Summer Assignment for students entering: Algebra 2 ...cherrycreek.cherrycreekschools.org/Departments/Math/Documents... · Summer Assignment for students entering: Algebra 2 Trigonometry

Summer Assignment for students entering: Algebra 2 Trigonometry Honors

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 Algebra 2 Trigonometry Honors , 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

1

Information Sheet

Quadratic Formula: 2 4

2

b b acx

a

Slope: 2 1

2 1

y yy risem

x x x run

Standard form of a line: Ax By C

Standard form of a Quadratic: 2 0Ax Bx C

Slope-Intercept form of a line: y mx b

Point-Slope form of a line: 1 1y y m x x

Pythagorean Theorem: 2 2 2a b c

Right Triangle Trig Ratios: length of the opposite side

sine=length of the hypotenuse

length of adjacent sidecosine=

length of the hypotenuse

length of the oppposite sidetangent=

length of the adjacent side

Properties of Exponents:

0 1, 0a a 1

, 0n

na a

a

m m mab a b

nm mna a

m n m na a a , 0m

m n

n

aa a

a

, 0

m m

n

a aa

b a

2

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] 27 18 6 2

3] 2

7 4 2 5 4] 26 3 9 5 2

5] 227 6 2 2 6]

2

8 4 2 1 3 6

7] 2

2 2 6 4 6 8] 3 4 24 3

9]

25 9 3

9

10]

16 4 5

2 6 8

11] 23( 2)

7 1

12]

18 4 12 3 2 1 2

2

13] 154 10 8 9 14] 7 4 2

13 13 13

15] 2 3

3 25 5 16]

3 3

8 4

3

17] 1 5

2 7 18]

3 3

8 4

19] 1 1

1 23 6 20]

1 27 5

6 3

21] 3

68

22] 4 3

5 8

23] 3 5 3

5 9 10

24] 1 1

2 23 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] 4

5 16]

9

8 17]

17

14 18]

3

8 19]

13

2 20]

11

2 21]

9

4 22]

3

10

23] 1

10 24]

21

4 25]

2

3 26]

13

8

4

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 yx y

x y

8] 3 1

4 2 , , 23

yy x y

x

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 10

5

x x

21] 2( 5) (2 5)x x

5

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 1

8 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

6

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

7 213

x

7] 3 10

54 3 2

xx 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) 22 5 4

x x x 12] 4 2( 11) 3( 4) 6x x

13] 1

4 x 10 2x4

14] 1 4

x 7 x5 5

15] 1 1

x 12 x4 4

7

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 4

x 7 x5 5

15] 1 1

x 12 x4 4

16] 1 1

x 8 14 x2 2

17] 2

3x 18 5x 93

18] 3

2 x 1 10 5x5

19] 16 21 3( 5)x x 20] 3 (15 ) 59n n 21] 6 5

3 14

tt

22] 1 4 3

2 5 10b b 23] 2( 2 3 4) 4( 3)p p p p 24]

36 81

4x

ANSWERS: 1) 7 2) 2 3) 15 4) 3

4 5) 40 6) 42 7)

100

3 8)

6

7 9) (all real numbers)

10) 10

3 11)

65

33 12) 4 13) 4 14) 7 15)24 16) No Solution 17) 7 18) 8 19) 5

20) 37 21) 2

17 22)

11

5 23) (no solution) 24) 100

8

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 5

x y 5] 3(2 ) 5 7x y x 6] 1

3 6 214

y x y

Solve each equation for the indicated variable.

7] 2 2p w for 8] 2LA rh for h 9] 1

( )3

V w h for w

10] 5

( 32)9

C F for F 11] 1 2

1( )

2A h b b for 1b 12] PV nrt for T

9

Solve each equation for the indicated variable.

