Cherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry

Transcription

1 Cherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry 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 this class, 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 Order of Operations Worksheet # NAME Do NOT use a calculator when completing this worksheet. Show work whenever possible. Evaluate each epression and leave your answer in simplest form. ] ( + ) (7 ) ] 6 ( 7 8 ) g + ] 7 6( 9 ) ] ( ) ( ) 6] ( ) 5] 5 6 ( ) ( ) ] + ( 6) 6 8] g ( ) ] ( ) 7g 9 0] [ 5( 0) ( 0) ] 0 ] 5 ( 6) + 7 ] ( 8 )( ) + ( ) ] ]

3 5] = 6] ] + 7 8] 8 9 9] + 0] 6 5 ] 5 7 ] 5 ] ] 5] 8 9 6] ANSWERS Worksheet #: ] 6 ] ] ] 9 5] 9 6] 6 7] 9 8] 9 9] 0] ] 99 ] ] 5 9 5] 6] 7] 7 ] ] 5] 0 8] 5 6 6] 5 9] 0] 7 0 ] 0 7 ] 5 ] 5

4 Simplifying and Evaluating Epressions Worksheet # Do NOT use a calculator when completing this worksheet. Show work whenever possible. Simplify each epression and leave your answer in simplest form. Also be sure your answer is in standard form. ] + 5 ] (7)(9) ] ( 7+ 5) 5] ( 7) ] ( ) + 6] 9 ( ) 7] ( y +y y +6) ( 5y + y ) 8] (- + 5) 9] y( y)+ y 0] 5( + y) ( y + ) ] ) ( 5) (+ 5) + ] ( 7) ( ) ] y y 5] (6 ) (0 0 ) 6] ( 6) + ( 9 )

5 Given a =, b = and c = -5, evaluate each epression. Include the substitution step. 7] ab c 8] ac 9] a bc 0] a bc ] a ( b+ c) ] ( ac) b ] c + b ] c 5] ( c) ANSWERS: ] 8 ] 6 ] ] 9 5] 6 6] + 7] y + y y+ 9 8] + 0 9] y + 8y 0] 7+ y ] 6 + ] 5 ] + y y ] ] 6] 7] 8] 0 9] 5 0] ] 8 ] 7 ] ] 5 5] 5 5

6 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 0 = ] 8 9 = 8 ] ( ) = 6 5] ( ) = + 5 6] (0 ) = ( + ) = 0 + 8] 7] ( ) = ] + = 0] 8= ] ( + ) = ] ( ) = ( 0+ 5) 5 6

7 ] ( ) = + ] 8 + ( + 7) = 6 ( ) 5] ( + ) = -( 8) 6] ( ) = 8 ( ) 7] + = 8] = + 7 9] + = 5 0] = + 5 ANSWERS: ] = ] = ] No Solution ] All Real Numbers 5] = 6] = 7] = 8] = 7 9] = 0] No Solution ] = 7 ] = 8 ] = ] = 5] = 6] = 7] = 8 8] = 7 9] = 0] = 7

8 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. ] ( 5,5 ), ( 7,) ] (, 7 ), (,0) ] (,8 ), ( 7,8) Graph the functions. ] y= + 6] y = 7] y= 6 8] y = 5 9] = 0] + y= 6 8

9 0] y = 8 ] y = + 5 ] + 5y= 0 Graph the inequalities. ] y > ] y 5] < 6] y 7] y> 8] + y 9

10 ANSWERS: ] m = ] m = ] m = 0 ] y= + 6] y = 7] y= 6 8] y = 5 9] = 0] + y= 6 0] y = 8 ] y = + 5 ] + 5y= 0 0

11 ] y > ] y 5] < 6] y 7] y> 8] + y

12 Systems of Equations Worksheet #5 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 = 5 y = + ] y = 6 y = ] + y= 8 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= 6 + y = 6 5] + 7y = y = 5 6] 6 + 7y = 5 y = 0 7] 5y = 9 7 9y = 5

13 8] y = 5 y = 7 9] 6 y = y = 0] 9y = + 6y = ] + y = + 5y = ] 5 + y = + y = ] y = 7 6 y = ANSWERS: ] (, ) ] no solution ] infinitely many solutions ]( ) 6], 7] ( 6, ) 8] (, ) 9] No solution 0], ], ] an infinite number of solutions, 5] (, ) ] 5, 7 7

