NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 04 MATHEMATICS: PAPER II MARKING GUIDELINES Tie: hours 50 rks These rking guidelines re prepred for use by exiners nd sub-exiners, ll of who re required to ttend stndrdistion eeting to ensure tht the guidelines re consistently interpreted nd pplied in the rking of cndidtes' scripts. The IEB will not enter into ny discussions or correspondence bout ny rking guidelines. It is cknowledged tht there y be different views bout soe tters of ephsis or detil in the guidelines. It is lso recognised tht, without the benefit of ttendnce t stndrdistion eeting, there y be different interprettions of the ppliction of the rking guidelines. IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge of 0 QUESTION A QUESTION () () x + 4 8 + 0 y x 6 y 4 () () ( ; ), ( p ; ) nd ( ; 6) re colliner points. 6 p (p ) 9 p p p 9p + 8 8p 0 5 p OR 6 6 + 6 OR (p ) + 9 y x + c p 4 p 9 subs (;) p 5 () + c 5 p 0 c y x (p ) p p 5 5 p (4) 0 ( 4) 4 4 (b) () OA Eqn of OA: y x 0 ( ) 4 q 4 () Alterntive: OA OT 4 q q 4 IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge of 0 () k is the x-intercept of TR 5 4 R ; ( ; ) 4 ( ) 7 TR 7 Eqn of TR: y + ( x ) 7 For K: 0+ ( x ) 6 7x 7 x (6) 7 7 () (i) ˆ TK tn K ˆK 74, 0 ( ) 7 80 Kˆ 47,5 Kˆ,5 5 7 (ii) KP (6) [] IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 4 of 0 QUESTION () () b () () 70 () () Indicted t A nd B () (4) See grph Verticl shift nd plitude Horizontl shift Shpe () (b) cos β sin 45 ( β ) cos β sin β sin β.cos 45 sin 45.cosβ ( cosβ sinβ)( cosβ+ sin β) sin β cosβ (cosβ sin β)(cosβ + sin β) (cosβ sinβ) cosβ+ sin β ( ) T or T (5) (c) () tn A tn5 A 5 (Answer only: full rks) Alternte: tn A A 60 45 5 () () A 495 or A 675 () (d) () OP 5 + 4 4 OP 4 4 cos( 90 +θ ) sin θ () 4 () 4 5 5 4 5 5 4 () [] IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 5 of 0 QUESTION () () 5± () () 55± () () 65 ± () (b) 700 () (c) 50± () (d) Upper liit Q +,5 IQR 65 +,5 0 0 Lower liit Q,5 IQR 5,5 0 0 Fro the cuultive frequency grph, rks of ll lerners were between 0 nd 90. Therefore, no isolted vlues. (5) [0] QUESTION 4 () () ˆB x ; tn/ chord th () () Ĉ 4 x ; tn/ chord th () () ˆT 80 x ; <'s of (4) (4) Â 80 y ; opp <'s of cyclic qud () (5) ˆB 80 y ; ngles in se segent () (b) () Co-int. ngles ; DE//PQ () () Sˆ ˆ Q; Ext. ngle of cyclic qud () () (i) Rˆ Rˆ ; coon (ii) Sˆ Eˆ ˆ + E ; both 90 () ER DR ; DER /// ESR SR ER 6 0 SR 6 SR, 6 DS 0, 6 6, 4 (5) [] (4) ( ) 75 rks IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 6 of 0 SECTION B QUESTION 5 () () LHS tn θ tn sin θ cos θ sin θ + cos θ sin θ cos θ+ sin θ cos θ cos θ sin θ cos θ cos θ sin θcos θ sin θ RHS (4) () ( ) + tn θ + tn θ tn θ + + sin θ + tn θ + tn θ + tn θ Therefore the xiu is () (b) sin θ.sin cos θ.cos + OR θ + 09,5 + k.60 sin θ.sin cos θ.cos θ + 50,5 + k.60 ( cos( θ+ )) θ 87,5 + k.60 cos( θ+ ) or θ 8,5 + k.60; k θ+ ± 09,5 + k.60 ; k Ζ θ 87,5 + k.60 ; k Ζor θ,5 + k.60 ; k Ζ (6) IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 7 of 0 (c) 4 5 + 6 (5)(6) cosy 6 5 + 6 60 cosy 45 cosy 60 cosy 4 6 4 + 5 (4)(5) cosz 5 cosz 40 cosz 8 ˆ ˆ 7 cosy + cosz + (5) 4 8 8 (d) V cylinder π r h Vpyrid Are of bse height 000 0 0 sin 60 h h 5,9654... r 0 sin 0 sin0 r,54700... Vcylinder π r h π,547... 5,965... 765,59... 8766 c (7) [5] Vreining IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 8 of 0 QUESTION 6 () () 5 5 M ; ; () 6 4 () MQA ( ) M OA y 5 y 6 ( x+ ) bisec tor of AC psses through centre : 5 6 (x + ) Therefore, x 6 5 Therefore, 6; is the centre of the circle. (5) 7 5 (b) () GH OR GH 8 7 5 HI HI 50 8 5 GH HI GI 58 GHI ˆ 90 GI GH + HI GHI ˆ 90 () () GH ( ) + (5 7) 8 GH 8 HI ( 8) + (7 ) 50 HI 50 Are of GHI 8 50 0 (5) () K lies on line to GH through I Eq KI : y ( x 8) 0 x 8 x 6 (4) [9] IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 9 of 0 QUESTION 7 () () True. The point is not prt of the trend. () () True. The point is not prt of the trend. (points closer to line) () () True. The line of best fit will be less steep. () (b) () A. The vlues re clustered round the en. () () Men 7 nd stndrd devition is,4. () () Men p, stndrd devition q () [] QUESTION 8 () () STATEMENT REASON   Given  Ĉ Alt. ngles AD//CE Ê Â Corres ngles. AD//CE () () CAE is isosceles. Ĉ Ê () BD AB () ; line // to one side of DC AE But AE AC ; isos tringle BD AB DC AE () (b) Join B to C Ĉ 90 ; ngle in sei circle. C ˆ ˆ A; tn/ chord th Dˆ Â; isos. DAC Aˆ + Aˆ + 90 + Aˆ 80 ngles of tringle  0 (5) IEB Copyright 04
NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Pge 0 of 0 (c) () Join O to B nd O to A. In BOA, +...cos Oˆ 7 cos Oˆ + 9 Ô 8,9 ˆD 9,5 ; ngle t centre. (4) () Dˆ ˆ D; equl chords; ngles in se segent ABC ˆ 80 Dˆ 4, ; opp. ngles of cyclic qud () [9] 75 rks Totl: 50 rks IEB Copyright 04