MATHEMATICS: PAPER II MARKING GUIDELINES

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NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 009 MATHEMATICS: PAPER II MARKING GUIDELINES Time: hours 50 marks These marking guidelines were used as the basis for the official IEB marking session.

1 NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 009 MATHEMATICS: PAPER II MARKING GUIDELINES Time: hours 50 marks These marking guidelines were used as the basis for the official IEB marking session. They were prepared for use by examiners and sub-examiners, all of whom were required to attend a rigorous standardisation meeting to ensure that the guidelines were consistently and fairly interpreted and applied in the marking of candidates' scripts. At standardisation meetings, decisions are taken regarding the allocation of marks in the interests of fairness to all candidates in the context of an entirely summative assessment. The IEB will not enter into any discussions or correspondence about any marking guidelines. It is acknowledged that there may be different views about some matters of emphasis or detail in the guidelines, and different interpretations of the application thereof. Hence, the specific mark allocations have been omitted. Please note that learners who provided alternate correct responses to those given in the marking guidelines will have been given full credit. IEB Copyright 009 PLEASE TURN OVER

2 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page of 0 SECTION A QUESTION (a) () TL () KL RT or OL (b) () 5 + a 5 + a a and p + 7 p p () EG 5 ( k + ) + ( ) ( 5 ) ( k + ) 49 k + ± 7 k 6 or k 8 n/a (c) () y x + 7 tan θ ref 7, 6 θ 08, 4 () m AD m AB y x + 7 For B, let y 0 x x 5 x 45 8 marks IEB Copyright 009

3 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page of 0 QUESTION (a) M T 0, ,4 ( 0,0685) (b) (c) sin A.cos A.tan A sin A.cos A. sin cos cos A A A cosθ ref 74,5 θ ,5 θ 54,5 sin A cos A (d) sin cos ( 80 β) ( 90 β) ( β) sin sin β sin β.cosβ sin β cosβ b (e) () tan0, 75 () a () b sin0 0, 94 () a + b 7 marks IEB Copyright 009 PLEASE TURN OVER

4 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 4 of 0 QUESTION (a) () () EF cos75 5 EF 6,47 units AB 50 AB 7,06 m ( 6,47) () (b) () (i) 4,4 + 4,4 79,8 cos DRˆ E (4,4)(4,4) DRˆ E,7 Alternative 0, ,4 R 4,4 D 9,9 9,9 E (ii) Area () (i) (ii) 9,9 sin θ θ 66,85 4,4 D Rˆ E θ, 7 ΔDRE π S πrh 4,4 680,9 m ( 54,864)( 45,7) 5760,6m 4,4 sin,7 Cost per square metre ,6 R05,88 per square metre () () 7 marks IEB Copyright 009

5 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 5 of 0 QUESTION 4 (a) () 9 () (b) b c d e (c) () B () A C B marks QUESTION 5 (a) () k () R( ; 6) 4 (b) () Reflection in y x line () () Rotation about the origin through 80 () OR Reflection about the origin (c) On Answer Sheet marks IEB Copyright 009 PLEASE TURN OVER

6 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 6 of 0 (c) K y a L' a K' a M' L M x marks Total for Section A: 7 marks IEB Copyright 009

7 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 7 of 0 SECTION B QUESTION 6 (a) sin sin tan ( 7D ).cos( D) cos( 7D ).sin( D) tan( D) ( 4D) ( D) ( D ).cos( D) cos( D) sin( D) ( D) sin cos cos(4d) (b) tan θ (5) tan θ ± ref < 0 θ k or θ k ; k Ζ Alternative tan θ tan 50 or tan θ tan50 θ k or θ k ; K Z (c) () () ( A + B ).cos( A B) [ cos A.cos B sin A.sin B][ cos A.cos B + sin A.sin B] cos cos cos cos cos cos cos A.cos ( sin B) ( cos ) A A cos A sin B sin 7,5 sin A.sin B ( 45 ).cos( 0 ) ,5 A.sin B sin B A.sin B B + sin B.cos A 7 marks (5) IEB Copyright 009 PLEASE TURN OVER

8 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 8 of 0 QUESTION 7 (a) () 60 () 0 θ 90 θ tan tan 45 cos BĈA BC CA sin EĈO (6) (b) () 5 cm () h 5cos θ θ 7 h 4,6 cm (c) () In Δ ERT, ET sin 9 sin 95 ET 7, In Δ SET, SE tan 49 ET SE 8,7 metres () Join E to Q, so that EQ is perpendicular to RT EQ sin 46 ET EQ 5,7 metres 7 marks IEB Copyright 009

9 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 9 of 0 QUESTION 8 (a) () 0 () (i) True (ii) True (iii) True (iv) False (5) (b) () 77 () 8 () (c) m 4 + m + m + + m + + m + 5 x m + x 5 σ , 5 σ 9,,0 marks (6) QUESTION 9 (a) x ( y + 4) 5 ( 4) +, therefore the coordinates of the centre are (0; 4) 4 m radius m tan Therefore equation is y + ( x + 4) (6) (b) () C( ; 4) Therefore equation is ( x ) + ( y + 4) () Area.6..sin θ 9sin θ () θ 90 () centre(8; ) and radius 4 units. Therefore equation is ( x 8) + ( y + ) 6 (c) () () TA 9r TA 8r tan ATˆ M r AM AT 8r ATˆ M 9,4706 ( 90 9,4706), 8 m AT tan 8 0 marks () IEB Copyright 009 PLEASE TURN OVER

10 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES Page 0 of 0 QUESTION 0 G (7,;6,6) G. G must be rotated 5 times to return to itself. After two rotations it transforms to G. Therefore the transformation that takes G to G is a rotation through The transformation is a rotation of 44 about the origin in an anticlockwise direction. x y G G x y G cosθ y 7,.cos44 6,6.sin44 9,8 G cosθ + x G G sin θ sin θ 6,6 cos44 + 7,.sin44,0 8 marks Total for Section B: 75 marks Total: 50 marks IEB Copyright 009

ADVANCED PROGRAMME MATHEMATICS MARKING GUIDELINES

GRADE EXAMINATION NOVEMBER 009 ADVANCED PROGRAMME MATHEMATICS MARKING GUIDELINES Time: hours 00 marks These marking guidelines were used as the basis for the official IEB marking session. They were prepared