14 Multiplying Epressions Worksheet #6 You should NOT use a calculator to complete this worksheet. Find each product. All answers should be in standard form. ] ( 5) ] mm ( 5) ] ( 8+ ) ] ( t+ 8)( t+ 5) 5] ( t )( t ) 6] ( + 5)( + 7) 7] ( )( 6) 8] ( 5)( + 6) 9] ( 7)( + 8) 0] ( )( + ) ] ( 6)( + 6) ] ( 7)( + 7) ] ( 9)( + ) ] ( )( + 8) 5] (+ )( 8) 6] (d + )(d + ) 7] (q )(q+ 8) 8] (z+ 7)(z+ ) 9] (5+ 6)(5 6) 0] (w 5)( w+ 5) ] ( 9)(+ 5)

15 Find each product. Your answers need to be in standard form. ] (5t )(t+ ) ] (w 5)( w+ ) ] (+ )( 8) 5] (b )( b 9) 6] (9w+ 8)(w 0) 7] (6 5)( ) 8] ( t + 6) 9] ( n 0) 0] (+ )( ) ] (a + ) ] (w+ )(w ) ] ( ) ANSWERS: ] ] m 5m ] 8 + ] t + t+ 0 5] t 7t+ 6] ] ] + 0 9] ] 9 ] 6 ] 9 ] 7 8 ] ] 0 6] 6d + d + 7] q + 9q 8 8] 6z + 5z+ 9] 5 6 0] w + 5w 5 ] 5 ] 0t + 9t 9 ] w + w 5 ] 6] 99w w 80 7] ] t + t+ 6 9] n ] a + a+ 9 ] w 9 ] ] 0n+ 00 0] 9 b 8b+ 9 5

16 Factoring and Solving Quadratic Equations Worksheet #7 You should NOT use a calculator to complete this worksheet. Factor each quadratic epression. Remember to check for common factors. ] 7+ 6 ] 6 6 ] ] 6 6 5] 6 6] 6 7] + 8] ] 9 6 0] + 5 ] + 56 ] t + t 9 8 ] ] 9 5 5] + 6] ] 5 0 8]

17 Factor each quadratic epression. Remember to check for common factors. 9] ] 0 + ] ] 5 + ] ] 8 5 Solve the equation by factoring. Include your algebra and be sure your solutions include statements =. Checking your solutions is advised. 5] 5 = 0 6] + 5 = 0 7] 9= 8] = 0 9] + 6= 5 0] + = 5 ] y y= 8 ] = 0 ] 7= 0 ] = 5] + = 56 6] 8 = 7

18 ANSWERS Worksheet #7 ] ( 6)( ) ] 6 ( ) ] 7] ( 8)( ) 8] ( + 5) ] ( 8)( ) ( 0) 9] ( )( ) + 5] ( 8)( + 8) 6] ( )( + ) + 0] ( + 9)( 6) ] ( + 8)( 7) ] ( t 8)( t ) ] ( )( ) ] ( 5)(+ 5) 5] + ( ) 6] (+ )( + ) 7] 5 ( ) 8] ] ( )( ) ( + ) 9] (5 )( ) + ] ( )( ) 0] ( 5)( ) ] 5( 6)( ) + + ] ( 5)(+ ) 5] = 5; = 5 6] = ; = 7 7] = 7; = 8] = 0; = 0 9] = 5; = 0] = 6; = 9 ] = 6; = ] = ; = 5 ] = 0; = ] = ; = 5 5] = 8; = 7 6] = ; = 8

19 More Simplification Worksheet #8 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. ] b 6 b ] ( )( ) 6y y ] ( m ) ] ( ) a 5] ( ) 6] m m 7] ] 0n 8 5n 5 9] y 0] c 5 ] a a 5 ] 0 ] ( 5a 5 )( a ) ] ( )( 5) ( 0) 5] b 9

20 Simplify each epression. Your answers cannot include negative eponents. 6] ( a ) 7] 8] 5 ( )( ) ( ) 5 9 9] 0] a + a a ] 8a ] 6 ] a b b ] a 5 5 n + n n + 6 5] a + 5a 7 6] 6 7] 8 ANSWERS: ] b 5 ] 9 y ] 6 m ] 6a 5] 6 8 6] 7] 6 8] 9] n y 8 0] 5 c 5 ] a ] ] 8 5a ] 5 5] 0] simplified now ] a b 6] a 7] 7 8] 5 9] ] ] ] simplified now 5] a 6] 7] 0