Summer Math Review Packet

Summer Math Review Packet Viewpoint School In Preparation for Algebra I and Algebra IA DUE THE FIRST WEEK OF SCHOOL We ask that all incoming and re...
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Summer Math Review Packet Viewpoint School

In Preparation for Algebra I and Algebra IA

DUE THE FIRST WEEK OF SCHOOL

We ask that all incoming and returning students who are enrolled in Algebra I or Algebra IA to complete the enclosed Math Review Packet. The problems are designed to help you review topics from previous mathematics courses that are important to your success in Algebra. Please try to do each problem and show the work that goes with that answer. Bring the completed packet with you to your Algebra class on the first week of school. This packet will count as part of your first quarter Algebra grade. If you have any questions, please email Mrs. Heather Meriwether, Department Chair, at [email protected]

Practice 1 – Order of Operations Objective: To evaluate expressions using the order of operations. Example: Simplify 9  3  4  7  20  5

3  4  7  20  5

Divide 9 by 3.

3  28  20  5

Multiply 4 and 7.

3  28  4

Divide 20 by 5.

31  4

Add 3 and 28.

27

Subtract 4 from 31.

Find the value of each expression. Show ALL work. 1.

4 16  8  0  5

2.

8  (16  6)  2

3.

16  39  2(5  3)

4.

8(3  4)  2  8  (5  3)

5.

30 3(5  3)

6.

(102  4  8)  (8  9)

Insert parentheses to make the following equations true:

7.

8  12  4  5  1

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8. 2

14  2  5  3  4

Practice 2 – Using Variables Objective: To model relationships with variables. Examples: Write an algebraic expression for each phrase. seven more than n

n7

“More than” indicates addition

the difference of n and 7

n7

“Difference” indicates subtraction

the product of seven and n

7n

“Product” indicates multiplication

the quotient of n and seven

n 7

“Quotient” indicates division

Write the algebraic expression for each phrase. 1.

the quotient of 4.2 and c

4.

the product of c and 15

2.

t minus 15

5.

6 more than 5 times n

3.

4 more than p

6.

7 minus the product of v and 3

Define variables and write an equation to model each situation. 7.

The total cost is the number of cans times $.70.

8.

You have $20. Then you buy a bouquet. How much money do you have left?

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Practice 3 – Adding and Subtracting Integers Objective: To add and subtract real numbers. Examples: Adding Integers with the Same Sign  Add their absolute values. Give the sum the same sign as the integers. -3 + -4 = -7

Add |-3| and |-4|. Both numbers are negative so the sum is negative.

Adding Integers with Different Signs  Subtract their absolute values. Give the result the same sign as the integer with the greater absolute value. -5 + 4 = -1

Subtract |4| from |-5|. The sum is negative because |-5|>|4|

Subtracting Integers  To subtract an integer, add its additive inverse. 9 – 17 = -8

To subtract 17, add -17.

Simplify each expression. 1.

-7 + (-4)

2.

6 + (-3)

3.

-3 + (-5)

4.

-36 + 19

5.

-19 + (-11)

6.

9 – 16

7.

7 – (-4)

8.

-8.7 + (-10.3)

9.

-2.3 + 4.5

10.

-14 – 4

11.

8 – (-6)

12.

-10 – (-6)

13.

2.4 + (-8.7) + 3.6

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14. 4

|-2| + (-4) + 10

Practice 4 – Multiplying and Dividing Integers Objective: To multiply and divide real numbers. Examples: -9(-4) = 36

The product of two positive or two negative numbers is positive.

5(-2) = -10

The product of a positive number and a negative number, or a negative number and a positive number, is negative.

6÷3=2

The quotient of two positive numbers or two negative numbers is positive.

-14 ÷ 2 = -7

The quotient of a positive number and a negative number, or a negative number and a positive number, is negative.

Simplify each expression. 1.

3(-5)

2.

-8(-4)

3.

18 3

4.

-121 ÷ 11

5.

-5³

6.

2 4   3 5

7.

-7.2(-3.1)

8.

-39 ÷ (-3)

9.

 5 9    18 

10.

(-6)(-2)(-5)

11.

(-2)(5)(-3)

12.

3  14 2

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Practice 5 – Evaluating Expressions Objective: To evaluate an algebraic expression. Example: Evaluate the expression c  b  23 if c  25 and b  16 Solution:

25+16-23

Substitute the given values for the variables.

