Students, This packet is to help you be more successful in Algebra II w/ Trig. next year. It would be very wise for you to try all of these problems. You may work with a friend, parent, neighbor, peer, etc. if you need help. All of the topics in this packet are prerequisites for Algebra II w/ Trig. That means that you really need to know all of the information in this packet before entering into Algebra II w/ Trig. I am here to help you if you need any help. If you were in my Honors Geometry class, I am keeping you in the Remind 101 app. If you are not in the app and would like to be able to receive the text messages sent out, here is how you can get it: To receive text messages: Send a text to this number: 81010 The text needs to have this: @4290b To receive emails: Send an email to the following address, and type your name in the subject line: [email protected]This app will allow me to communicate with you over the summer without me having your number, nor you mine. If you were not one of my students, but still need help, please do not hesitate to ask me. I will be on campus in the mornings most of the summer. If there are questions that you have that require face-to-face help, just let me know in advance so I can arrange a time to tutor you on campus. Sincerely, Mrs. Singleton
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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=
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
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� �
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.
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
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.
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
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.”
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.