2x – 1) – 3x 6. 2x + 3(x – 4)

7. 3 – 4(x + 3)

8. 4x – 2(x + 4)

9. 2(x + 2) + 2(x – 3)

10. 3x – 4(x – 5)

11. 3(x + 2) – 2(x + 2) 12. 2x – 4(x + 1)

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F. Evaluate Expressions

Evaluate each expression when a = -2, b =4, and c = -10. Replace each variable with the assigned value and simplify using the order of

operations.

1. 2a + b

2. ab 3. ab + c

4. 3a – b

5. ac – b 6. 4a – b

7. 6a + 5b

8. a

ba

9. 5

3

c

10. 3(a + b)

11. -2 + a(b) 12. -4a – b

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G. Solve Equations

Simplify first if needed. Combine like terms using inverse operations to isolate the variable.

Show all your steps. NO Calculator.

1. 2x – 3x + 5 = 18

2. 18 – 3x + 12 = 57 3. 20 = 8x + 5 – 5x – 5

4. 15 = 7x – 3x – 2

5. 16 – 3x – 4x = 37 6.

2

3x+ 4 = 7

7. -4

5x -3= 9

8. 2(x – 3) = -20

9. -2(3x – 7) = 56

10. 1

9 33

x

11. 2(5 – 3x) + 3x = 28

12. 13x + 7(-3x – 1) = -63

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H. Problem Solving

Identify a variable, translate into an equation, and solve the equation to answer the question. You may use a calculator.

1. Five more than three times a number is 197. Find the number.

2. The two angles shown form a right angle. Write and solve an equation to find the value of x.

3. You want to purchase a new LCD TV for $699. If you have $150 saved already and you earn $25 per hour babysitting, how many hours babysitting will it take you to save enough money for the TV?

4. For his cell phone service, Hunter pays $32 a month, plus $0.75 for each minute over the allowed minutes in his plan. Hunter received a bill for $47 last month. For how many minutes did he use his phone beyond the allowed minutes?

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I. Solve & Graph Inequalities

Simplify first if needed. Combine like terms using inverse operations to isolate the variable.

Show all your steps. NO Calculator. Graph the solutions on a number line.

1. 7 – y ≤ 2

2. -5b + 9 ≥ 24

3. 4a + 7 > 37

4. -3m + 22 < 4

5. 1-5

4x ³ 6

6. 7(b – 4) > -7

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J. Problem Solving

Identify a variable, translate into an inequality, and solve the inequality to answer the question. You may use a calculator.

1. The sum of 38 and twice a number is less than 124. Find the number(s).

2. Jenna needs an average of at least 70 on her three history tests. She has already scored 85 and 60 on the first two tests. What is the minimum grade Jenna needs on her third test?

3. Fashion Statement, Inc. makes men's shirts for department stores. A store needs at

least 525 shirts. The company has 84 shirts in its stock. Find the lowest number of

shirts the company will have to make to fill the store's order.

4. An elevator has an inspection certificate stating that the maximum weight the elevator can carry is 2100 lb. Suppose each person who takes the elevator weighs 140 lb. Find the greatest number of persons the elevator can carry.

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K. Geometry

Solve. Show All Work!

1. Find the volume of a rectangular prism if x = 2.5 cm.

2. Find the area of the shaded region. Each circle has a radius of 3cm.

3. Find the area of a triangle whose base is 7.5 cm and whose height is 3.7cm. Round to the nearest tenth.

4. Find the volume of a cube whose side is 14 meters.

5. Find the circumference of a circle whose radius is 2.75 feet. Round to the nearest tenth.

6. Find the area of a square whose side

is 3

25 m.

7. Find the area of the square given a radius of 5 in.

8. Find the perimeter of a square with a

side of 9

13 in.

Area of square: 2s Area of trapezoid: 1 2

2

b bh

Perimeter: add all sides

Area of rectangle: bh Area of circle: 2r Circumference: 2 r or d

Area of parallelogram: bh Area of triangle:2

bh Volume of prism: Area of base x height

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L. Proportional Reasoning

Set up a proportion (two equal ratios) if not already done. To solve, cross multiply. You may use a calculator.

1. 5

4 36

t

2. 3

8

3

12

x

3. 1.25 3.6

144y

4. x

1.8

8.0

4.6

5. Given the scale 2 cm = 3 m, how long is the scale drawing of a basketball rim that is 16 m. tall?

6. To tie dye a shirt orange, you need 2 parts red to 5 parts yellow. How much yellow do you need if you have 13 parts red?

7. Find the unit price of a case (12 cans) of soda for $2.25.

8. Rocky left his office at 12:00 pm and by 3:00 pm he had driven 126 of the 189 miles between his office and the office of a client. If he continued driving at the same speed, at what time would he expect to arrive at the client’s office?