Cherry Creek High School Summer Assignment for students entering:

Accelerated CP Algebra 2 Please have the following worksheets completed and ready to be handed in on the first day of class, August 18, 2021. Make sure you show your work where appropriate. Answers are provided for you to check; however, you need to show work on problems that require it. Please neatly organize your work and use notebook paper when there is not enough room to show all of your work on these worksheets. It is expected that you have a good understanding of this material coming into Accelerated CP Algebra 2, as teachers will not be doing an extensive review of previously learned material. Have a great summer and we look forward to seeing you in the fall!

The CCHS Math Department

Order of Operations Worksheet #1 NAME ________________________ Period _____ Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each expression and leave your answer in simplest form. 1] 3(3 + 2) – 2(5– 1) 2] 3] 4] 5] 6] 7] 8]

9] 10]

11] 12]

13] 14]

15] 16] 1

( )27 18 6 2- - ÷

7− 4i2+ −5( )2 ( )26 3 9 5 2- - ÷

( )( )227 6 2 2- - - ( )( )28 4 2 1 3 6- + - - + ×

( )22 2 6 4 6+ - - × 3i4 − 24 ÷ 3

5i 9 − 3( )29

16 − 4i52i6+8

23( 2)7 1-+

( )( ) ( )18 4 12 3 2 1 22é ù- - - +ë û

154 −10i8+ 9 7 4 213 13 13- -

2 33 25 5- =

3 38 4+

17] 18]

19] 20]

21] 22]

23] 24]

25] 26]

ANSWERS Worksheet #1: 1] 7 2] 12 3] 24 4] 30 5] ─47 6] 46

7] ─6 8] 4 9] 20 10] 11] 12] 34 13] 83 14]

15] 16] 17] 18] 19] 20] 21] 22]

23] 24] 25] 26]

2

1 52 7+

3 38 4-

1 11 23 6+

1 27 56 3-

368æ öç ÷è ø

4 35 8•

3 5 35 9 10

æ öæ öæ ö- - -ç ÷ç ÷ç ÷è øè øè ø

1 12 23 4•

4 29 3÷

3 4110 5

÷

15

-32

113

45

98

1714

38

-132

112

94

310

110

-214

23

138

Simplifying and Evaluating Expressions Worksheet #2

Do NOT use a calculator when completing this worksheet. Show work whenever possible.

Evaluate each expression for the given value of x and/or y. 1] 2] 3] 4] 5] 6]

7] 8] 9]

Simplify each expression and leave your answer in simplest form. Also be sure your answer is in standard form.

10] 3x + 9x 11] (3x)(-5x) 12]

13] 14] 15]

16] 17] -3x + 5(-2x + 1)

18] 19] 3(x + 2y) – 4(5x – 3y + 4)

20] 21]

3

4( 7), 2x x- = 25 , 6x x x+ = 2 ( 4), 18x x x- + =

211 7 , 2y y y- = - 5 22 , 1, 4x y x y- = - = 5 (4 ), 3, 2x x y x y+ - = =

, 5, 32( )x y x yx y-

= = -+

3 14 2 , , 23

y y x yx

æ ö - = - =ç ÷è ø

2 3(3 ) 2 , 4, 3x y x y- = = -

( )3 5x x- -

2 (7 5 )x x- - ( )3 2 4 5x- - ( )4 3 2 1x- -

( ) ( )3 2 32 7 3 6y y y y y+ - + - + -

( ) 23 4 2y y y- +

220 30 105

x x+ --

2( 5) (2 5)x x- - +

Simplify each expression and leave your answer in simplest form. Also be sure your answer is in standard form.

