Name: A2RCC Midterm Review Unit 1: Functions and Relations Know your parent functions!

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A meteorologist drew the ccompyig grph to show the chges i reltive humidity durig 4-hour period i New

1 Nme: ARCC Midterm Review Uit 1: Fuctios d Reltios Kow your pret fuctios! 1. The ccompyig grph shows the mout of rdio-ctivity over time. Defiitio of fuctio. Defiitio of 1-1. Which digrm represets oe-to-oe fuctio? 1) ) ) 4) Domi d Rge 4. A meteorologist drew the ccompyig grph to show the chges i reltive humidity durig 4-hour period i New York City. Stte the domi i itervl ottio: Stte the rge i itervl ottio:

2 Evlutig fuctio 5. The fuctio y = f() is show grphed. Determie f(). 6. Fid ll the reltive mimum d miimum vlues of the fuctio. Stte the vlues of where they occur s well. Coordites of reltive mimums: Coordites of reltive miimums: Is there bsolute mimum? Absolute miimum? Why or Why ot? Fid ll the itervls where this fuctio is icresig: Fid ll the itervls where this fuctio is decresig: Where is this fuctio egtive? Is this fuctio positive over (0, 5)? Evlutig compositios of fuctios 7. Iverse of fuctio 8. f ( ) 7 5 f 1 ( ) Is the iverse fuctio?

3 Set Nottio 9. Write set for ech umber lie grph usig BOTH set builder d Itervl ottio. A) B) Set builder: Itervl: Set builder: Itervl: Restricted Domis 10. Fid the domi for ech d write it i set builder ottio. 5 A) f()= 5 1 B) g()= 10 C) h()= 5 Uit : Lier fuctios Averge rte of chge 11. The verge rte of chge of f ( ) 5 14 from 1to is Regrdig the grph t the right, wht is the verge rte of chge over the itervl 1 5? Direct Vritio 14. y vries directly s. If y = 4, whe = -, fid whe y =

Forms of Lier Equtios Write the slope-itercept form of lie : Write the poit-slope form of lie : 14. The poit-slope form 1... 4.

Prllel d Perpediculr lies 17. Write lie i slope-itercept form prllel to the lie y= --5 d psses through the poit (4, 7). 18.

4 Forms of Lier Equtios Write the slope-itercept form of lie : Write the poit-slope form of lie : 14. The poit-slope form Writig lier equtio give poits 16. Write the poit-slope AND the slope-itercept form of the lie tht psses through the poits (, 5) d (-4, 8). Prllel d Perpediculr lies 17. Write lie i slope-itercept form prllel to the lie y= --5 d psses through the poit (4, 7). 18. Write lie i slope-itercept form perpediculr to the lie y= --5 d psses through the poit (4, 7). Piece-wise d Step fuctios 19. I the piecewise fuctio. The vlue of f(-7) equls Write the Domi, Rge d the equtio(s) for the grph:

5 Absolute Vlue EQ. d INEQ. 1. Solve the followig iequlity or Solve for grphiclly. 1 7 Systems of Lier Equtios. Solve for, y d z lgebriclly. 4z 19 y 5 z 4 5y z 5

6 Lier word problem 4. The dmissio fee t smll fir is $1.50 for childre d $4.00 for dults. O certi dy, 00 people eter the fir d $5050 is collected. How my childre d how my dults tteded? Solve this lgebriclly usig system of equtios. Check it grphiclly! Uit : Epoets d Logs Epoet rules 5 5. Simplify u v 4 1) 81 v 8 0 u ) 6. The epressio 6 9 1) 4 u 8 v 0 81 is equivlet to ) 4 ) u v ) ) 4 4) 8 0 u v Simplify: Frctiol epoets d Rdicl form 8. Write s frctiol epoet: 6 5 b 9. Write s simplified rdicl 7 11 Epoetil Log form B E N log B N E 0. Rewrite the epoetil equtio i logrithmic form. ) 64 4 b) Rewrite the logrithmic equtio i epoetil form. ) log 49 b) log 8 7

7 Log Properties log y z. The epressio log log 1) z log ) y ) z y log 4). The epressio log 4 1) log log 4log is equivlet to log log is equivlet to z y z y ) log 4log ) log( ) 4log 4) log( ) 4log Solvig epoetil equtios 4 Use commo bses to solve for Use logs to solve for. e 7 6. Use log properties to solve for. ( 5 14) log ( ) 4 log 7. Use log properties to solve for. ( 1) log ( 4) log 6 log

