Summer Assignment for students ENTERING: Algebra 2 Trigonometry Honors

Transcription

1 Summer Assignment for students ENTERING: Algebra Trigonometry Honors Please have the following worksheets completed and ready to be handed in on the first day of class, August 1, 017. Make sure you show your work where appropriate. Answers are provided for you to check at the end of this packet; however, you will not be given credit if you don t show work on problems that require it. Please neatly organize your work, show all of your work, and place all of your work and answers ON these worksheets. It is epected that you have a good understanding of this material coming into Algebra Trigonometry Honors, as teachers will not be doing an etensive review of previously learned material. Have a great summer and we look forward to seeing you in the fall! The CCHS Math Department 1

2 Worksheet #1 Fractions Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each epression and leave your answer in simplest form. 1] 7 ] = ] + 8 ] 1 + ] 7 ] ] 1 7 8] 8 9] 8 10] ] 1 1 1] 9 1] 1 10

3 Worksheet # Simplifying/Evaluating Epressions Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each epression for the given value of and/or y. 1] y, = 1, = ], =, y= ( + y) y y ] 1 y y, =, y = ] ( ) y, =, y= Simplify each epression and leave your answer in simplest form. Also, be sure your answer is in standard form. ] ( ) y y + y ] ] ( ) ( ) 8] 1 ( 9 ) (0 10 ) 1 1 9] ( 8 ) + ( 9) Let p represent a positive number and n represent a negative number. Determine if the given epressions will be always positive, always negative or sometime positive and sometimes negative. Be prepared to support your decision. 10] np 11] ( n) 1] ( p)

4 Worksheet # Solving Linear Equations Do NOT use a calculator when completing this worksheet. Show work whenever possible. Solve the following equations for. You must show all algebraic steps. Please also include a CHECK of your solution. 1] 10 = + ] 1 (+ ) = + ( 1) + 1 ] =.8( + 1) ] ( 11) ( ) = + ] ( ) 1 = 10 + ] 1 = 7 7] = 8] ( 1) ( 10 ) = + 9] ( p p+ p ) = ( p ) 10] t = t + 1

5 Worksheet # Solving Literal Equations Do NOT use a calculator when completing this worksheet. Show work whenever possible. For each equation below, a) Solve each equation for y in terms of, showing your work. b) Then evaluate when =. 1] 1 + y= 1 ] 1 1 y+ = y+ Solve each equation for the indicated variable. ] p= l + w for l ] LA = π rh for h ] V = 1 (liwih) for w ] C = ( F ) for F 7] A= 1 h ( b ) 1+ b for b 1 8] PV = nrt for t 9 9] d = + w + h I = P + r for P l for l 10] (1 ) t

6 Worksheet # Linear Functions and Inequalities Do NOT use a calculator when completing this worksheet. Show work whenever possible. Please DO use a straightedge when graphing. Find the slope of the line passing through the given points. Include your work. 1] (, ), ( 8,1) ] (,8 ), (, ) Find the equation of the line in slope-intercept form ( y = m+ b) using the given information. ] slope =, y int = ] m=, b= 9 ] m =, goes through ( 1, ) ] goes through (,7) & (8,1) Graph the functions. 7] y = 8] y = 9] y =

7 Graph the functions. 10] = 11] + y= 8 Graph the inequalities. 1] y 1] y> 1 7

8 Worksheet # Systems of Equations Do NOT use a calculator when completing this worksheet. Show work whenever possible. Please DO use a straightedge when graphing. Solve each system of equations by graphing. 1] y = + 1 y = + ] + y = 1 y = + ] y = 1 y = + Solve the following systems of equations using the substitution method or the elimination method. Remember to write your solution as an ordered pair. CHECK your solution in both original equations. ] y= + + y = 1 ] 8 y = y = ] y = 1 y = 7] + y = 1 y = 8

9 Worksheet #7 Multiplying Epressions and Factoring Do NOT use a calculator when completing this worksheet. Show work whenever possible. Find each product. All answers should be in standard form. 1] + ] ( 8)( + 7) ] ( )(+ ) ( ) ] (d + )(d + 7) ] (7+ )(7 ) ] ( w ) 7] ( ) a + 8] ( + )( 9) Factor each quadratic epression. Remember to check for common factors. If the epression cannot be factored, so state. 9] ] 81 11] 1+ 1] ] + 1] ] ] 9

10 Worksheet #8 Factoring and Solving Quadratic Equations Do NOT use a calculator when completing this worksheet. Show work whenever possible. Factor each epression. Remember to check for common factors. If the epression cannot be factored, so state. 1] 0 ] 9 ] ] ] 11 1 ] + + 7] + 9 Solve the equation by factoring. Include your algebra and be sure your solutions include statements =. Checking your solutions is advised. 8] + 70= 0 9] 0 = 10] + 8= 0 10

11 Solve the equation by factoring. Include your algebra and be sure your solutions include statements =. Checking your solutions is advised. 11] = 1] = 1] 8 + = 1] = 0 1] 11 = 0 1] + 1+ = 0 17] = 0 Use the quadratic formula or completing the square to solve the following equations. 18] + = 0 19] 7= 0 0] + + 7= 0 11