22] 23]

24] 25]

ANSWERS: 1] -20 2] 66 3] 14 4] 58 5] -33 6] 25 7] 2 8] -40 9] 198 10] 11] 12] 13] 14] 15] 16] 17] 18] 19] 20] 21] 22] 23] 24] 25] 1

4

4 3 5x xy x y+ - - 3(5 3) (2 )x x x- - - -

1 3(6 9 ) (20 10 )3 5

x x- - - ( ) ( )1 18 4 6 92 3

x x- + -

12x 215x- 23 5x x- + 210 14x x- 8 13x- + 6 7x- +3 2 2 13y y y- + - + 13 5x- + 2 12y y- + 17 18 16x y- + - 24 6 2x x- - +

15- 3 3 5x xy y+ - 13 7x- + 3 10x -

Solving Linear Equations Worksheet #3 Solve the following equations for x. You must show all algebraic steps. Please also include a CHECK of your solution. Do not use a calculator when completing the worksheet. 1] 2] 3]

4] 5] 6]

7] 8] 9]

10] 11] 12]

13] 14] 15]

5

5 11 24x - = 17 3 23x- = 3 8 5 22x x- = +

18 3( 5)y y- - = - 7 (12 ) 228x x- + =2 7 213x - =

3 10 54 3 2

xx - = +59(3 2) 32

x x- = + 14 (6 4) 3 5( 1) 1x x x x- + = + - +

6.2 11.8 3.8( 1)x x+ = +1 2 3( 5) 22 5 4x x x- + = - 4 2( 11) 3( 4) 6x x- - = + -

( )1 4 x 10 2x4

- = +1 4x 7 x5 5

= -1 1x 12 x4 4

-+ =

Solve the following equations for x. You must show all algebraic steps. Please also include a CHECK of your solution. Do not use a calculator when completing the worksheet.

13] 14] 15]

16] 17] 18]

19] 20] 21]

22] 23] 24]

ANSWERS: 1) 7 2) -2 3) -15 4) 5) 40 6) 42 7) 8) 9) (all real numbers)

10) 11) 12) 4 13) -4 14) 7 15)-24 16) No Solution 17) 7 18) -8 19) -5

20) 37 21) 22) 23) (no solution) 24) 100

6

( )1 4 x 10 2x4

- = +1 4x 7 x5 5

= -1 1x 12 x4 4

-+ =

1 1x 8 14 x2 2

- = + ( )2 3x 18 5x 93

+ = - ( ) ( )32 x 1 10 5x5

- = +

16 21 3( 5)x x- + = - + 3 (15 ) 59n n- + =6 5 3 14t t-= +

1 4 32 5 10b b+ = - 2( 2 3 4) 4( 3)p p p p- + - = -

3 6 814x + =

34

-1003

67

Â

103

-6533

Æ

217

115

Æ

Linear Functions Worksheet #4 You should NOT use a calculator to complete this worksheet. Please DO use a straightedge when graphing. Find the slope of the line passing through the given points. Include your work.

1] 2] 3] Graph the functions.

4] 6] 7]

8] 9] 10]

7

( ) ( )2,5 , 8,1- - ( ) ( )1, 4 , 2,2- - ( ) ( )3,8 , 3,4- -

2 3y x= - y x= - y = 32x + 4

4y = 4x = - 2 4 8x y+ =

Graph the functions. 10] 11] 12]

Graph the inequalities. 13] 14] 15]

16] 17] 18]

8

2 4x y- = - 1y x= - - 3 4 12x y- + =

4y £ - 1y x£ - - 3x < -

23

y x³ - 4 2 12x y- > 3 5 15x y- + £

ANSWERS:

1] 2] 3] slope is undefined

4] 6] 7]

8] 9] 10]

10] 11] 12]

9

23

m = 2m =

2 3y x= - y x= -3 42

y x= +

4y = 4x = - 2 4 8x y+ =

2 4x y- = - 1y x= - - 3 4 12x y- + =

Graph the inequalities. 13] 14] 15]

16] 17] 18]

10

4y £ - 1y x£ - - 3x < -

23

y x³ - 4 2 12x y- > 3 5 15x y- + £

Systems of Equations Worksheet #5 You should NOT use a calculator to complete this worksheet. Please DO use a straightedge when graphing. Solve each system of equations by graphing.

4] 6] 7]

Solve the following systems of equations using the substitution method or the elimination (linear combination) method. Remember to write your solution as an ordered pair. CHECK your solution in both original equations.

4] 5]

6] 7]

11

31 62

y x

y x

= +ìïí

= - +ïî

4 3 124 43

x y

y x

+ =ìïí

= - +ïî

4 2 122 6

x yy x- =ì

í = +î

y x 43x y 16= +ì

í + =î

3x y 1x y 7+ =ì

í - =î

3x 5y 172x 3y 11+ =ì

í + =î

6x 7y 125x 4y 10

- =ìí - =î

Solve the following systems of equations using the substitution method or the elimination (linear combination) method. Remember to write your solution as an ordered pair. CHECK your solution in both original equations.

