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 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 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

2 Information Sheet Quadratic Formula: b b ac a y y y rise Slope: m run Standard form of a line: A By C Standard form of a Quadratic: A B C 0 Slope-Intercept form of a line: y m b Point-Slope form of a line: y y m Pythagorean Theorem: Right Triangle Trig Ratios: a b c length of the opposite side sine= 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 Eponents: a 0, a 0 a n, a n 0 a ab a b m m m a m n a mn m m m n m n a a a a mn a a a, a 0, a 0 n n a b a m

3 Order of Operations Worksheet # NAME Period Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each epression and leave your answer in simplest form. ] ( + ) ( ) ] 7 8 ] 7 ] 9 ] 7 ] 8 7] 8] 9] 9 9 0] 8 ] ( ) 7 ] 8 ] ] 7 ] ] 8

4 7] 8] 7 8 9] 0] 7 ] 8 ] 8 ] 9 0 ] ] ] 9 0 ANSWERS Worksheet #: ] 7 ] ] ] 0 ] 7 ] 7] 8] 9] 0 0] ] ] ] 8 ] ] ] 9 7] 7 8] 9] 0] ] 9 ] ] ] ] ] 0 8

5 Simplifying and Evaluating Epressions Worksheet # Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each epression for the given value of and/or y. ] ( 7), ], ] ( ), 8 ] y 7 y, y ] y,, y ] ( y),, y y 7],, y ( y) y 8] y,, y 9] ( ) y,, y Simplify each epression and leave your answer in simplest form. Also be sure your answer is in standard form. 0] + 9 ] ()(-) ] ] ] (7 ) ] ] y y y 7 y y 7] - + (- + ) 8] y y y 9] ( + y) ( y + ) 0] 0 00 ] ( ) ( )

6 Simplify each epression and leave your answer in simplest form. Also be sure your answer is in standard form. ] ( ) ( ) ] y y ] ( 9 ) (0 0 ) ] 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. ] pn 7] p n 8] np 9] n 0] np ] n ] p ] p n ] p n ANSWERS: ] 0 ] ] ] 8 ] ] 7] 8] 0 9] 98 0] ] ] ] 0 ] 8 ] 7 ] y y y 7] 8] y y 9] 78 y 0] ] ] y y ] 7 ] 0 ] ] always negative 7] sometimes positive/sometimes negative 8] always positive 9] always positive 0] always negative ] always negative ] always negative ] sometimes positive/sometimes negative ] always positive

7 Solving Linear Equations Worksheet # Solve the following equations for. You must show all algebraic steps. Please also include a CHECK of your solution. Do not use a calculator when completing the worksheet. ] ] 7 ] 8 ] y8 ( y ) ] 7 ( ) 8 ] 7 7] 0 8] 9( ) 9] ( ) ( ) 0]..8.8( ) ] ( ) ] ( ) ( ) 0 ] ] 7 ] 7

8 Solve the following equations for. You must show all algebraic steps. Please also include a CHECK of your solution. Do not use a calculator when completing the worksheet. 0 ] ] 7 ] ] ] 8] 0 9] ( ) 0] n( n) 9 ] t t ] b b ] ( p p p ) ( p ) ] 8 0 ANSWERS: ) 7 ) ) ) 0 0) ) 0) 7 ) 7 ) 0 ) 7) 00 8) 7 9) (all real numbers) ) ) ) 7 ) ) No Solution 7) 7 8) 8 9) ) ) (no solution) ) 00 8

9 Solving Literal Equations Worksheet # For each equation below, a) Solve each equation for y in terms of, showing your work. b) Then evaluate when =. ] y 8 ] y ] y ] y ] ( y) 7 ] y y Solve each equation for the indicated variable. 7] p w for 8] LA rh for h 9] V ( w h ) for w 0] C ( F ) for F ] A h ( b ) b for b ] PV nrt for T 9 9

10 Solve each equation for the indicated variable. ] h gt for g ] d w h for ] I P( r) t for P 8 Answers: ) y, y 0 ) y, y ) y, y 7 p w ) y ( ), y ) y, y ) y, y 8 7) LA V 9 A PV h 8) h 9) w 0) F C ) b b ) T ) g r h h nr t I ) d w h ) P ( r) t 0

