Preliminary Examinations: Upper V Mathematics Paper 1

Transcription

1 relmr Emtos: Upper V Mthemtcs per Jul 03 Emer: G Evs Tme: 3 hrs Modertor: D Grgortos Mrks: 50 INSTRUCTIONS ND INFORMTION Ths questo pper sts of 0 pges, cludg swer Sheet pge 8 d Iformto Sheet pges 9 d 0 lese check tht our pper s complete Red the questos crefull 3 swer ll the questos o the seprte pper provded, ecept Questo 7c whch must be swered o the swer Sheet 4 Number our swers ectl s the questos re umbered 5 You m use pproved o-progrmmble d o-grphcl clcultor, uless otherwse stted 6 Roud off our swers to oe decml dgt where ecessr 7 ll the ecessr workg detls must be clerl show Equtos m ot be solved solel wth clcultor 8 It s essetl tht ou preset our work etl d logcll ge of 0

2 SECTION Questo NB clcultor m ot be used ths questo Workg must be show Solve for f: 3 0 Solve for f: c Solve for m f: m 4m d rove tht the equto 3 hs o soluto 4 e Solve for d f: log log 4 d + = Mrks Questo Fd f ' f f t 3t 4 Gve: 3 f q ; f 3 d f ' Wrte epresso for f ' Clculte the vlues of d q respectvel 5 Fd the equto of the orml to the curve t = 3 c dre s requred test to fd the dervtve of fucto f However, b mstke he fds the verse sted He fds tht: f 7 3 Fd the correct swer to the problem 5 8 Mrks ge of 0

3 Questo 3 Wrte dow the th term of the sequece: ; ; ; ; ; It s gve tht 8 d 3 9 re the d d 6 th terms of geometrc sequece Determe the frst term d commo rto 4 c Cosder the 3 terms of sequece: 3; ; 7 Clculte f the sequece s: rthmetc 3 geometrc 3 d Evlute: Mrks Questo 4 Ig vests R o Jul 04 wth terest rte of 8% per um compouded mothl O November 06, the terest rte creses to 9,5% compouded mothl Clculte the blce o November 06 3 How much c Ig wthdrw o Jul 07? Clculte the effectve ul terest rte over the perod of the vestmet 4 Sve mkes qurterl pmets of R5 000 strtg mmedtel, the lst pmet beg mde 4 ers tme The compoud terest rte s 3% per qurter Clculte the vlue of Sve s vestmet fter 4 ers 4 Determe the crese the fl mout f Sve were to double hs 9 th pmet 3 6 Mrks ge 3 of 0

4 Questo 5 Ftts's lw s model of hum movemet prmrl used humcomputer tercto d ergoomcs tht predcts tht the tme, T, requred to rpdl move to trget re s fucto of the dstce, D, to the trget d the wdth of the trget, W The vrbles re coected b the equto: T blog D W where d b re tts If =, b = d W =, wrte the formul for D terms of T 4 4 Mrks SECTION B Questo 6 The dgrm shows the fesble rego for ler progrmmg problem where, R Descrbe the rego usg set of equltes 6 Mmse the objectve fucto 4 3 c The further trts re ow gve: ; N0 d ; 0 Mmse the fucto: 3 Determe the possble vlues of k f 3 k s mmsed t ; 5 3 ge 4 of 0 5 Mrks

5 Questo 7 The grph show s defed b f q p Determe the vlues of, p d q 4 Fd the equtos of the es of smmetr of f 4 c Sketch, o the es provded, the grph of g d Hece, use the grph to solve the eqult: g f e Usg the grph, fd the vlue of f Wrte the equto of h f t s the reflecto of g the -s 7 Mrks Questo 8 Determe the sum of the frst 50 terms of the sequece: Ht: It m be helpful to group terms 5 The sum to terms of sequece s gve b: S 3 3 Show tht the frst three terms of the sequece re -; 5; 3 3 Fd formul for the th term of the sequece the form T b c 4 Mrks ge 5 of 0

6 Questo 9 c Wrte: 4 6 the form p q 4 Hece, wrte dow the mmum vlue of the epresso: 46 3 Deduce tht the grph of f 6 s cresg for ll 3 vlues of 3 9 Mrks Questo 0 The dgrm shows pl for rectgulr prk BCD, whch B = 40 m d D = 60 m ots X d Y le o BC d CD respectvel d X, XY d Y re pths tht surroud trgulr plgroud The legth of DY s m d the legth of XC s m Wrte epresso for the legth BX, terms of Show tht the re, m, of the plgroud s gve b = c Gve tht c vr, fd the mmum re of the plgroud 5 Mrks ge 6 of 0

7 Questo sqush pler hts bll gst the wll 4 m w d t rebouds s show the dgrm The tl pth of the bll s t s struck b the pler s gve b the equto: p 4 4 From wht heght s the sqush bll struck? Gve tht the bll strkes the wll t grdet of, clculte the vlue of p 4 c The bll rebouds off the wll log the curve defed b Determe the vlue of t whch the bll hts the groud 3 t wht gle to the -s does the bll ht the groud 3 Mrks ge 7 of 0

8 Dgrm Sheet Nme: Mths Set: QUESTION 7c ge 8 of 0

9 ge 9 of 0 INFORMTION SHEET c b b 4 T d S d T r ; r S r r S r ; r, 0 r c b T h f h f f h 0 lm F d ; M c m m m t m r b

10 ge 0 of 0 BC : I C c B b s s s b c c b C b BC re s s s s s s s s s s s s s s s f vr vr d s S B d B B or s ; s ;