Pre-Calculus Summer Assignment

Transcription

1 Pre-Calculus Summer Assgnment Dear Future Pre-Calculus Student, Congratulatons on our successful completon of Algebra! Below ou wll fnd the summer assgnment questons. It s assumed that these concepts, along wth man others, have been mastered b ou, the ncomng Pre-Calculus student. There wll be an assessment on ths materal wthn the frst fve das of school. Ths assessment wll be an ndcator of our foundaton for the course, hence our success wth the new materal Pre-Calculus offers. It s strongl suggested that ou take ths assgnment serousl. Ths assgnment should be completed pror to the frst da of school. Watng to start t the nght before the frst da of school s not a wse dea. When ou fnd ourself unable to answer a queston, do not skp t research t. That research can be n the form of a parent, a frend, free on-lne help lke brghtstorm.com and kahnacadem.org, or our old Algebra notebook. The webstes are user-frendl and offer ecellent eplanatons. Defntel check them out as a resource. When ou return to school n September, we epect that ou wll have gone through all of the questons. Feel free to ask specfc questons pertanng to the summer assgnment wthn the frst few das of school. The Pre-Calculus teachers are here to help. Enjo our summer and we look forward to meetng ou n September.

2 Name Pre-Calculus Date Summer Assgnment Drectons: Please do all work on a separate sheet of paper. You ma draw the graphs on the coordnate planes that appear wthn ths packet. It s strongl recommend that these problems be completed wthout the ad of a calculator, unless ou are drected to use one. You wll not be permtted to use a calculator on man of the Pre-Calculus assessments throughout the ear, so ths gves ou an opportunt to sharpen our mental math sklls. There wll be an assessment on ths materal wthn the frst fve das of school. Good luck! Wrte an equaton n slope-ntercept form for the lne that satsfes each set of condtons. ) slope, passes through ( 6, 9) ) passes through ( 8, 5) and (, 0) ) passes through ( 6, 6) ) passes through (, ), parallel to =, perpendcular to = + Fnd the -ntercept and the -ntercept of each equaton. 6) f ( ) = 0 5) + 8 = 0 Graph each lnear equaton. 7) = 8) = f = + 0) + = 6 9) ( ) 5

3 Graph each lnear nequalt. ) > + ) 0 5 Solve each sstem b graphng. Descrbe t as consstent and ndependent, consstent and dependent, or nconsstent. Tpe of Sstem The Graph Soluton consstent and ndependent ntersectng lnes one soluton, (, ) consstent and dependent concdng lnes nfntel man solutons nconsstent parallel lnes no soluton ) = = ) + = = Solve each sstem algebracall (substtuton or elmnaton). 5) + 6 = 5 + = 6) = 5 = 7 7) 5 = 5 + =

4 Solve the sstem of nequaltes b graphng. 8) < 6 > 6 9) + + Smplf each epresson usng the laws of eponents. No negatve eponents n our fnal answer. 0) ( ) ) ( )( 7 ) ) a b 5 5c d ) 7 8c d Smplf each epresson. ) ( m + )( m 5) 5) ( + 5) 6) ( + 5)( 0 + 5) 7) 5c ( c c + ) c( 7c 8) 8) a b 6ab + ab ab 9) ( ) Smplf each radcal epresson. No decmal appromatons! 0) 7 c 8 6 ) 8 b ) 8 ( + ) ) 75 ) 5) 0 6) d c 7) 8 8) ) ) ) ( 7 )( 7 + )

5 Ratonalze each denomnator. (Use conjugates to ratonalze bnomal denomnators.) ) ) 5 5 ) 5 5) Evaluate each epresson nvolvng ratonal eponents. 6) 9 7) 5 8) 7 9) 6 5 Perform each operaton f f ( ) = 7 and ( ) = + g. 50) f ( 0) 5) g ( a ) 5) g [ f ( ) ] 5) f [ g( ) ] Graph each quadratc functon and complete the chart. Remnder: The formula for the equaton of the as of smmetr s = b a 5) f ( ) = + opens up or down? -ntercept As of Smmetr Verte (, ) Doman Range 55) f ( ) = opens up or down? -ntercept As of Smmetr Verte (, ) Doman Range

6 Mr. Goodman, who knows a lot about phscs, s gong to fre a rocket to start off ths ear s Battle of the Classes. He has done testng on the rocket to ensure t wll not ht an students. If the rocket s launched upwards wth an ntal veloct of 00 feet per second, ts heght h (t) (n feet) can be found b the functon h ( t) = 6t + 0t, where t s the number of seconds snce t was launched. 56) How long wll t take for the rocket to reach ts hghest pont? 57) What s the mamum heght that the rocket wll reach? Gudelnes for Factorng: Alwas look for a GCF before dong anthng else. Consder the number of terms n the polnomal. Two Terms: Tr factorng as a dfference of two squares, or a sum or dfference of two cubes. a b = ( a + b)( a b) ( )( b = a b a + ab b ) + b = ( a + b)( a ab b ) a + a + Three Terms: Trnomals of the form a + b + c can be factored nto the product of two bnomals. (Use a method that our Algebra teacher taught ou.) More Than Three Terms: Tr factorng b groupng. Make sure the polnomal s factored completel. Ths means that each remanng factor s prme. Factor each polnomal completel. 58) 8ab ab 59) + 60) ) 9 d c 9 6) 90 6) ) ) ) ) 5 68) ) 8a ab + 6b

7 The magnar unt s defned as the prncpal square root of and can be wrtten as =. Snce =, t naturall follows that ( ) = ( ) = Hgher powers of can be found Here are the frst eght powers of. usng the followng method. = = = ( )( ) = ( )( = ) = A comple number s a number that can be wrtten n a + b form. Smplf each epresson. 70) 7) 6 7) 7) ( ) ( 5) 7) ( 5 ) + 75) + Solve each equaton b factorng. Epress our solutons n smplfed radcal form, f necessar. 76) 0 = 0 77) = 8 78) = Solve each equaton b completng the square. Answer n smplfed radcal form, f necessar. 79) = 0 80) = 0 Solve each equaton b usng the Quadratc Formula. Answer n smplfed radcal form, f necessar. 8) + 6 = 0 8) + 8 = 6 5 b ± = b ac a Solve each quadratc equaton usng an method. Answer n smplfed radcal form, f necessar. 8) ( + 5 )( ) = 8) + 7 = 0 85) Normal sstolc blood pressure s a functon of age. For a woman, the normal sstolc blood pressure (n mllmeters of mercur) s gven b the functon P = , where s the woman s age. Use ths functon to fnd the age of a woman whose sstolc blood pressure s measured to be mllmeters of mercur. (Hnt: Use the Quadratc Formula)

8 Smplf each epresson. 86) k k 5 k k + 0 u 5 87) 5 5z u 88) ) 6ab 8a 90) ) ) + + Match each parent graph to ts equaton. A) f ( ) = B) f ( ) = C) f ( ) = D) f ( ) = E) f ( ) = F) ( ) = log G) f ( ) = H) f ( ) = [ ] f 9) 9) 95) 96) 97) 98) 99) 00)