For students entering Honors Precalculus Summer Packet
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1 Hoors PreClculus Summer Review For studets eterig Hoors Preclculus Summer Pcket The prolems i this pcket re desiged to help ou review topics from previous mthemtics courses tht re importt to our success i Hoors Preclculus. Show ll work tht leds ou to ech solutio o seprte sheets of pper. You m use our otes from previous mthemtics courses or olie serches to help ou. These prolems re to e completed without clcultor, uless otherwise idicted. This pcket will e collected d grded the secod d of school. You will e tested the first week of school over this mteril. It will e recorded s our first test d cot e retke. ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL. Qudrtic Formul: Give c 0, the Referece Iformtio. Not provided o the test. 4c. 3 3 Fctorig: 3 3 Lws of Epoets: ( ) m m Forms of Equtios of Lies: Geerl ( Stdrd ) Form: m ( ) m 1 m m or A B C Slope-Itercept Form: m m Poit Slope Form: m ) Verticl Lie: 1 ( 1 Horizotl Lie: Distce Formul (give poits, ) d, ) ): ( 1 1 ( d 1 ) ( 1 ) ( c d Midpoit Formul (give poits (, ) d ( c, d) ): M, Chgig etwee Logrithmic d Epoetil Form: log ( ) Bsic Properties of Logrithms: log 1 0 log 1 iff log log
2 Hoors PreClculus Summer Review Properties of Logrithms: Product Rule: log Quotiet Rule: log Power Rule: ( RS) log R S c log log R c log Imgir Numers: i 1 i 1 R log R log R S S Comple Numer writte i Stdrd Form: + i Properties of Asolute Vlue: 0 Simplif ech epressio. SHOW ALL WORK ON A SEPARATE SHEET OF PAPER. Uless otherwise specified, if deciml pproimtio is used, it must e ccurte to three plces fter the deciml poit ( i 7) (3 + i) + (5 + 7i) 6. i (3 - i) 7. (3 + i) (3 - i) 8. (3 5) i 9. 8 i ( 9)(6 5) Fctor ech polomil completel. 1. t 4t d + 6d c d. 3 15e f. 3 15g h
3 Hoors PreClculus Summer Review Simplif ech epressio (5 )( ) ( t )( t ) 19. ( c ) 6 Solve ech equtio. 0. (5-)(3+1)=0 1. ( 4) (4 ) = = 0 3c d e. z 1 z 1 4 = 0 3f. ( 1)( 3) = 15 Multipl. 4. ( + 3) 5. (15 + )(15 ) 6. ( + 5) 3 Give f ( ) 4d g ( ) 4, determie ech of the followig. 7. f (3) 8. f ( ) 0, whe =? 9. f (g(4)) 30. f ( g( )) 31. Domi of g() 3. f 1 ( ) 33. Rge of f() Simplif ech d write our swer s sigle frctio. Stte restrictios o the vrile
4 Hoors PreClculus Summer Review Solve ech equtio for Fid the solutio(s) of the give sstems of equtios. Write swers i the form (, ) Solve for the missig side of the trigle usig the Pthgore Theorem, + = c. 4. = 6 ft., = 8 ft. 43. = 17 ft., c = 19 ft. c Solve for d usig (rtio of sides 1:1: ) or trigle (rtio of sides 1: 3 : ) i ft cm Give the right trigle, determie the trigoometric rtios. B 47. si A 48. cos A t A 50. si B 51. cos B 5. t B C 15 A Use trig rtios to solve for d (to the erest thousdth) i ech right trigle
5 Hoors PreClculus Summer Review Evlute ech logrithmic epressio without clcultor. 55. l 1 e log log log 5 5 Solve ech equtio or iequlit. Write i itervl ottio Fid equtio i slope itercept form for the lie descried. 6. The lie through ( 3, - ) with slope m = 4/5 63. The lie through the poits ( -1, -4 ) d ( 3, ) 64. The lie through ( -, 4 ) with slope m = The lie through (, -3 ) d prllel to the lie + 5 = The lie through (, -3 ) d perpediculr to the lie + 5 = 3 Fid the distce etwee the two poits. The fid the midpoit of the segmet joiig the two poits. 67. (-4, -3), (1, 1) Simplif. No decimls. 68. (5 6 )( ) i 98 Divide usig sthetic divisio Simplif comple frctios.
6 Hoors PreClculus Summer Review z z Write ech epressio s sigle logrithm. The simplif if possile. log log5 4log5 77. Write ech epressio s sum or differece of logrithms. Do ot use epoets. Simplif. log log3 3 c 9 Solve for. Use clc o 85, = log log () = 80. log = log8 = log log log log log ( 3) log144= = 90 Solve completig the squre. Show ll steps. No decimls i swers Solve the sstem Fid ceter d rdius for the circle Grph. Write domi d rge. 93. f() = f() = f() = log 96. f() = l = = 3 1 The ed. See ou i August.
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