8 Epoetil growth d decy 8. You drik beverge with 10 mg of cffeie. Ech hour, the cffeie i your system decreses by 1%.. Write equtio to model the umber of mg of cffeie i your system fter drikig the beverge. b. Accordig to this model, lgebriclly determie how log it tkes to the erest hour, util you hve 10 mg of cffeie left i your system. Cotiuous d compoud iterest 9. Cody d Eryl both ivest $10,000 t.% iterest. Eryl s bk compouds iterest cotiuously, rt ccordig to the formul A Pe. Cody s bk compouds iterest mothly, usig the formul t r A P 1, where P is the iitil pricipl, r is the rte of iterest, is umber of times compouded per yer, d t is time, i yers. Determie, to the erest dollr, the mout of moey ech will hve fter 10 yers. You must show lgebric work!

9 Uit 4: Arithmetic d Geometric Sequeces Arithmetic Equtio Type Lier Formul for the th term: 1 d( 1) where 1 is the iitil term d d is the commo differece 40. Fid the two-hudredth term, 00, of the sequece, 5, 8, 11, Write equtio for the th term of the rithmetic sequece 8, 17, 6, 5, Geometric Equtio Type Epoetil Formul for the th term: 1 ( r where 1 ) 1 is the iitil term d r is the commo rtio 4. Which formul represets the th term i the sequece? 1 1. ( ). ) (. 1 () 4. ( ) 4. Wht is the commo rtio of the geometric sequece whose first term is 1 d fifth term is 60.75? Write the eplicit equtio of the geometric sequece whose first term is 1 d fifth term is Sigm ottio 45. Simplify. (Show work) 1 Arithmetic d Geometric Series 46. Fid the sum of the first 7 terms i the rithmetic series

10 Use your referece sheet 47. Fid the sum of the first 17 terms of the geometric series 6, -1, , Recursive sequeces 48. Wht is the fifth term of this sequece? Uit 5: Qudrtic Fctorig 49. GCF: DOPS: Triomil: Triomil: 4 5. Groupig: Solve ech qudrtic equtio usig the method specified. 54. ) Fctorig5 16 = 0 b) Qudrtic Formul (Leve roots i simplest rdicl form)

11 c) Squre Root Property d) Completig the Squre (Roud to the erest hudredth) (Leve roots i simplest rdicl form) ( 4) Polyomil idetity ( b) b b ( b) b b 55. ( + 4) = 56. ( - 5) = Qudrtic Iequlities 57. ) Grph 4 0 b) Solve d grph o #lie Circles. Write the equtio of the circle i ceter-rdius form. 58. ) Ceter: (, -) rdius: 4 b) Ceter: (-5, 4) poit o circle: (1, ) Use distce formul to fid the rdius! c) 8 y 6y 16 (You must complete the squre!)

12 Verte-form of qudrtic equtio 59. Put ito verte form to determie the turig poit = 0 Is the verte mimum or miimum? Locus defiitio 60. Determie the equtio of the prbol whose focus is the poit (. 5) d whose directri is y = Determie the equtio of the prbol whose focus is the poit (-1, 4) d whose turig poit is (-1, 1).

Qudrtic word problem Show work!!!! 6. We re stdig o the top of 1680 ft tll buildig d throw smll object upwrds. At every secod, we mesure the distce of the object from the groud.

13 Qudrtic word problem Show work!!!! 6. We re stdig o the top of 1680 ft tll buildig d throw smll object upwrds. At every secod, we mesure the distce of the object from the groud. Ectly t secods fter we threw the object, its height, (mesured i feet) is h (t) = -16t + 54t ) Sketch the grph. Lbel es d your widow! b) Fid h () d epli the cotetul meig. c) How much does the object trvel durig the two secods betwee 5 secods d 7 secods? d) How log does it tke for the object to rech its mimum height? Wht is the mimum height? Roud to the erest teth. d) How log does it tke for the object to hit the groud roudig to the erest secod? Check your swers with the key o my website!!

For students entering Honors Precalculus Summer Packet

For students entering Honors Precalculus Summer Packet 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