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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 in the fall. Make sure you show your work where appropriate. Answers are provided for you to check; however, you will not be given credit if you don’t 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 Honor’s Geometry, 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

                                     

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 Order of Operations Worksheet #1 NAME ________________________  

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] ( )27 18 6 2− − ÷ 3] ( )27 4 2 5− + −g 4] ( )26 3 9 5 2− − ÷ 5] ( )( )227 6 2 2− − − 6] ( )( )28 4 2 1 3 6− + − − + ⋅ 7] ( )22 2 6 4 6+ − − ⋅ 8] 3i4− 24 ÷ 3

9] ( )25 9 39−g 10]

16− 4i52i6+8

11] 23( 2)

7 1−+

12] ( )( ) ( )18 4 12 3 2 1 22⎡ ⎤− − − +⎣ ⎦

13] 154−10i8+ 9 14] 7 4 2

13 13 13− −

15] 2 33 2

5 5− = 16] 3 3

8 4+

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17] 1 52 7+ 18] 3 3

8 4−

19] 1 11 2

3 6+ 20] 1 27 5

6 3−

21] 368

⎛ ⎞⎜ ⎟⎝ ⎠

22] 4 35 8•

23] 3 5 35 9 10

⎛ ⎞⎛ ⎞⎛ ⎞− − −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠ 24] 1 12 2

3 4•

25] 4 2

9 3÷ 26] 3 41

10 5÷

ANSWERS Worksheet #1: 1] 7 2] 12 3] 24 4] 30 5] ─47 6] 46 7] ─6 8] 4 9] 20 10] 1

5− 11] 3

2 12] 34 13] 83 14] 1

13

15] 45

16] 98

17] 1714

18] 38

− 19] 132

20] 112

21] 94

22] 310

23] 110

− 24] 214

25] 23

26] 138

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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] 4( 7), 2x x− = 2] 25 , 6x x x+ = 3] 2 ( 4), 18x x x− + = 4] 211 7 , 2y y y− = − 5] 5 22 , 1, 4x y x y− = − = 6] 5 (4 ), 3, 2x x y x y+ − = =

7] , 5, 32( )x y x yx y− = = −+

8] 3 14 2 , , 23

y y x yx

⎛ ⎞ − = − =⎜ ⎟⎝ ⎠ 9] 2 3(3 ) 2 , 4, 3x y x y− = = −

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] ( )3 5x x− −

13] 2 (7 5 )x x− − 14] ( )3 2 4 5x− − 15] ( )4 3 2 1x− −

16] ( ) ( )3 2 32 7 3 6y y y y y+ − + − + − 17] -3x + 5(-2x + 1)

18] ( ) 23 4 2y y y− + 19] 3(x + 2y) – 4(5x – 3y + 4)

20] 220 30 105

x x+ −−

21] 2( 5) (2 5)x x− − +

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

22] 4 3 5x xy x y+ − − 23] 3(5 3) (2 )x x x− − − −

24] 1 3(6 9 ) (20 10 )3 5

x x− − − 25] ( ) ( )1 18 4 6 92 3

x x− + −

Let p represent a positive number and n represent a negative number. Determine if the given expressions will be always positive, always negative or sometime positive and sometimes negative. Be prepared to support your decision.

26] pn 27] p n+ 28] np−

29] 6n 30] 2np 31] 2n−

32] 2p− 33] 2p n+ 34] p n−

ANSWERS: 1] −20 2] 66 3] 14 4] 58 5] −33 6] 25 7] 2 8] −40 9] 198 10] 12x 11] 215x− 12] 23 5x x− + 13] 210 14x x− 14] 8 13x− + 15] 6 7x− + 16] 3 2 2 13y y y− + − + 17] 13 5x− + 18] 2 12y y− + 19] 17 18 16x y− + − 20] 24 6 2x x− − + 21] 15− 22] 3 3 5x xy y+ − 23] 13 7x− + 24] 3 10x − 25] 1 26] always negative 27] sometimes positive/sometimes negative 28] always positive 29] always positive 30] always negative 31] always negative 32] always negative 33] sometimes positive/sometimes negative 34] always positive

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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] 5 11 24x − = 2] 17 3 23x− = 3] 3 8 5 22x x− = + 4] 18 3( 5)y y− − = − 5] 7 (12 ) 228x x− + = 6] 2 7 21