=41-23

Simplify by adding 25 and 16.

=18

Subtract 23 from 41.

Evaluate each expression if x=2 and y = -3. Show ALL work. 1.

2x  y

3 y  (2  x)

2.

(7  x)( y  1)

3.

Evaluate each expression if r=6 and t = 8. Show ALL work.

4.

(r  4)  2t

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5.

10  (r  3)  2t

6

6.

3  (t  1)  r

Practice

6 – Combining Like Terms

Objective: To simplify an algebraic expression by combining like terms. Example: Simplify the expression 10 x  7  9  x Solution:

10 x  x  7  9

Rewrite the expression so that the like terms are together.

9x  2

Combine like terms (10x and –x and 7 and -9)

Simplify each expression. Show ALL work. 1.

10 x  7  3x

2.

14  9 x  6

3.

3 y  9 y  12

4.

11n  2  5  3n

5.

3x  8 y  7 x

6.

18g  7h  4 g  9h

7.

3t  t

8.

3x 2  5 x 2

9.

7q  8 pq  4 pq  9q

Write an equation to model the situation. Then solve. 10.

Tyler can do x number of pull-ups. Ryan can do 5 more pull-ups than Tyler. They can do 85 pullups in all. How many pull-ups can Ryan?

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Practice 7 – Distributive Property Objective: To simplify an algebraic expression by using the distributive property. Example: Simplify the expression 2(5x  3)

2(5x  3)  2(5x)  2(3)

Use the Distributive Property.

 10 x  6

1.

7( x  4)

2.

Simplify.

2(n  9)

3( x  5)

3.

4.

7(1  4 x)

5.

(3 y  7)(6)

6.

2 (6 x  9) 3

7.

(w  3)

8.

2( x  2 y 11)

9.

4.5(b  3)

10. A planter weighs 2 pounds and holds 3 pounds of soil. Write two equivalent expressions for the total weight of nine planters. Then find the weight.

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Practice 8 – Solving One-Step Equations Objective: To solve equations using inverse operations. Example:

Check: x – 3 = -8

Solve for x.

-5 – 3 = -8

x  3  8

-8 = -8

Add 3 to each side to get the variable alone on one side of the equal sign.

+3 +3 x  5

Simplify.

Solve each equation. Check your answer. 1.

x  8  10

4.

4 x  48

7.

10.

x  10  24

x

4 3  7 7

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n  2  5

2.

3.

c4 9

5.

x  2 4

8.

6 x  36

9.

2 x 8 3

x  2.5  4.5

12.

2  x6 3

11.

9

6.

6 

x 3

Practice 9 – Solving Two-Step Equations Objective: To solve equations using two transformations. A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order. First, undo addition/subtraction. Then, undo multiplication/division.

Example:

Solve

x  13  7 2

Add 13 to each side.

+13 +13 x  20 2  x   2  20  2  2

Multiply each side by 2.

x  40 **For some problems, it may be necessary to combine like terms before solving.

Solve each equation. Check your solution. 1.

2x  5  7

2.

5t  2  7

3.

16  2w  6

4.

4a 10  42

5.

10  5x  25

6.

x 6 8 4

7.

k  3  11 9

8.

12a 14a  8

9.

n  8  22 3

10.

16  8r  4r  4  24

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11.

10

6   x  42  2 x

Practice 10 – Solving One-Step Inequalities and Graphing Objective: To solve an inequality and graph the solution on a number line. Example: Solution:

Reminder:

Solve x  4  9 . Graph the solution.

≤,≥ use a solid line.

x49

-4 -4 x5

use an open dot.

Subtract 4 from both sides. Simplify.

Plot an open dot on 5 and shade everything greater than 5.

Solve each inequality. Graph and check your solution. 1.

x 1  6

4.

4  w  2

2.

5.

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t  3  2

7  d 3

3.

x  2  0.5

11

6.

14  7x

Practice 11 – Solving Proportions Objective: To solve a proportion using cross-multiplication.

Example:

Solve

x 4  . 9 6

9 4  6 x

Write cross products.

36  6x

Simplify.

36 6 x  6 6

x6

Divide each side by 6. Simplify.

Solve each proportion by using cross products. 1.

x 4  9 12

2.