11 Linear Functions Worksheet # 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. ],, 8, ],,, ],8,, Graph the functions. ] y ] y 7] y 8] y 9] 0] y8

12 Graph the functions. 0] y ] y ] y Graph the inequalities. ] y ] y ] ] y 7] y 8] y

13 ANSWERS: ] m ] m ] slope is undefined ] y ] y 7] y 8] y 9] 0] y8 0] y ] y ] y

14 Graph the inequalities. ] y ] y ] ] y 7] y 8] y

15 Systems of Equations Worksheet # You should NOT use a calculator to complete this worksheet. Please DO use a straightedge when graphing. Solve each system of equations by graphing. ] y y ] y y 7] y y 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. ] y y ] y y 7 ] y 7 y 7] 7y y 0

16 8] y y 0 9] 8 y y 0] 7 0y y 7 ] y y ] 9y 9 y 0 ] y y ANSWERS: ] (,) ] infinitely many solutions ] no solution ] (, 7) ] (, ) ] (,) 7] (, 0) 8] (0, ) 9] no solution 0] (, ) ] infinitely many solutions ] (,) ],

17 Multiplying Epressions Worksheet #7 You should NOT use a calculator to complete this worksheet. Find each product. All answers should be in standard form. ] ( ) ] yy ( ) ] ( ) ] ( y)( y ) ] ( c)( c ) ] ( )( 9) 7] ( )( 7) 8] ( )( 9) 9] ( 8)( 7) 0] ()( ) ] ( 7)( 7) ] ()( ) ] ( )( ) ] ()( ) ] ()( 9) ] (d)(d 7) 7] (q7)(q 8) 8] (z7)(z ) 9] (7)(7 ) 0] ( w ) ] ( 9) 7

18 Find each product. Your answers need to be in standard form. ] (t ) ] ()( ) ] ()( 7) ] (b ) ] (9w 8) 7] ()( ) 8] (t ) 9] ( n 0) 0] ()( ) ] (a ) ] (w)(w ) ] ( ) ] ] 8 9 ] ( ) 7] 7 7 8] 0 0 9] 0] ] 9 ] 7 y y ANSWERS: ] ] y y ] ] y 9 y ] c c 8 ] 7] 8 8] 9] 0] 9 ] 9 ] 9 ] 0 ] 7 ] ] 0d 7d 7] q q 8] 0z z 9] 9 0] w 0w ] 8 8 ] t t 9 ] 7 0 ] ] 9b b ] 8w w 7] 8] t 0t 9] n 0n 00 0] 9 ] a a 9 ] w 9 ] 9 0 ] ] 7 ] 7 7 7] 9 8] ] 0] ] 0 ] 7 0y y 8

19 Factoring and Solving Quadratic Equations Worksheet #8 You should NOT use a calculator to complete this worksheet. Factor each quadratic epression. Remember to check for common factors. If the epression cannot be factored, so state. ] 9 0 ] 9 9 ] ] ] 8 ] 7] 8] 8 8 9] 9 0] ] ] t t 7 ] ] ] 0 ] 0 9 7] 8] 8 9] 8 0] 0 7 ]

20 Factor each quadratic epression. Remember to check for common factors. ] ] 0 ] Solve the equation by factoring. Include your algebra and be sure your solutions include statements =. Checking your solutions is advised. ] 0 ] ] 8 8] 0 9] 9 8 0] 8 0 ] y 7y 8 ] 7 0 ] 0 0 ] ] 8 ] 8 0

21 7] 0 0 8] ] 9 0] 0 ] ] 0 ] 0 ] 0 ] Use the quadratic formula or completing the square to solve the following equations. ] 0 7] 7 0 8] 7 0 More factoring practice. 9] 0] 0 ] ] 9 ] ] ] 7 ] 0 7]