3x − =

7] 3 10 5

4 3 2xx − = + 8] 59(3 2) 3

2x x− = + 9] 14 (6 4) 3 5( 1) 1x x x x− + = + − +

10] 6.2 11.8 3.8( 1)x x+ = + 11] 1 2 3( 5) 2

2 5 4x x x− + = − 12] 4 2( 11) 3( 4) 6x x− − = + −

13] ( )1 4 x 10 2x4

− = + 14] 1 4x 7 x5 5

= − 15] 1 1x 12 x4 4

−+ =

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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] ( )1 4 x 10 2x4

− = + 14] 1 4x 7 x5 5

= − 15] 1 1x 12 x4 4

−+ =

16] 1 1x 8 14 x2 2

− = + 17] ( )2 3x 18 5x 93

+ = − 18] ( ) ( )32 x 1 10 5x5

− = +

19] 16 21 3( 5)x x− + = − + 20] 3 (15 ) 59n n− + = 21] 6 5 3 1

4t t− = +

22] 1 4 3

2 5 10b b+ = − 23] 2( 2 3 4) 4( 3)p p p p− + − = − 24] 3 6 81

4x + =

ANSWERS: 1) 7 2) −2 3) −15 4) 3

4− 5) 40 6) 42 7) 100

3 8) 6

7 9) ℜ (all real numbers)

10) 103

− 11) 6533

12) 4 13) −4 14) 7 15)−24 16) No Solution ∅ 17) 7 18) −8 19) −5

20) 37 21) 217

22) 115

23) ∅ (no solution) 24) 100

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Solving Literal Equations Worksheet #4

For each equation below,

a) Solve each equation for y in terms of x, showing your work.

b) Then evaluate when x = 2.

1] 4 3 8x y+ = 2] 2 3 5x y− = − 3] 2 5 16xy x− =

4] 2 1 13 5x y− + = 5] 3(2 ) 5 7x y x− = + 6] 1 3 6 21

4y x y+ − = +

Solve each equation for the indicated variable.

7] 2 2p w= +l for l 8] 2LA rhπ= for h 9] 1 ( )3

V w h= l g g for w

10] 5 ( 32)9

C F= − for F 11] 1 21 ( )2

A h b b= + for 1b 12] PV nrt= for T

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Solve each equation for the indicated variable.

13] 212

h gt= for g 14] 2 2 2d w h= + +l for l 15] (1 )tI P r= + for P  

 

 

 

 

 

 

 

 

 

Answers: 1) 8 4 , 03xy y−= = 2) 2 5 1,

3 3xy y− += = 3) 16 5 13,

2 2xy y

x+= =

4) 2 355(1 ),3 3

y x y= + = 5) 7 5,3 3xy y− += = −−

6) 4 36, 28y x y= − = − 7) 22

p w−=l

8) 2LAhrπ

= 9) 3Vwh

=l g

10) 9 325

F C= + 11) 1 22Ab bh

= − 12) PVTnr

= 13) 2

2hgt

=

14) 2 2 2d w h= − −l 15) (1 )tIPr

=+

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Linear Functions Worksheet #5 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] ( ) ( )2,5 , 8,1− − 2] ( ) ( )1, 4 , 2,2− − 3] ( ) ( )3,8 , 3,4− − Graph the functions.

4] 2 3y x= − 6] y x= − 7] 3 42

y x= +

8] 4y = 9] 4x = − 10] 2 4 8x y+ =

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Graph the functions. 10] 2 4x y− = − 11] 1y x= − − 12] 3 4 12x y− + =

Graph the inequalities. 13] 4y ≤ − 14] 1y x≤ − − 15] 3x < −

16] 2

3y x≥ − 17] 4 2 12x y− > 18] 3 5 15x y− + ≤

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ANSWERS: 1] 2

3m = 2] 2m = 3] slope is undefined

4] 2 3y x= − 6] y x= − 7] 3 42

y x= +

8] 4y = 9] 4x = − 10] 2 4 8x y+ =

10] 2 4x y− = − 11] 1y x= − − 12] 3 4 12x y− + =

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Graph the inequalities. 13] 4y ≤ − 14] 1y x≤ − − 15] 3x < −