13] 21

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

Answers: 1) 8 4

, 03

xy y

2)

2 5 1,

3 3

xy y

3)

16 5 13,

2 2

xy y

x

4) 2 35

5(1 ),3 3

y x y 5) 7 5

,3 3

xy y

6) 4 36, 28y x y 7)

2

2

p w

8) 2

LAh

r 9)

3Vw

h 10)

932

5F C 11)

1 2

2Ab b

h 12)

PVT

nr 13)

2

2hg

t

14) 2 2 2d w h 15) (1 )t

IP

r

10

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

11

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

12

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

13

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

16] 2

3y x 17] 4 2 12x y 18] 3 5 15x y

14

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]

3

16

2

y x

y x

6]

4 3 12

44

3

x y

y x

7] 4 2 12

2 6

x y

y 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 4

3x y 16

5]

3x y 1

x y 7

6] 3x 5y 17

2x 3y 11

7]

6x 7y 12

5x 4y 10

15

8] 4x 3 y 10 29

8x 5y 2x 50

9]

8x 4y 4

4x 2y 3

10] 7x 10y 13

3x 2y 7

11]

6x 2y 12

3x y 6

12] 2x 9y 39

5x y 20

13]

4x 5y 12

6x 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

16

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

19] (7 4)(7 4)x x 20] 2( 5)w 21] 2( 9)x

17

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

34] 4 ( 6)x x 35] 4 3x x 36] 8 9x x

37] 7 7x x 38] 10 10x x 39] 2

11x

40] 3 1 4 3x x 41] 5 4 2 9x x 42] 7 3x y x y

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 34] 24 24x x 35] 2 7 12x x

36] 2 17 72x x 37] 2 49x 38] 2 20 100x x 39] 2 22 121x x 40] 212 5 3x x

41] 210 53 36x x 42] 2 27 20 3x xy y

18

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

19] 24 21 18x x 20] 210 7 12x x 21] 250 350 300x x

19

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

20

37] 2 14 40 0x x 38] 2 15 100 0x x 39] 2 22 9x x

40] 2 121 0x 41] 29 49 0x 42] 2 12 36 0x x

43] 23 14 5 0x x 44] 26 5 6 0x x 45] 3 28 48 0x x x

Use the quadratic formula or completing the square to solve the following equations.

46] 2 4 2 0x x 47] 2 5 7 0x x 48] 2 5 7 0x x

More factoring practice.

49] 23 15x x 50] 24 20x x 51] 3 25 35x x

52] 2 9x 53] 24 25x 54] 2 36x

55] 2 7 12x x 56] 2 12 20x x 57] 2 14 32x x

21

58] 2 42x x 59] 2 2 63x x 60] 2 56x x

61] 22 11 21x x 62] 212 5 2x x 63] 26 15x x

64] 3 26 5x x x 65] 3 211 30x x x 66] 4 3 22 9 5x x x

ANSWERS

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] 2

2 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] 1

3;2

x x 33] 1

0;4

x x 34] 5 2

;2 3

x x 35] 8; 6x x 36] 3 1

;4 2

x x

37] 4,10x 38] 20,5x 39] 2,11x 40] 11x 41] 7

3x 42] 6x 43]

15,

3x

44] 2 3

,3 2

x 45] 12,0,4x 46] 2 2x 47] 5 53

2

48] 49] 3 5x x

50] 4 5x x 51] 25 7x x 52] 3 3x x 53] 2 5 2 5x x 54] 2 36x

55] 3 4x x 56] 10 2x x 57] 16 2x x 58] 7 6x x 59] 9 7x x

60] 8 7x x 61] 2 3 7x x 62] 4 1 3 2x x 63] 3 5 2 3x x

64] 5 1x x x 65] 6 5x x x 66] 2 2 1 5x x x

22

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] 4

3n

4] 2

2a 5] 3

32x 6] 8

8

n

n

7] 3

72x

9x

8]

3

8

10n

20n

9]

23

5

x

y

10]

542x

c

11] 3

4

3a

15a

12] 05m

13] 4 57a a 14]

6

2

2x 5x

10x

15]

5

1

n

23

Simplify each expression. Your answers cannot include negative exponents. If an expression

cannot be simplified, state “simplified now.”

