Middle School Math Review for CC Algebra 1 · Section 1: GCF & LCM Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 24 and 32. GCF LCM 2 24 32 224 32 412 16

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Name:

Summer Math Packet Middle School Math Review for CC Algebra 1

Table of Contents

Section Topic Page # 1. GCF & LCM 3 2. Rounding Numbers 4 3. Statistics (Mean, Median, Mode, Range) 5 4. Operations with Signed Numbers 6 – 7 5. Order of Operations 8 – 9 6. Evaluating Expressions 10 – 11 7. Properties of Operations 12 8. Algebraic Translations 13 – 14 9. Combining Like Terms 15

10. Fractions 16 – 17 11. Solving Basic Linear Equations 18 – 19 12. Solving Multi-Step Equations 20 13. Inequalities 21 – 23 14. Word Problems 24 – 25 15. Graphing 26 – 29 16. Linear Functions 30 – 31 17. Polynomials 32 18. Exponents 33 – 34 19. Solving Systems of Linear Equations 35 – 39

This packet is to be completed in its entirety over the summer to be best prepared for your upcoming algebra course.


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Directions/Information:

• This packet contains review problems from prior math classes and represents the types of mathematics knowledge you should master to be successful in CC Algebra 1.

• It is NOT recommended to complete this packet immediately following school dismissal in June nor the night before the packet is due. Student learning is most effective if the packet is completed during the months of July and August.

• A mastery of the material in this packet is essential to a successful first semester in CC Algebra 1.

• You should be completing the problems in this packet without a calculator. In many instances the

use of a calculator actually slows you down. Your brain can actually operate faster than your fingers can.

• You should show all your work for each problem. Use and attach additional paper if needed to

show your work.

• When you complete the entire packet you may check your answers at the end of the packet.

• If you need a little help remembering, you can consult these web sites: § www.analyzemath.com§ www.freemathhelp.com§ www.sosmath.com

• Have a great summer. See you in September.


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Section 1: GCF & LCM

Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 24 and 32.

GCF LCM

2 24 32 2 24 32 412 16 412 16 3 4 3 4 GCF = 2 4 8× = LCM = 2 4 3 4 96× × × = Exercises Find the GCF: 1. 42 60, 2. 224 42,xy xy 3. 2 2 227 45,x y x 4. 11 21,

Find the LCM:

5. 27 18, 6. 15 18,x xy

7. 2 29 15,x y xy 8. 64 48,

CommonFactors


4

Section 2: Rounding Numbers

Round odd numbered problems to the hundredths place and even numbered problems to the tenths place.


5

Section 3: Statistics (Mean, Median, Mode and Range)


6

Section 4: Operations With Signed Numbers

Simplify. Do not use a calculator for this section.


7

Simplify. Do not use a calculator for this section.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.


8

Section 5: Order of Operations

Evaluate each expression using the order of operations process (PEMDAS). Do not use a calculator.


9


10

Section 6: Evaluating Expressions

Example:

Evaluate each of the following expressions when 5x = .

Evaluate each expression (do not use a calculator) given that: 5x = , 4y = - and 6z =


11


12

Section 7: Properties of Operations

Distributive Property: ( )a b c ab ac+ = + or ( )a b c ab ac- = -

Simplify each expression using the distributive property.

Example: ( ) ( ) ( )4 5 4 4 5 4 20x x x+ = + = +

11. ( )3 9b+ 12. ( )5 2 3x - 13. ( )3 4 9x- +

14. ( )2 4x x+ 15. ( )1 4 122

r + 16. ( )6 11p- -


13

Section 8: Algebraic Translations (Translating from English to Mathematics)


14

Practice: Translate each phrase into a mathematical statement. Let n = a number.

1. Seven plus five times a number is greater than or equal to -9.

2. Eight times a number increased by 6 is 62.

3. One half of a number is equal to 14.

4. six less than 8 times a number

5. a number divided by 9

6. a number decreased by 5

7. Twice a number decreased by 15 is equal to -27.

8. Nine less than 7 times a number is -6.

9. The sum of a number and eight is less than 2.

10. Eleven increased by a number is -12.

11.

12.

13.

14.

15.


15

Section 9: Combining Like Terms


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Section 10: Fractions

Write the fractions in lowest terms.

1. 824

= 2. 1824

=

3. 215

20x yxy

= 3. 4

3 2

3645abca bc

=

Solve for x.

5. 1648 12

x= 6. 12 4

42 x=

7. 2032 16

x= 8. 6 12

9 x=

Write as improper fractions.

9. 123= 10. 64

7- =

Write as mixed numbers.

11. 94

- = 12. 383=


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18

Section 11: Solving Basic Linear Equations


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20

Section 12: Solving Multi-Step Equations

Solve and check each equation.