5 9  x 27

3.

6.

4.

4 m  6 9

5.

r 5  9 20

7.

8 12  d 30

8.

9.1 1.3  14.7 p

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9.

2 n  8 20

1 x  10 12

1 2x  3 18

Practice 12 – Graphing Points on the Coordinate Plane Objective: To plot points on a coordinate plane.

Example: Plot the points A (-1,5) and B (2,-3) on the coordinate plane. Label the points using their coordinates.

Points can located on the plane using an ordered pair (x,y).

A (-1,5)

(x-coordinate, y-coordinate) left or right, (-) B (2,-3)

up or down

(+)

(+)

(-)

For (-1, 5) you must travel LEFT 1 and UP 5. For (2,-3) you must travel RIGHT 2 and Down 3.

Plot the points on the coordinate plane and label them.

Name the ordered pair where each point is located.

1. 2. 3. 4.

5. 6. 7. 8.

A (4,5) B (-3,-2) C (0,-4) D (1,-5)

E F G H H E F

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Algebra I/IA Summer Packet - Answer Key Practice 1 – Order of Operations 1. 72 2. 13 3. 1 4. 48 5. 5 6. 4 7. 8 + 12 ÷ ( 4 · 5 ) = 1 8. 14 – (2 + 5) – 3 = 4 Practice 2 – Using Variables 1. 2. 3. 4. 5. 6.

4.2 𝑐

𝑡 − 15 𝑝+4 15𝑐 5𝑛 + 6 3𝑣 − 7

Practice 3 – Adding and Subtracting Integers 1. -11 2. 3 3. -8 4. -17 5. -30 6. -7 7. 11 8. -19 9. 2.2 10. -18 11. 14 12. -4 13. -2.7 14. 8 Practice 4 – Multiplying and Dividing Integers 1. -15 2. 24 3. 6 4. -11 5. -125 8

6.

− 15

7.

22.32

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8. 9. 10. 11. 12.

13 -2.5 -60 30 5.5

Practice 5 – Evaluating Expressions 1. 7 2. -9 3. -36 4. 18 5. 24 6. 21 Practice 6 – Combining Like Terms 1. 13𝑥 + 7 2. 9𝑥 + 8 3. −6𝑦 + 12 4. −8𝑛 + 7 5. 4𝑥 − 84 6. −22𝑔 − 2ℎ 7. 2𝑡 8. 8𝑥 2 9. −2𝑞 + 4𝑝𝑞 10. 45 push-ups Practice 7 – Distributive Property 1. 7𝑥 − 28 2. −2𝑛 + 18 3. −3𝑥 − 15 4. −7 − 28𝑥 5. 18𝑦 − 42 6. 4𝑥 + 6 7. −𝑤 + 3 8. −2𝑥 + 4𝑦 − 22 9. −4.5𝑏 + 13.5 10. 45 pounds Practice 8 – Solving One-Step Equations 1. 𝑥 = −2 2. 𝑛 = −3 3. 𝑐 = 13 4. 𝑥 = 12

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5. 6. 7. 8. 9. 10. 11. 12.

𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥

= −8 = −18 = 34 =6 = 12 =1 =2 = −9

Practice 9 – Solving Two-Step Equations 1. 𝑥=6 2. 𝑡=1 3. 𝑤=5 4. 𝑎 = 13 5. 𝑥 = −3 6. 𝑥=8 7. 𝑘 = −72 8. 𝑎 = −4 9. 𝑛 = −42 10. 𝑟=1 11. 𝑥 = 12 Practice 10 – Solving One-Step Inequalities 1. 𝑥>7 2. 𝑡 2.5 6. −2 > 𝑥 Practice 11 – Solving Proportions 1. 𝑥=3 2. 𝑥 = 15 3. 𝑛=5 4. 𝑚=6 5. 𝑟 = 2.25 6. 𝑥 = 1.2 7. 𝑑 = −20 8. 𝑝 = 2.1 9. 𝑥=3

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Practice 12 – Graphing Points on a Coordinate Plane

Plot the points on the coordinate plane and label them.

Name the ordered pair where each point is located.

1. 2. 3. 4.

5. 6. 7. 8.

A (4,5) B (-3,-2) C (0,-4) D (1,-5)

E (3,5) F (-6,0) G (2,-5) H (-3,8) H E F

G

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