NATIONAL SENIOR CERTIFICATE GRADE SEPTEMBER 06 MATHEMATICS P MARKS: 50 TIME: 3 hours *MATHE* This questio pper cosists of pges icludig iformtio sheet
MATHEMATICS P (EC/SEPTEMBER 06 INSTRUCTIONS AND INFORMATION Red the followig istructios crefull before swerig the questios This questio pper cosists of TWELVE questios Aswer ALL the questios Clerl show ALL clcultios, digrms, grphs, et ceter tht ou hve used i determiig our swer 3 You m use pproved scietific clcultor (o-progrmmble d ogrphicl, uless stted otherwise 4 Aswers ol will ot ecessril be wrded full mrks 5 If ecessr, roud off swers to TWO deciml plces, uless stted otherwise 6 Digrms re NOT ecessril drw to scle 7 Number the swers correctl ccordig to the umberig sstem used i this questio pper 8 Write etl d legibl 9 A iformtio sheet with formule is icluded t the ed of the questio pper Copright reserved Plese tur over
(EC/SEPTEMBER 06 MATHEMATICS P 3 QUESTION Solve for : 4 = (3 3 + 6 = 0 (correct to two deciml plces (3 3 3 = 7 3 (4 Give the equtio: + = For which vlue(s of is the equtio udefied? ( Solve for (5 [7] QUESTION Solve for d simulteousl i the followig equtios: = 3 d = 8 (6 Solve for QUESTION 3 Give the ptter below: 4 + 3 d > 0 (4 [0] Row Row 3 5 Row 3 7 9 Row 4 3 5 7 9 Row 3 Determie the vlue of the first term i Row 80 (5 3 Clculte the sum of the terms i Row 80 ol (4 [9] Copright reserved Plese tur over
4 MATHEMATICS P (EC/SEPTEMBER 06 QUESTION 4 4 The sum of the first p terms of sequece of umbers is give b: S p = p(p + (p + Clculte the vlue of T 0 (3 4 Clculte: (r p p r= (4 [7] QUESTION 5 The followig sequece represets geometric progressio: ; + ; 5 Write dow the third term i terms of ( 5 Clculte the vlue of if it is give tht S = 8 (4 [6] Copright reserved Plese tur over
(EC/SEPTEMBER 06 MATHEMATICS P 5 QUESTION 6 6 The t price of cr is R635 000 The vlue of the cr deprecites ccordig to the reducig blce method t rte of 5% p Clculte the vlue of the cr ectl 5 ers fter it ws bought (3 6 A lo of R50 000 is to be repid i 48 equl mothl pmets Pmets strt oe moth fter the lo hs bee grted The iterest rte o the lo is 6,75% p compouded mothl 6 Clculte the vlue of the equl mothl pmets (4 6 Clculte the outstdig blce immeditel fter the 30th pmet hs bee mde Give our swer to the erest Rd (5 63 How m ers will it tke for ivestmet to double its vlue if the compoud iterest rte is 4,75% p? Leve our swer correct to oe deciml digit (4 [6] Copright reserved Plese tur over
6 MATHEMATICS P (EC/SEPTEMBER 06 QUESTION 7 7 The sketch below shows the grph of f( = + p + q d g( = b + c The -itercept of f is t ( 6; 0 d the -itercept of f d g is t (0; 3 The poit (; 5 lies o the grph of g (; 5 ( 6; 0 - g - (0; 3 f - 4 7 For which vlue(s of is f( = g(? ( 7 For which vlues of is f( < g(? ( 73 Write dow the equtio of the smptote of g ( 74 Determie the equtio of g (4 75 Write dow the equtios of the smptotes of f ( 76 Determie the equtio of f (3 77 Determie the equtios of the es of smmetr of f (3 Copright reserved Plese tur over
(EC/SEPTEMBER 06 MATHEMATICS P 7 7 Give f( = log 7 Write dow the equtio of f, the iverse of f, i the form = ( 7 Drw et sketch grph of f Clerl show ll itercepts with the es d other poit o the grph (3 73 Write dow the equtio of the fuctio g if g is the mirror imge of f i the -is ( 74 For which vlue(s of is: f( f ( < 0? ( [5] Copright reserved Plese tur over
8 MATHEMATICS P (EC/SEPTEMBER 06 QUESTION 8 The sketch below, which is ot drw to scle, shows the grph of f( = + b + c d stright lie g, psg through the origi The -itercept of f is (0; 4 Poit A ( 3; 5 is the turig poit of f f (0; 4 g A( 3; 5 8 Write dow the equtio of the is of smmetr of f ( 8 Show b clcultio tht = d b = 6 (3 83 Discuss the ture of the roots of f (3 84 g is tget to f d the grdiet of lie g is Determie the coordites of the poit of cotct (4 [] Copright reserved Plese tur over
(EC/SEPTEMBER 06 MATHEMATICS P 9 QUESTION 9 9 Give: f( = 3 Determie f ( from first priciples (5 9 Determie: 9 d d if = 5 + (3 9 D [ 6 4 3 ] (3 93 Give s(t = t 3 Show tht the grdiet of tget to s will ever be egtive ( [3] Copright reserved Plese tur over
0 MATHEMATICS P (EC/SEPTEMBER 06 QUESTION 0 The sketch below shows the grph of the fuctio f( = 3 8 + A is -itercept d B turig poit of the grph The poits C(0; d D(; 0, the other turig poit, re give o the sketch B C(0; A D(;0 0 Determie the coordites of A (4 0 Determie the coordites of B (5 03 Clculte the -coordite of the poit of iflectio ( 04 Write dow the vlue(s of for which f ( > 0 ( 05 How m rel roots will the equtio 3 8 + = k hve if k < 0? ( [5] Copright reserved Plese tur over
(EC/SEPTEMBER 06 MATHEMATICS P QUESTION A wter tk hs both ilet d outlet which regulte the depth of wter it cotis The depth D (i metres is give b the fuctio: D(t = 3 + t 4 t3 where D is mesured i metres d t is mesured i hours strtig from 08h00 Clculte the depth of the wter t 08h00 ( Clculte the rte t which the depth is chgig t h00 (3 3 Wht hppes to the depth of the wter t h00? ( 4 At wht time will the iflow of wter be the sme s the outflow? (4 [9] QUESTION A d B re mutull eclusive evets If it is give tht the P(A = 0,35 d P(B = 0,5 determie: P(A ( P(A d B ( 3 P(A or B ( Three mrried couples Mr d Mrs Brow, Mr d Mrs Gree d Mr d Mrs White re to be seted o bech How m differet rrgemets re possible? ( If Mr d Mrs Gree must be seted i the middle, how m differet rrgemets re possible for the remiig persos? ( 3 Determie the probbilit tht Mr d Mrs Gree will sit et to ech other (4 [] TOTAL: 50 Copright reserved Plese tur over
MATHEMATICS P (EC/SEPTEMBER 06 Copright reserved Plese tur over INFORMATION SHEET: MATHEMATICS c b b 4 P ( i A P ( i A i P A ( i P A ( d T ( d ( S T r r r S ; r r S ; r i i F [ ( ] i P i h f h f f h ( ( lim ( ' 0 ( ( d M ; c m ( m m t m r b I ABC: C c B b A A bc c b C b ABC re i i S A A P ( ( P(A or B = P(A + P(B P(A d B b ˆ ( ( b