12 Worksheet #9 Eponents and Simplifying Epressions Do NOT use a calculator when completing this worksheet. Show work whenever possible. Simplify each epression. Your answers cannot include negative eponents. If an epression cannot be simplified, state simplified now. 1] c c ] ( ) n ] ( ) 7 ] 9 ] y ] a 1a 7] 0 m 8] ( 7a )( a ) 1 9] n 10] 9 a 11] 1] a 1] a b b 1] a a + 7a 1] 1

13 Simplify each epression. Your answers cannot include negative eponents. If an epression cannot be simplified, state simplified now. 1] 17] 7 18] y m y m 8 19] ( ) 0] y 1] y y ] m ] ( a+ b) ( a+ b) 7 10 ] ( ) ] 7y y 0 ] a a 1 1

14 Worksheet #10 Simplifying Radical Epressions Do NOT use a calculator when completing this worksheet. Show work whenever possible. Simplify each epression, that is, write it in simple radical form. If an epression cannot be simplified, state simplified now. Answers should be rationalized with no radicals in the denominator. 1] 108 ] 80 ] 1 ] 00 ] 1 10 ] 10 7] 1 8] 9] 1 10] + 11] ] 8 1] + 0 1] ] 1 1

15 Simplify each epression, that is, write it in simple radical form. If an epression cannot be simplified, state simplified now. Answers should be rationalized with no radicals in the denominator. 1] 7 17] 18] 19] 7 0] 1 1] 1+ ] 8 ] 10 1

16 Worksheet #11 Pythagorean Theorem and Right Triangle Trig Solve for in each of the following right triangles. Find eact answers. Show work whenever possible. 1] ] ] 10 ] ] ] 0 1 7] 8] 9] ] 11] 1]

17 Using the given right triangle and without a calculator find the following trig ratios. 1] Solve for sinθ. 1] Solve for tanθ. 1] Solve for cosθ. 7 θ θ θ Using the given right triangle and a calculator find the measure of θ to the nearest hundredth of a degree. 1] 17] 18] 7 θ θ θ 17

18 WORKSHEET ANSWERS Worksheet #1 Answers: 1] 1 ] 1 9] 10 10] ] ] 1 10 ] ] ] 11 ] 7 8 1] 1 8 7] 8] 9 Worksheet # Answers: 1] ] ] 0 ] 198 ] y + 1y ] + 7] 1 7 9] 1 10] always negative 11] always negative 1] always positive + 8] 10 Worksheet # Answers: 1] ] R (all real numbers) ] ] ] ] 7 7] 8] 8 9] (no solution) 10] 17 Worksheet # Answers: p w LA V 1] y= (1 + ), y= ] y=, y= 8 ] l = ] h = ] w = π r lgh 9 A PV I ] F = C+ 7] b 1 = b 8] t = 9] l = d w h 10] P = h nr (1 + r) t Worksheet # Answers: 1] m = ] m= undefined ] y = + ] y = 9 ] y = ] y=

19 7] y = 8] y = Worksheet # Answers (con t): 9] y = 10] = 11] + y= 8 1] y 1] y> 1 19

20 Worksheet # Answers: 1] (,) ] infinitely many solutions ] (no solution) ] (,7) ] (no solution) ] infinitely many solutions 7] 1, Worksheet #7 Answers: 1] ] ] 9 ] 0d + 7d + 1 ] 9 1 ] w 10w+ 7] 1a + a+ 9 8] ] ( )( ) 10] ( 9)( + 9) 11] ( 9)( ) 1] ( )( 1) 1] cannot be factored 1] 0( )( 1) 1] ( ) + 1] ( )(+ ) Worksheet #8 Answers: 1] ( + ) ] ( + )( ) ] ( + )( + ) ] ( 7)( + ) ] ( + )( 7) ] ( + )( + 1) 7] ( 1)( ) 11] 1 = ; = 1] 1] = 17] + 8] = 7; = 10 9] = 0; = 10 10] = ; = 10 = ; = 1] =, 18] = ± 19] 1 = ; = 1] = 0, 1] =± 11 ± 0] (no solution) Worksheet #9 Answers: 1] c ] 1 n ] ] ] y 10 ] 1 7] 8] a 9 7a 9] n 10] ] 1] 1 a 1] 1 1] a 1] 1] 8 17] 18] y m 19] 0] 9y 8 1] 1 1 y 1 ] m ] 1 ( a+ b) ] ] 1 ] a Worksheet #10 Answers: 1] ] ] ] 10 ] ] 0 7] 8] 1 9] 1 10] 11] simplified now 1] 1] 1 1] 11 1] 10 1] ] 18] 0

21 19] 1 0] 1] + ] 8+ ] + Worksheet #11 Answers: 1] ] ] 7 ] 1 ] 1 ] 7] 1 8] 9] 0 10] 11] 1] 1] 8 8 1] 1] 1].0 17] 18].1 1