16] 2

3y x≥ − 17] 4 2 12x y− > 18] 3 5 15x y− + ≤

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Systems of Equations Worksheet #6 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] 31 62

y x

y x

= +⎧⎪⎨ = − +⎪⎩

6] 4 3 12

4 43

x y

y x

+ =⎧⎪⎨ = − +⎪⎩

7] 4 2 122 6

x yy x

− =⎧⎨ = +⎩

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

4] y x 43x y 16= +⎧

⎨ + =⎩ 5] 3x y 1

x y 7+ =⎧

⎨ − =⎩

6] 3x 5y 172x 3y 11

+ =⎧⎨ + =⎩

7] 6x 7y 125x 4y 10

− =⎧⎨ − =⎩

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8] 4x 3 y 10 298x 5y 2x 50

− + − =⎧⎨ − − =⎩

9] 8x 4y 44x 2y 3

− =⎧⎨ − = −⎩

10] 7x 10y 133x 2y 7

+ = −⎧⎨ − =⎩

11] 6x 2y 123x y 6

− =⎧⎨ − =⎩

12] 2x 9y 395x y 20

+ =⎧⎨ − = −⎩

13] 4x 5y 126x 3y 3

+ =⎧⎨ − = −⎩

ANSWERS: 1] (2,5) 2] infinitely many solutions 3] no solution 4] (3,7) 5] (2, 5)− 6] (4,1) 7] (2,0) 8] (10,2) 9] no solution 10] (1, 2)− 11] infinitely many solutions

12] ( 3,5)− 13] 1 , 22

⎛ ⎞⎜ ⎟⎝ ⎠

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 Multiplying Expressions Worksheet #7 You should NOT use a calculator to complete this worksheet. Find each product. All answers should be in standard form. 1] (6 1)x x− − 2] 2 ( 3)y y − 3] 23 ( 4 3)x x x− + 4] ( 3)( 2)y y+ + 5] ( 2)( 4)c c− − 6] ( 6)( 9)x x+ + 7] ( 4)( 7)x x− − 8] ( 4)( 9)x x− + 9] ( 8)( 7)x x− + 10] (2 3)(2 3)x x− + 11] ( 7)( 7)x x− + 12] (3 5)(3 5)x x− + 13] ( 4)( 14)x x− + 14] (2 3)( 5)x x− + 15] (4 5)( 9)x x+ − 16] (5 3)(4 7)d d+ + 17] (4 7)(3 8)q q− + 18] (2 7)(5 3)z z+ +

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19] (7 4)(7 4)x x+ − 20] 2( 5)w− 21] 2( 9)x − Find each product. Your answers need to be in standard form. 22] 2(2 3)t + 23] (3 5)( 4)x x− + 24] (4 5)( 7)x x+ − 25] 2(3 1)b− 26] 2(9 8)w+ 27] (6 5)(6 5)x x− + 28] 2(5 6)t + 29] 2( 10)n− 30] (3 2)(3 2)x x+ − 31] 2(4 3)a + 32] (2 3)(2 3)w w+ − 33] 2(3 5)x− ANSWERS: 1] 26x x− + 2] 22 6y y− 3] 3 23 4 9x x x− + 4] 2 5 6y y+ + 5] 2 6 8c c− + 6] 2 15 54x x+ + 7] 2 11 28x x− + 8] 2 5 36x x+ − 9] 2 56x x− − 10] 24 9x − 11] 2 49x − 12] 29 25x − 13] 2 10 56x x+ − 14] 22 7 15x x+ − 15] 24 31 45x x− − 16] 220 47 21d d+ + 17] 212 11 56q q+ − 18] 210 41 21z z+ + 19] 249 16x − 20] 2 10 25w w− + 21] 2 18 81x x− + 22] 24 12 9t t+ + 23] 23 7 20x x+ − 24] 24 23 35x x− − 25] 29 6 1b b− + 26] 281 144 64w w+ + 27] 236 25x − 28] 225 60 36t t+ + 29] 2 20 100n n− + 30] 29 4x − 31] 216 24 9a a+ + 32] 24 9w − 33] 29 30 25x x− +

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Factoring and Solving Quadratic Equations Worksheet #8 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 9 20x x− + 2] 29 9x x+ 3] 2 16 64x x+ + 4] 2 2 15x x− − 5] 2 81x − 6] 2 56x x− − 7] 2 13 36x x− + 8] 2 18 81x x− + 9] 2 9 36x x+ − 10] 2 3 54x x+ − 11] 2 42x x+ − 12] 2 17 16t t− + − 13] 26 11 4x x− + 14] 2 25x + 15] 25 10x x+ 16] 210 19 6x x+ + 17] 26 15x x− 18] 2 8 16x x+ +