1. 2 7 25x- + = 2. 3 8 141x- = -

3. ( )15 2 5 11w- + = 4. 12 4 6 2r r- = +

5. ( )4 5 32n- + = - 6. 12 2 5 1x- + = -

7. 3 2 15x- = 8. 7 122x- =

9. 17 3 4 9x x+ = - 10. ( )3 6 12 36 18x x- - = -

Check:2x+3=72(2)+3=74+3=77=7Check


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Section 13: Inequalities


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7.

6.

5.

10.

9.

8.


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Solving Multi-step Inequalities

Determine and graph the solution set of each inequality.

11. 3 8 17x + > 12. 6 3 9 7y y- + > -

13. 2 7 11v + ³ 14. 7 33b

> +

15. 2 43c -

£ 16. ( )4 4 4 5 3b b+ < -

17. 2 5 21 2z z- < - - 18. ( )8 10 6 3b b- ³ -

19. 3 5 6 13x x- > + 20. ( )7 5 10 2y y+ - £


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Section 14: Word Problems

Translate each word problem into an algebraic equation, using “x” for the unknown, and solve. Process: Write a “Let x = for the unknown”; write an equation; solve the equation; substitute the value for x into the let statement to answer the question.


25

more


26

Section 15: Graphing


27


28


29


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Section 16: Linear Functions

Determine the x and y-intercept of the following linear functions.

Determine the slope 2 1

2 1

y ymx x

æ ö-=ç ÷-è ø

through the given points.

Determine the slope and y-intercept of the line with the given equation. Remember y mx b= + ?

Write an equation of the line that is parallel to the given line and passes through the given point. Remember parallel lines have the same slope but different y-intercepts.


31

Graph the equation using any method.

11. 2 3y x= -

12. 2 3 12x y- - =


32

Section 17: Polynomials


33

Section 18: Exponents


34

1.

8.7.6.

3.2.

5.

4.

12.11.10.9.

16.15.14.13.

20.19.18.17.

21. 24.23.22.


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Section 19: Solving Systems of Linear Equations

The two lines intersect in ( )3 4,- which is the solution to this system of equations.

A system of equations is two equations with two variables, usually x and y. You can’t solve each equation individually, but with 2 equations you can solve either graphically or algebraically (substitution or elimination). The solution of the system is the ORDERED PAIR that works in both equations. If you remember that each equation represents a line, you are just trying to find the ordered pair where the two lines intersect.


36


37

8.7.


38

10.9.

12.11.


39

14.13.

15. 16.


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Answers Section 1 12. 13 Section 6 8. 7 9 6n - = - 22. -45/56 1. 6 13. 15 1. 15 9. 8 2n + = 23. 1/48 2. 6xy 14. 7 2. 50 10. 11 12n+ = - 24. 27/16 3. 29x 15. -3 3. 71 11. b 4. 1 16. -12 4. 26 12. d Section 11 5. 54 17. 8 5. 0 13. e 1. 2x = 6. 90xy 18. -2 6. 24 14. a 2. 14w = 7. 245xy 19. 3 7. -14 15. c 3. 3c = - 8. 192 20. -14 8. -8 4. p = 3 21. 5 9. 17 Section 9 5. 2k = - Section 2 22. 20 10. -10 1. 11n 6. 17x = 1. 18.62 23. -2 11. 77 2. 40b 7. 15h = 2. 0.3 24. -10 12. 20 3. 41z 8. 56m = 3. 25.05 13. 21 4. 4x- 9. 15d = 4. 100.9 Section 5 14. 53 5. 9n + 10. j = 16 5. 3.92 1. 4 15. 6 6. 9 2f + 11. 8x = 6. 20.0 2. -8 16. -12 7. 3 12t + 12. 2n = 7. 36.99 3. 21 8. 6 3k- + 13. j = 3 8. 17.1 4. 6 Section 7 9. 7 4r y+ 14. 1x = - 9. 15.92 5. -8 1. Comm Prop of × 10. 4 4g h+ 15. 4x = 10. 0.7 6. 34 2. Assoc Prop of × 11. 2 2m n- + 16. 2x = 7. 25 3. Comm Prop of + 12. 14a b- + 17. 15f = Section 3 8. 1 4. Ident Prop of + 18. 42a = 1. Mean = 353.5 9. 61 5. Ident Prop of × Section 10 19. 6b = Median = 318 10. 9 6. Comm Prop of + 1. 1/3 20. 21x = Mode = None 11. -36 7. Comm Prop of + 2. 3/4 21. No

Range = 673 12. 31 8. Ident Prop of × 3. 3

4x

22. No

13. 20 9. Assoc Prop of + 4.