8] 9]

10] 11]

12] 13]

ANSWERS: 1] 2] infinitely many solutions 3] no solution 4] 5] 6] 7] 8] 9] no solution 10] 11] infinitely many solutions

12] 13]

12

4x 3 y 10 298x 5y 2x 50

- + - =ìí - - =î

8x 4y 44x 2y 3- =ì

í - = -î

7x 10y 133x 2y 7

+ = -ìí - =î

6x 2y 123x y 6

- =ìí - =î

2x 9y 395x y 20

+ =ìí - = -î

4x 5y 126x 3y 3

+ =ìí - = -î

(2,5) (3,7) (2, 5)-(4,1) (2,0) (10,2) (1, 2)-

( 3,5)-1 , 22

æ öç ÷è ø

Multiplying Expressions Worksheet #6 You should NOT use a calculator to complete this worksheet. Find each product. All answers should be in standard form. 1] 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12] 13] 14] 15] 16] 17] 18] 19] 20] 21] 13

(6 1)x x- - 2 ( 3)y y - 23 ( 4 3)x x x- +

( 3)( 2)y y+ + ( 2)( 4)c c- - ( 6)( 9)x x+ +

( 4)( 7)x x- - ( 4)( 9)x x- + ( 8)( 7)x x- +

(2 3)(2 3)x x- + ( 7)( 7)x x- + (3 5)(3 5)x x- +

( 4)( 14)x x- + (2 3)( 5)x x- + (4 5)( 9)x x+ -

(5 3)(4 7)d d+ + (4 7)(3 8)q q- + (2 7)(5 3)z z+ +

(7 4)(7 4)x x+ - 2( 5)w- 2(2 9)x-

Find each product. Your answers need to be in standard form. 22] 23] 24] ANSWERS: 1] 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12] 13] 14] 15] 16] 17] 18] 19] 20] 21] 22] 23] 24]

14

2(2 3)t + (3 5)(3 5)x x- + (4 3)(4 3)x x+ -

26x x- + 22 6y y- 3 23 4 9x x x- + 2 5 6y y+ +2 6 8c c- + 2 15 54x x+ + 2 11 28x x- + 2 5 36x x+ - 2 56x x- -

24 9x - 2 49x - 29 25x - 2 10 56x x+ - 22 7 15x x+ - 24 31 45x x- -220 47 21d d+ + 212 11 56q q+ - 210 41 21z z+ + 249 16x - 2 10 25w w- +

24 36 81x x- + 24 12 9t t+ + 29 25x - 216 9x -

Factoring and Solving Quadratic Equations Worksheet #7

You should NOT use a calculator to complete this worksheet. Factor each quadratic expression. Remember to check for common factors. If the expression cannot be factored, so state. 1] 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12] 13] 14] 15] 16] 17] 18] 19] 20] 21]

15

2 9 20x x- + 29 9x x+ 2 16 64x x+ +

2 2 15x x- - 2 81x - 2 56x x- -

2 13 36x x- + 2 18 81x x- + 2 9 36x x+ -

2 3 54x x+ - 2 42x x+ - 2 17 16t t- + -

26 11 4x x- + 2 25x + 25 10x x+

210 19 6x x+ + 26 15x x- 2 8 16x x+ +

24 21 18x x- - 210 7 12x x+ - 250 350 300x x- +

Factor each quadratic expression. Remember to check for common factors. 22] 23] 24] Solve the equation by factoring. Include your algebra and be sure your solutions include statements “x = .” Checking your solutions is advised. 25] 26] 27] 28] 29] 30] 31] 32] 33] 34] 35] 36]

16

23 31 36x x- + 24 20 25x x+ + 24 25x -

2 36 0x - = 2 3 70 0x x+ - = 2 8 15x x- = -

23 30x x= - 2 19 18x x+ = - 2 8 20x x+ =

2 7 18y y- = 22 7 3 0x x+ + = 220 5 0x x- =

26 19 10 0x x+ + = 22 48x x- + = 28 2 3x x+ =

ANSWERS Worksheet #7 1] 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12] 13] 14] cannot be factored 15] 16] 17] 18] 19] 20] 21]