22 8] 9] 0] ] ] ] ] ] 0 ] 9 ANSWERS ] ( )( ) ] 9 ( ) ] 7] ( 9)( ) 8] ( 8) ] ( )( ) ( 9) 9] ( )( ) ] ( 9)( 9) ] ( 8)( 7) 0] ( 9)( ) ] ( 7)( ) ] ( t)( t ) ] ()( ) ] cannot be factored ] ( ) ] ()( ) 7] ( ) 8] ] ] ( )( 9) ( ) 9] ( )( ) 0] ()( ) ] 0( )( ) ] ()( ) ] ; ] 7; 0 7] ; 8] 0; 0 9] 8; 0] ; 0 ] 9; ] ; ] 0; ] ; ] 8; ] 7],0 8] 0, 9], 0] ] ], ],0, ] 7] ; 7 ] ] 8] 9] 0] ] 7 ] ] ] ] ] 0 7] 8] 7 9] 9 7 0] 8 7 ] 7 ] ] ] ] ],

23 More Simplification Worksheet #9 You should NOT use a calculator to complete this worksheet. Simplify each epression. Your answers cannot include negative eponents. If an epression cannot be simplified, state simplified now. ] c c ] y y ] n ] a ] ] n n ] 9 8] 0n 8 0n 9] y 0] c ] a a ] 0 m ] 7a a ] 0 ] n

24 Simplify each epression. Your answers cannot include negative eponents. If an epression cannot be simplified, state simplified now. ] a 7] 8] 9 9] 0] a a a ] a ] 9 ] a b b ] a n n n 0 ] a 7a ] 0 7] 8] 7 7 9] 0] y 7 y ] 7 ] 0y 9 y ] y m y m 8 ] ] ] y

25 7] y 8] y y 9] m 0] y ] a b a b 7 ] ] 0 ] 7y y 0 ] a a ANSWERS: ] c ] 8 y ] n ] a ] ] 7] 8] 9] n y 0 0] c 0 ] ] ] a 0] simplified now ] a 9] 8 0] 9 y ] 9 7a ] ] 0 n ] 0 a 7] 9 8] 7 9] ] ] ] simplified now ] a ] 7] 8] ] 7 y ] y m 7 ] 0 ] ] 8 y 7] 7 9y 8 8] y 9] m 0] 0 y ] a b ] ].7 0 ] ] a

26 Simplifying Radical Epressions Worksheet #0 You should NOT use a calculator to complete this worksheet. Simplify each epression, that is, write it in simple radical form. If an epression cannot be simplified, state simplified now. ] 08 ] 7 ] 7 ] 80 ] 8 ] 7] 8] 0 9] 0 0] 00 ] ] ] 0 ] a a ] ] 0 7] 8] 8 9] 0] 9 ] 0 9 ] ] ]

27 Simplify each epression, that is, write it in simple radical form. If an epression cannot be simplified, state simplified now. ] ] 7 7] 8] 9] 7 0 0] ] 0 ] 8 8 ] 00 ] 8 ] 7 ] 0 7] 0 8] 8 9] 0 7 0] ] 0 ] 7 ] ] 7 ] 99 7

28 Answers should be rationalized, no radicals in the denominator. ] 7] 7 8] 9] 0] 8 ] 0 ANSWERS: ] ] ] 7 ] ] ] 7 7] 8] 9] 0] 0 ] ] ] ] a ] 7 ] 0 7] 8] 9 9] 0] ] 7 ] 7 ] ] ] ] 7 7] 8] 9] 0] 0 ] simplified now ] ] ] ] ] 0 7] 8] 9] 0] 0 ] ] 80 ] ] ] ] 7] 8] 9] 0] 8 ] 8

29 Pythagorean Theorem and Right Triangle Trig Worksheet # Solve for in each of the following right triangles. Find eact answers. ] ] ] 0 ] ] ] 0 7] 8] 9] ] ] ] 0 9

30 Using the given right triangle and without a calculator find the following trig ratios. ] Solve for sin. ] Solve for tan. ] Solve for cos. 7 Using the given right triangle and a calculator find the measure of to the nearest hundredth of a degree. ] 7] 8] 7 ANSWERS: ] ] ] 7 ] ] ] 7] 8] 9] 0 0] ] ] ] 8 8 ] ] ].0 7] 8]. 0