2

2

45ca

23. No

2. Mean = 31.66 14. -10 10. Comm Prop of × 5. 4x = 24. Yes Median = 35.5 15. -326 11. 3 27b + 6. 14x = Mode = 35.5 16. 0.5 12. 10 30x - 7. 10x = Section 12 Range = 33.2 17. 8 13. 12 27x- - 8. 18x = 1. 9x = - 18. 13 14. 22 4x x+ 9. 7/3 2. 18x = Section 4 19. 30 15. 2 6r + 10. -34/7 3. 3w = - 1. 5 20. -18 16. 6 11p- + 11. -2 ¼ 4. 1r = 2. 26 21. -2 12. 12 2/3 5. 3n = 3. -1 22. -7 Section 8 13. -5/12 6. 9x = 4. -3 23. 6 1. 7 5 9n+ ³ - 14. 5 13/18 7. 6x = - 5. -20 24. 6 2. 8 6 62n + = 15. -1/2 8. 38x = 6. 1 25. 180 3. 5 14. n = 16. 5 ½ 9. 26x = 7. -39 4. 8 6n - 17. 2 23/33 10. Infinite Solutions 8. -4 5. 9/n 18. -7 1/12 9. -6 6. 5n - 19. -1/3 10. -15 7. 2 15 27n - = - 20. 4/3 11. 9 8. 7 9 6n - = - 21. -9


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Answers Continued

11.

12.

Section 13 Section 14 1. 1x < - 1. 6 videos 2. 3x > 2. 4 days 3. 3x ³ - 3. 3 t-shirts 4. 6x £ - 4. Janet 135 pounds

Anna 115 pounds

5. 5. 1640 students

6. 6. 90 students

7. 7. $4.77

8. 8. $2.15

9. 9. $3.25 10.

10. Michael 17 hours Sarah 20 hours

11. Section 15 Answers are at the end.

12. Section 16

13. 1. Yes 2. No

14.

3. 4 3,x y= - = 4. 4 8,x y= - = -

15. 5. 1

7m =

16. 6. m is undefined 7. m = 2, y = -12

17. 8. 2 2

3,m y= =

18. 9. 2 4y x= - -

10. 23

y x=

19. 11. & 12. Next Column

20.


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Section 19

1. (3, -2)

2. (-1, -1)

3. (4, -3)

4. (2, -1)

Section 17 1. 33 4 13x x- + 2. 34 3 6y y- + 3. 28 4 3x x+ - 4. 25 7 8y y+ - 5. 33 15x x- 6. 4 224 30 12z z z- + 7. 24 2 3y y- + 8. 4 26 3 1z z- + + 9. 2 5 6x x+ + 10. 2 7 30y y+ - Section 18 1. 106 7 10. × 2. 49 213 10. -× 3. 114 10-× 4. 153 201 10. × 5. 0 0000592. 6. 11,000,000 7. 0.00000006733 8. 327

9. 9

1w

10. 3m 11. 8f

12. 6

3

hg

13. 10a 14. 3b 15. 1 16. 924r

17. 3

2

3qp

18. 54dc

19. 144g 20. 1 21. 4 89n k

22. 9

9 9

wx y

23. 43 10× 24. 36 10×

y=1/3x-3

y=-5/3x+3

y=-x-2

y=4x+3

y=1/4x-4

y=-1/2x-1

y=-1

y=-5/2x+4


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5. (2, 2)

6. No solution – the lines are parallel

7. (-5, 3) 8. No solution 9. (2, 1) 10. (1, 1) 11. (3, -5) 12. (10, 2) 13. (-3, 2) 14. (-2, 5) 15. (5, 1/2) 16. (1/2, -2)

Section 15

#s 1 – 5 6. (3, 2) 7. (-1, 4)

8. (0, 1) 9. (4, 3)

10. (-1, -1) 11. (-4, 0)

12. (-3, 1) 13. (-4, -3)

y=3x-4

y=-1/2x+3

y=-2x-2

y=-2x+2


44

14. 2y x= + 15. 2y x=

X Y 0 2 1 3 2 4

16. y x= - 17. 2 3y x= -

18. 1 12

y x= + 19. 3 12

y x= -

X Y 0 0 1 2 2 4 3 6

X Y 0 -3 1 -1 2 1 3 3

X Y -3 3 -1 1 1 -1 3 -3

X Y -2 -4 0 -1 2 2

X Y 0 1 2 2 4 3 6 4


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20. 2 13

y x= - +

X Y -3 3 0 1 3 -1

Documents

Middle School Math Review for CC Algebra 1 · Section 1: GCF & LCM Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 24 and 32. GCF LCM 2 24 32 224 32 412 16