22] 23] 24] 25] 26]

27] 28] 29] 30] 31]

32] 33] 34] 35] 36]

17

( 5)( 4)x x- - 9 ( 1)x x + 2( 8)x + ( 5)( 3)x x- + ( 9)( 9)x x- + ( 8)( 7)x x- +

( 9)( 4)x x- - 2( 9)x - ( 12)( 3)x x+ - ( 9)( 6)x x+ - ( 7)( 6)x x+ -1( 16)( 1)t t- - - (3 4)(2 1)x x- - 5 ( 2)x x + (2 3)(5 2)x x+ +

3 (2 5)x x - 2( 4)x+ (4 3)( 6)x x+ - (2 3)(5 4)x x+ - 50( 6)( 1)x x- -

(3 4)( 9)x x- - ( )22 5x+ (2 5)(2 5)x x- + 6; 6x x= = - 7; 10x x= = -

3; 5x x= = 0; 10x x= = - 18; 1x x= - = - 2; 10x x= = - 9; 2x x= = -

13;2

x x= - = -10;4

x x= =5 2;2 3

x x= - = - 8; 6x x= = -3 1;4 2

x x= - =

More Simplification Worksheet #8

You should NOT use a calculator to complete this worksheet. Simplify each expression. Your answers cannot include negative exponents. If an expression cannot be simplified, state “simplified now.”

1] 2] 3]

4] 5] 6]

7] 8] 9]

10] 11] 12]

13] 14] 15]

18

4 2c c× ( )( )2 64y y- ( )43n

( )22a- ( )332x-8

8

nn

3

72x9x

--

3

8

10n20n-

23

5

xy

æ öç ÷è ø

542xc

æ ö-ç ÷è ø

3

4

3a15aæ ö-ç ÷è ø

05m

( )( )4 57a a-( )( )( )

6

2

2x 5x

10x

-5

1n-

Simplify each expression. Your answers cannot include negative exponents. If an expression cannot be simplified, state “simplified now.”

16] 17] 18]

19] 20] 21]

22] 23] 24]

ANSWERS: 1] 2] 3] 4] 5] 6] 7]

8] 9] 10] 11] 12]

13] 14] 15] 16] 17] 18] 19]

20] simplified now 21] 22] 23] ─1 24]

( )25a 3 5x x x- × ×( )( )

( )

4 5

2

4x x

2x

-

5 9x x-×2 3aa+

236aa

9x3x-

3 4

4 3

a bb a

-× 5x 10

5-

6c 84y- 12n 24a 98x- 1

28x 5

12n

-6

10xy

20

532xc

- 15a

- 5

97a-5

10x

- 5n 10a 9x- 7x- 41x

12a

3- 2x -

19 Simplifying Radical Expressions Worksheet #9

You should NOT use a calculator to complete this worksheet. Simplify each expression, that is, write it in simple radical form. If an expression cannot be simplified, state “simplified now.”

1] 2] 3]

4] 5] 6]

7] 8] 9]

10] 11] 12]

13] 14] 15]

16] 17] 18]

19] 20] 21]

108 72 147

80 18 112

125 50 20

300 3 12× 15 5×

15 10× a a× 14 21×

2 10 3 5× 3 33 11- × 4 2 6 8×

1625

19

2049

22] 23] 24]

Simplify each expression, that is, write it in simple radical form. If an expression cannot be simplified, state “simplified now.”

25] 26] 27]

28] 29] 30]

31] 32] 33]

ANSWERS: 1] 2] 3] 4] 5] 6] 7]

8] 9] 10] 11] 12] 13] 14] 15]

16] 17] 18] 19] 20] 21] 22] 23]

24] 25] 26] 27] 28] 29] 30]

31] simplified now 32] 33]

5636

536

253

125

27

35

2 23 4+ 75 50+ 36 64+

6 10+ 8 18- 100 64-

6 3 6 2 7 3 4 5 3 2 4 7 5 5

5 2 2 5 10 3 6 5 3 5 6 a 7 6

30 2 33 3- 96 45

13

2 57

73

56

5 33

2 155

147

155

5 5 3 5 2+ 10

2- 2

20

21