16] 2

5a 17] 3 5x x x 18]

4 5

2

4x x

2x

19] 20] 2 3a

a

21]

2

3

6

a

a

22] 9x

3x 23]

3 4

4 3

a b

b a

24]

2

2

n 5n

n 10

25] 5a 7a

6

26]

5x 10

5

27]

2

3x4x

6x

28] 3 117 7 29] 2 6x x 30] 4 5 56 7x y x y

31] 7

2

x

x 32]

9 5

2

30

6

x y

x y 33]

5 3 2

2 8 6

x y m

x y m

34] 5

43 35] 3

2x 36] 3

52x y

24

5 9x x

37]

23

4

2

3

x

y

38]

46

4 2

6

3

yx

y x

39]

22

3

2x

m

40] 4

5 32x y 41]

3

7

a b

a b

42]

222x

43] 3

53 10 44]

05 2

2 5

7

4

x y

x y

45]

61

2

2

3

a

a

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

8

x 8]

5

1

2n 9]

6

10

x

y 10]

20

5

32x

c

11] 1

5a 12] 5 13] 97a 14]

5

10

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

4

1

x

20] simplified now 21] 1

2a 22] 3 23] 1 24] simplified now 25] 2a 26] 2x 27] 2 28] 147

29] 8x 30] 9 642x y 31] 5x 32] 7 45x y 33] 11

7 4

y

x m 34] 203 35]

6

1

x 36] 15 38x y 37]

2

8

4

9

x

y

38] 16

12

16x

y 39]

6

44

m

x 40] 20 1216x y 41]

4

1

a b 42]

4

4

x 43] 162.7 10 44] 1 45] a

25

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] 16

25 20] 1

9 21]

20

49

22] 56

36 23]

5

36 24]

25

3

26

Simplify each expression, that is, write it in simple radical form. If an expression cannot be

simplified, state “simplified now.”

25] 12

5 26]

2

7 27]

3

5

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

31] 6 10 32] 8 18 33] 100 64

34] 8 35] 27 36] 40

37] 4 45 2 20 38] 5 8 32 39] 50 16 72

40] 6 15 41] 30 55 42] 4 3 5 27

43] 36

25 44]

75

25 45]

44

99

27

Answers should be rationalized, no radicals in the denominator.

46] 5

3 47]

7

2 48]

6

12

49] 4

1 3 50]

8

2 2 51]

10

5 5

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] 4

5 20]

1

3 21]

2 5

7 22]

7

3 23]

5

6

24] 5 3

3 25]

2 15

5 26]

14

7 27]

15

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

31] simplified now 32] 2 33] 2 34] 2 2 35] 3 3 36] 2 10 37] 16 5

38] 6 2 39] 11 2 4 40] 3 10 41] 5 66 42] 180 43] 6

5 44] 3 45]

2

3 46]

5 3

3

47] 14

2 48]

2

2 49] 2 2 3 50] 8 4 2 51]

5 5

2

28

Pythagorean Theorem and Right Triangle Trig Worksheet #11

Solve for x in each of the following right triangles. Find exact answers.

1] 2] 3]

4] 5] 6]

7] 8] 9]

10] 11] 12]

29

5 10

2 6

12

45 45

45

10

12

21

x

x

x

60

30

3 6 6 3

13 5

22 20

x x

x

3

5

5

10

x

x

4

2 3

x

30

Using the given right triangle and without a calculator find the following trig ratios.

13] Solve for sin . 14] Solve for tan . 15] Solve for cos .

Using the given right triangle and a calculator find the measure of to the nearest hundredth of a degree.

16] 17] 18]

ANSWERS:

1] 5 5 2] 2 3] 2 7 4] 2 21 5] 12 6] 3 6 7] 21 3

2 8] 4 3 9]

10 3

3 10] 6 2

11] 4 3 12] 5 5 13] 3 58

58 14] 2 15]

3

5 16] 23.20 17] 45 18] 53.13

30

3

5 4

4 3

7

3

5 4

3 2

7

3

4