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Information Sheet

Quadratic Formula: 2 4

2b b acx

a� r �

Slope: 2 1

2 1

y yy risemx 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 sidesine=

length of the hypotenuse

length of adjacent side

cosine=length of the hypotenuse

length of the oppposite side

tangent=length of the adjacent side

Properties of Exponents:

0 1, 0a a z 1, 0n

na aa

� z � �m m mab a b nm mna a

m n m na a a �x , 0m

m nn

a a aa

� z , 0m m

n

a a ab a

§ · z¨ ¸© ¹

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� � y 3] � �27 4 2 5� � � 4] � �26 3 9 5 2� � y 5] � �� �227 6 2 2� � � 6] � �� �2

8 4 2 1 3 6� � � � � � 7] � �22 2 6 4 6� � � � 8] 3 4 24 3� y

9] � �25 9 39�

10] 16 4 52 6 8��

11] 23( 2)

7 1��

12] � �� � � �18 4 12 3 2 1 2

2ª º� � � �¬ ¼

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 52 7� 18] 3 3

8 4�

19] 1 1

1 23 6� 20] 1 2

7 56 3�

21] 36

8§ ·¨ ¸© ¹

22] 4 35 8x

23] 3 5 35 9 10

§ ·§ ·§ ·� � �¨ ¸¨ ¸¨ ¸© ¹© ¹© ¹

24] 1 12 2

3 4x

25] 4 2

9 3y 26] 3 4

110 5

y

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] 13

2 20] 1

12

21] 94

22] 310

23] 110

� 24] 214

25] 23

26] 138

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 y x yx y�

��

8] 3 14 2 , , 2

3y y x yx

§ · � � ¨ ¸© ¹

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

5x 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 5x 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 213x �

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

13] � �14 x 10 2x

4� � 14] 1 4

x 7 x5 5

� 15] 1 1x 12 x

4 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] � �14 x 10 2x

4� � 14] 1 4

x 7 x5 5

� 15] 1 1x 12 x

4 4�

�

16] 1 1x 8 14 x

2 2� � 17] � �2

3x 18 5x 93

� � 18] � � � �32 x 1 10 5x

5� �

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

3 14t t� �

22] 1 4 3

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

6 814x �

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) 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

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 11

3 5x y� � 5] 3(2 ) 5 7x y x� � 6] 1

3 6 214y x y� � �

Solve each equation for the indicated variable.

7] 2 2p w � for 8] 2LA rhS for h 9] 1( )

3V w h for w

10] 5( 32)

9C 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] 212

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

Answers: 1) 8 4, 0

3xy y�

2) 2 5 1,

3 3xy y� �

3) 16 5 13,

2 2xy y

x�

4) 2 355(1 ),

3 3y x y � 5) 7 5

,3 3

xy y� � �

� 6) 4 36, 28y x y � � 7) 2

2p w�

8) 2LAhrS

9) 3Vwh

10) 932

5F C � 11) 1 2

2Ab bh

� 12) PVTnr

13) 2

2hgt

14) 2 2 2d w h � � 15) (1 )tIPr

�

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 d � 14] 1y xd � � 15] 3x � �

16] 2

3y xt � 17] 4 2 12x y� ! 18] 3 5 15x y� � d

12

ANSWERS: 1] 2

3m 2] 2m 3] slope is undefined

4] 2 3y x � 6] y x � 7] 34

2y 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 d � 14] 1y xd � � 15] 3x � �

16] 2

3y xt � 17] 4 2 12x y� ! 18] 3 5 15x y� � d

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 3 124

43

x y

y x

� ­°®

� �°̄ 7] 4 2 12

2 6x 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

� ­® � ¯

15

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] 1,2

2§ ·¨ ¸© ¹

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] � �211x � 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] � �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;

2x x � � 33] 1

0;4

x x 34] 5 2;

2 3x x � � 35] 8; 6x x � 36] 3 1

;4 2

x x �

37] 4,10x 38] 20,5x � 39] 2,11x � 40] 11x r 41] 73

x r 42] 6x � 43] 15,

3x �

44] 2 3,

3 2x � 45] 12,0,4x � 46] 2 2x r 47] 5 53

2r 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] � �43n

4] � �22a� 5] � �332x� 6] 8

8

nn

7] 3

72x9x

��

8] 3

8

10n20n� 9]

23

5

xy

§ ·¨ ¸© ¹

10] 542x

c§ ·�¨ ¸© ¹

11] 3

4

3a15a§ ·�¨ ¸© ¹

12] 05m

13] � �� �4 57a a� 14] � �� �� �

6

2

2x 5x

10x

� 15] 5

1n�

23

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

3x4x

6x�

�

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

31] 7

2

xx

32] 9 5

2

306x yx y�

33] 5 3 2

2 8 6

x y mx y m

�

�

34] � �543 35] � �32x� 36] � �352x y�

24

5 9x x��

37] 23

4

23xy

§ ·¨ ¸© ¹

38] 46

4 2

63yxy x

§ ·¨ ¸© ¹

39] 22

3

2xm

�§ ·¨ ¸© ¹

40] � �45 32x y� 41] � �� �

3

7

a b

a b

�

� 42] � � 222x

���

43] � �353 10u 44] 05 2

2 5

74x yx y

§ ·¨ ¸© ¹

45]

612

23

a

a

�

�

§ ·¨ ¸¨ ¸¨ ¸© ¹

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

20] simplified now 21] 12a

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

yx m

34] 203 35] 6

1x

36] 15 38x y� 37] 2

8

49xy

38] 16

12

16xy

39] 6

44mx

40] 20 1216x y 41] � �4

1a b�

42] 4

4x 43] 162.7 10u 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] 1625 20] 1

9 21] 20

49

22] 5636

23] 536

24] 253

26

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�

34] 8 35] 27 36] 40

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

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

43] 3625

44] 7525

45] 4499

27

Answers should be rationalized, no radicals in the denominator.

46] 53

47] 72

48] 612

49] 41 3�

50] 82 2�

51] 105 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] 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 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] 65

44] 3 45] 23

46] 5 33

47] 142

48] 22

49] 2 2 3� � 50] 8 4 2� 51] 5 52�

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 sinT . 14] Solve for tanT . 15] Solve for cosT .

Using the given right triangle and a calculator find the measure of T 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 32

8] 4 3 9] 10 33

10] 6 2

11] 4 3 12] 5 5 13] 3 5858

14] 2 15] 35

16] 23.20q 17] 45q 18] 53.13q

30

3

T

T

5 4 4 3

T 7

3 T

5 4

T 3 2 7

3 T

4