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19] 24 21 18x x− − 20] 210 7 12x x+ − 21] 250 350 300x x− + Factor each quadratic expression. Remember to check for common factors. 22] 23 31 36x x− + 23] 24 20 25x x+ + 24] 24 25x − Solve the equation by factoring. Include your algebra and be sure your solutions include statements “x = .” Checking your solutions is advised. 25] 2 36 0x − = 26] 2 3 70 0x x+ − = 27] 2 8 15x x− = − 28] 23 30x x= − 29] 2 19 18x x+ = − 30] 2 8 20x x+ = 31] 2 7 18y y− = 32] 22 7 3 0x x+ + = 33] 220 5 0x x− = 34] 26 19 10 0x x+ + = 35] 22 48x x− + = 36] 28 2 3x x+ =

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ANSWERS Worksheet #7 1] ( 5)( 4)x x− − 2] 9 ( 1)x x + 3] 2( 8)x + 4] ( 5)( 3)x x− + 5] ( 9)( 9)x x− + 6] ( 8)( 7)x x− + 7] ( 9)( 4)x x− − 8] 2( 9)x − 9] ( 12)( 3)x x+ − 10] ( 9)( 6)x x+ − 11] ( 7)( 6)x x+ − 12] 1( 16)( 1)t t− − − 13] (3 4)(2 1)x x− − 14] cannot be factored 15] 5 ( 2)x x + 16] (2 3)(5 2)x x+ + 17] 3 (2 5)x x − 18] 2( 4)x+ 19] (4 3)( 6)x x+ − 20] (2 3)(5 4)x x+ − 21] 50( 6)( 1)x x− −

22] (3 4)( 9)x x− − 23] ( )22 5x+ 24] (2 5)(2 5)x x− + 25] 6; 6x x= = − 26] 7; 10x x= = −

27] 3; 5x x= = 28] 0; 10x x= = − 29] 18; 1x x= − = − 30] 2; 10x x= = − 31] 9; 2x x= = −

32] 13;2

x x= − = − 33] 10;4

x x= = 34] 5 2;2 3

x x= − = − 35] 8; 6x x= = − 36] 3 1;4 2

x x= − =

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More Simplification Worksheet #9

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] 4 2c c⋅ 2] ( )( )2 64y y− 3] ( )43n

4] ( )22a− 5] ( )332x− 6] 8

8

nn

7] 3

72x9x

−−

8] 3

8

10n20n− 9]

23

5

xy

⎛ ⎞⎜ ⎟⎝ ⎠

10] 542x

c⎛ ⎞−⎜ ⎟⎝ ⎠

11] 3

4

3a15a

⎛ ⎞−⎜ ⎟⎝ ⎠

12] 05m

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13] ( )( )4 57a a− 14] ( )( )( )

6

2

2x 5x

10x

− 15] 5

1n−

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

16] ( )25a 17] 3 5x x x− ⋅ ⋅ 18] ( )( )( )

4 5

2

4x x

2x

−

19] 20] 2 3aa+ 21] 2

36aa

22] 9x3x−

23] 3 4

4 3

a bb a

−⋅ 24] 2

2

n 5nn 10

++

25] 5a 7a6+ 26] 5x 10

5− 27] 2

3x 4x6x

⋅−

ANSWERS: 1] 6c 2] 84y− 3] 12n 4] 24a 5] 98x− 6] 1 7] 2

8x

8] 5

12n

− 9] 6

10

xy

10] 20

5

32xc

− 11] 15a

− 12] 5

13] 97a− 14] 5

10x− 15] 5n 16] 10a 17] 9x− 18] 7x− 19] 4

1x

5 9x x−⋅

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20] simplified now 21] 12a

22] 3− 23] ─1 24] simplified now 25] 2a

26] 2x − 27] 2−

Simplifying Radical Expressions Worksheet #10

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] 108 2] 72 3] 147

4] 80 5] 18 6] 112

7] 125 8] 50 9] 20

10] 300 11] 3 12⋅ 12] 15 5⋅

13] 15 10⋅ 14] a a⋅ 15] 14 21⋅

16] 2 10 3 5⋅ 17] 3 33 11− ⋅ 18] 4 2 6 8⋅

19] 1625 20] 1

9 21] 20

49

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22] 5636

23] 536

24] 253

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

25] 125

26] 27

27] 35

28] 2 23 4+ 29] 75 50+ 30] 36 64+

31] 6 10+ 32] 8 18− 33] 100 64−

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

8] 5 2 9] 2 5 10] 10 3 11] 6 12] 5 3 13] 5 6 14] a 15] 7 6

16] 30 2 17] 33 3− 18] 96 19] 45

20] 13

21] 2 57

22] 73

23] 56

   

24] 5 33

  25] 2 155

26] 147

27] 155

28] 5 29] 5 3 5 2+ 30] 10

31] simplified now 32] 2− 33] 2