SUMMER ASSIGNMENT FOR Pre-AP FUNCTIONS/TRIGONOMETRY Due Tuesday After Labor Day!

Transcription

1 SUMMER ASSIGNMENT FOR Pre-AP FUNCTIONS/TRIGONOMETRY Due Tuesdy After Lor Dy! This summer ssignment is designed to prepre you for Functions/Trigonometry. Nothing on the summer ssignment is new. Everything is review of topics students lerned in Alger I & II nd Geometry. If you wnt to e successful during Functions/Trig, you must e le to understnd nd pply this informtion throughout net yer. The ssignment my e completed with nother student ut e certin tht YOU understnd how to complete every prolem. Since new lesson will e tught nd homework ssigned the first dy of school, we suggest you complete this ssignment efore the end of summer. Netly show ll work for ech prolem, using pencil. Clcultors re only necessry for #8, nd should not e relied upon for the reminder of the ssignment. During the second week of school, you will hve quiz covering ll of the mteril from the summer ssignment. If you need to review these topics or see emples, we recommend the wesite which lists mny Alger review topics. If, fter reviewing, you need further ssistnce, plese e-mil Mrs. Krimmer t krimmedc@pwcs.edu or Ms. Binotto t inotter@pwcs.edu with questions or to mke rrngements to meet with techer fter the school yer egins. The ssignment will count for etr credit on your mrking period grde if completed correctly, with ll work shown, nd on time. Properties of Eponents: n m n n ( ) m n mn ( )( ) 0 1 mn PurpleMth Topics: Beginning Alger Topics: Eponents: Bsic Rules Negtive Eponents Simplifying with Eponents Simplify the following epressions using the properties ove. Leve no negtive eponents w p 8. (w )(5w ) y t. 4. ( 1 y z ) ( ) (6 ) y z y z

2 Rtionl Eponents: n m m n PurpleMth Topics: Beginning Alger Topic: Eponents: Frctionl Eponents Simplify the following epressions using the property ove. Epress rdicls s frctionl eponents n t Comple Numers: 1 i PurpleMth Topic: Advnced Alger Topics: Comple Numers Simplify the following epressions using imginry numers i 1. 5 i i Qudrtic Formul: 4c PurpleMth Topic: Intermedite Alger Topics: Qudrtic Formul Solve the following qudrtic equtions using the qudrtic formul. Simplify s much s possile y 1 y 17. 4w 11w c c 7 0

3 Fctoring: Alwys look for gretest common fctor first: ( 1) Perfect Squre Trinomils: or ( ) ( Difference of Squres: ( )( ) Sum of Cues: ( )( ) Difference of Cues: ( )( ) ) PurpleMth Topics: Beginning Alger Topics: Simple Fctoring Intermedite Alger Topics: Fctoring Qudrtics Solving Qudrtic Equtions Specil Fctoring Formuls Solve the following equtions using fctoring. Show fctored eqution nd give ll solutions (rel nd imginry) p p 5p p 19 p n 5n 6 0

4 Pythgoren Theorem: c PurpleMth Topic:...nd the eginnings of trig: Pythgoren Theorem Solve for the unknown in ech of the figures elow. Give nswers s simplified rdicl or frctions if possile in. 4 in. ft 4 ft Trigonometry: sin cos tn opposite hypotenuse djcent hypotenuse opposite djcent PurpleMth Topic:...nd the eginnings of trig: Bsic Trigonometric Rtios Inverses of Trigonometric Rtios Specil Angle Vlues Use the following right tringles to find the vlue of the unknown. Give nswers s simplified rdicl or frctions if possile p 8 yd mm z 51 cm r 68 cm

5 Lines: slope: m midpoint: y y1 1 y1, 1 y eqution of line: distnce: r = y m ( ) ( y y ) 1 1 PurpleMth Topics: Beginning Alger Topics: Slope of Stright Line Midpoint Formul Stright-line Equtions Distnce For ech of the following sets of points, find: ) the slope ) the eqution of the line tht fits these points 4. (, 8) (6, 0) c) the midpoint d) the distnce from point to point 5. ( 5, 4) (10, 8) 6. ( 0, 4) (0, )

6 Binomil Epnsion: ( ) ( )( ) PurpleMth Topic: Beginning Alger Topics: Polynomils: Multiplying Epnd the following epressions. 7. ( 4) 8. ( 1)( ) Rtionl Epressions: p( ) If f ( ) q( ) p( ) s( ), then f ( ), r( ) q( ) r( ) s( ) where q( ) 0, s( ) 0, r( ) 0 PurpleMth Topics: Advnced Alger Topics: Rtionl Epressions: Simplifying Rtionl Epressions: Adding Rtionl Epressions: Multiplying Comple Frctions Simplify the following rtionl functions. Stte ny domin restrictions (No zeros in the deomintor) y y y

7 Grphing: Chnges to the outside of f () ffect grph verticlly. Chnges to the inside of f () ffect grph horizontlly. Domin is the set of possile -vlues. Rnge is the set of possile y-vlues. PurpleMth Topics: Intermedite Alger Topics: Domin nd Rnge Grphing Qudrtic Equtions Grph the following functions. Stte the domin nd rnge of ech. 44. f ( ) ( ) 46. f ( ) 45. f ( ) 4

8 Systems of Equtions: f ( ) The solution to system of equtions,, g( ) is the point of intersection, (, y), of the functions. 47. Solve the system using sustitution: 4 + y = 9 y = 4 PurpleMth Topics: Advnced Alger Topics: Solving Systems of Liner Equtions Sections: Sustitution (p. 4) Elimintion/ddition (p. 5) 48. Solve the system using elimintion: m n = -1 m + n = 0 Common Mistkes in Alger Decide whether ech of the following simplifictions is ccurte. If it is not, correct the right side of the eqution to mke it true ( ) ( ) ( ) 55. ( 5) ( 5)( 5) ( ) y 7y

9 y y

10 69. y y 70. ) ( w z y z w y