MATHEMATICS: PAPER II MARKING GUIDELINES

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NATIONAL SENIOR CERTIFICATE EXAMINATION SUPPLEMENTARY EXAMINATION MARCH 08 MATHEMATICS: PAPER II MARKING GUIDELINES Time: 3 hours 50 marks These marking guidelines are prepared for use by examiners

1 NATIONAL SENIOR CERTIFICATE EXAMINATION SUPPLEMENTARY EXAMINATION MARCH 08 MATHEMATICS: PAPER II MARKING GUIDELINES Time: 3 hours 50 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of whom are required to attend a standardisation meeting to ensure that the guidelines are consistently interpreted and applied in the marking of candidates' scripts. 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. It is also recognised that, without the benefit of attendance at a standardisation meeting, there may be different interpretations of the application of the marking guidelines. IEB Copyright 08

2 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page of 8 SECTION A QUESTION (a) () 0,93 () () Strong, positive () (b) y 0, + 0,6x () y 0, ,005( 0) y 0,8 OR 0,80 (calculator) () (d) No, as this would be extrapolation. () [0] QUESTION (a) 6y + 5( 0) 30 y 5 T(0; 5) () (b) Area 9 5 N(9; 0) () (d) y x + 3 (3) 3 m MN 5 x + 3 x x + 8 5x x x 4 S 5 4; 3 For R: 6(0) + 5x 30 R 6;0 ( ) 5 Area RSN (9 6) 3 5 Area RSN units (8) [5] IEB Copyright 08

3 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page 3 of 8 QUESTION 3 B (a) Construction: refer to the diagram () R.T.P: ABC ˆ ADC ˆ () Proof: Dˆ ˆ ˆ B + A (Ext angle of triangle) D Dˆ ˆ ˆ B + C (Ext angle of triangle) but C Bˆ ˆ ˆ ˆ A and B C (Isos triangle radii) Therefore A D ˆ ˆ ˆ ˆ + D B + B ABC ˆ ADC ˆ (4) (b) OM ON (radii) OMN ˆ 55 ( s in an isos ) MON ˆ 0 Ŝ 35 (Angle at centre is twice the angle at the circumference) Ŝ STR ˆ 35 (tan chord theorem) (6) [] QUESTION 4 (a) a 5 and b () (b) y 5sin( x 30 ) () max of g 4 8 min 4 () (d) k > 5 or k < 5 () (e) 5sinx 4cosx 4 tanx 5 x 38,66 + k 80 A( 4,34 ; 3,) (5) [3] IEB Copyright 08

4 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page 4 of 8 QUESTION 5 Alternative: (a) sinθcosθ + cosθ 0 cos θ(sinθ + ) 0 sinθ cos θ sinθ sin(90 θ) θ θ + 360k cosθ 0 or sinθ 3θ k θ 90 + k 360 θ 0 + k 360 θ k or or OR θ 0 + k 360 θ k 360 θ 360 (90 θ) + 360k Alt: θ k θ k k Alternative: sinθ sin( θ 90 ) θ θ k or θ 80 ( θ 90 ) + 360k θ k 3θ k θ k (8) (b) () Compound angle cos4 p cos4 + p + (3) () sin 4 + cos 4 sin 4 p sin θ θ ( sin ) + cosθ cosθ sin θ( cos θ) + sin θ(+ cos θ) (+ cos θ)( cos θ) sinθ cos θ sinθ sin θ sinθ o 4 p p (3) (6) [0] IEB Copyright 08

5 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page 5 of 8 QUESTION 6 (a) 9,9 () (b) mark for the starting point shape mark for the curve going through the points and finishing at correct place (3) (d) ,% 86,43% 85% (Any answer between 85% and 86,5%) () Decrease The difference between the new mean and new data is reduced. () [9] 9 marks IEB Copyright 08

6 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page 6 of 8 SECTION B QUESTION x 0x y p + 00 ( x 0) + y p + 00 Centre (0; 0) Equation of line from centre through M is: y x + c 0 (0) + c y x + 5 x x + 5 M (; 4) [8] QUESTION 8 (a) False Only one diagonal bisects the interior angles. () (b) Construction NS SNT ˆ 4 ; angles in same segment but SMN ˆ SNT ˆ, Diagonal of kite NMST bisects MNT ˆ MNT ˆ 84 M N T 3 P o 4 Construct NS ˆ ˆ SNR SPR 4 ; angles in same segment R but SNM ˆ SNT ˆ ; diagonals of kite S MNT ˆ 84 (5) [] QUESTION 9 (a) E ˆ Fˆ (Angles in same segment) Aˆ Fˆ (Alt angles AB//DF) Therefore Eˆ ˆ A Cˆ C ˆ 3 ; given CBA D CDE ( A. A. A) (4) IEB Copyright 08

7 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page of 8 (b) Bˆ Dˆ ˆ + D3 ( CBA/// C E ) Therefore ABCD is a cyclic quad (Converse: Ext angle of cyclic quad interior opp angle) (3) Eˆ Dˆ + Dˆ (tan chord theorem) Aˆ + Cˆ ˆ ˆ D + D3 (Ext angle of triangle) Therefore Eˆ ˆ 3 Aˆ + C (4) [] 3 3 QUESTION 0 (a) RPS ˆ 90 (Line from centre drawn to midpoint of chord MS) RVT ˆ 90 (Line from centre perpendicular to tangent) (4) (b) 0 RN (Prop Theorem) 6 60 RN 60 NK 0 NK 0 (5) 60 WV WV 0,598 PN RN ( RPN/// RVW) WV RW 60 PN 0, PN 6,3 Alternative RP RS (SP//TV) RV RT RP 0 0 RP RN 0 PN RN RP ,863 PN 6,3 (8) [] IEB Copyright 08

8 NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II MARKING GUIDELINES SUPPLEMENTARY Page 8 of 8 QUESTION A(3; ) and B(9; ) AB 45 6, Sum of radii AB > sum of radii circles do not intersect [5] QUESTION ( x + r) + ( y r) r subs ( ; 4) ( + r) + (4 r) r 4 4r + r + 6 8r + r r r r ( r 0)( r ) 0 r 0 or r ( x + 0) + ( y 0) 00 And ( x + ) + ( y ) 4 [8] QUESTION 3 (a) Coordinates of point B OB (4)(4)cos0 OB 48 or 4 3 C (; 4 3 ) (5) (b) Base of OCG OG 4 + 4cos60 OG 6 units Area of OCG OCG 3 units (5) m OC m CG 6 m 3 CG tana 3 α 3,9 tan β 3 β 0 OCG ˆ 0 3,9 OCG ˆ 46, (5) [5] marks IEB Copyright 08 Total: 50 marks

MATHEMATICS: PAPER II MARKING GUIDELINES

NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 05 MATHEMATICS: PAPER II MARKING GUIDELINES Time: 3 hours 50 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of