()( k ) La Salle College Form Six Mock Examination 2013 Mathematics Compulsory Part Paper 1 (Section A) Marking Scheme. Solution Marks Remarks

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1 La Salle College Form Si Mock Eamination Mathematics Compulsory Part Paper (Section A) Marking Scheme. 6m n 5 ( mn ) 5 6m n 4 9m n M for ( ab) m m m a b 5 4 6m n 9 6m m a m n 6 for a or a n 9n a m 6 n () n or ( m ) n a n a a mn. (a) a ab b ( a b)( a b) a ab b a b ( a ab b ) ( 4a 6b) M for grouping of terms ( a b)( a b) ( a b) ( a b)( a b ) (). y ( )( ) k k ( ) + + k+ Always lie above the -ais Δ< ()( k ) 4 + < M for discriminant 9 k 8< k < k > () -LSC-F6-MOCK-MATH-CP -MS

2 ( ) ( )( ) 6 M can be absorbed or (rejected) log log 6 M log log r.t (a) f () + f ( ) () () ( ) ( ) + k + k+ + k + k M for substitution k+ k+ k k When g f. The curve has been reflected about the -ais and k, ( ) ( ) translated to the right by unit. 6. (a) Radius Area 4 4 π 6π The coordinates of the centre 8 4, ( 4, ) pp for missing ( or ) The distance between the points ( 4 ) ( 5) r.t LSC-F6-MOCK-MATH-CP -MS

3 7. (a) ( )( ) < < > For + and 4<, and > 4 < The integers are and. 8. Let ACD. ODC (alt. s, AC// DO) In Δ OCD, OCD (base s, isos. Δ ) M ce OAC ( at centre, twice at ) OAC 5 either one In Δ OAC, OCA 5 (base s, isos. Δ ) + 5 M 5 5 ACD 5 C A O B D -LSC-F6-MOCK-MATH-CP -MS

4 9. (a) Andrew s standard score in Chemistry 7 67 M 6.5 Let be Andrew s score in Economics. pp for undefined symbols 4.5 M for using the result in (a) 4 4 Thus, Andrew s estimated score in Economics is 4. (c) Let y be the score and before the adjustment. pp for undefined symbols The standard score before the score adjustment y 4 The standard score after the score adjustment ( y + 5) ( 4+ 5) M y 4 Thus, there is no change in the standard score. f.t.. (a) Inter-quartile range ( ) (6) 66 5 kg M 4 kg u for missing unit for minimum and maimum data for median -LSC-F6-MOCK-MATH-CP -MS 4 4

5 . (a) Maimum absolute error. mm.5 mm u for missing unit Percentage error.5 % M %.8% r.t..8 % (c) Upper limit of the actual thickness mm 5.95 mm >.9 mm Thus, Chris is incorrect. M (5). (a) () f () () () M accept using long division Thus, is a factor of f ( ). (i) g( ) ( ) ( ) ( ) M k k 6 k (ii) When g ( ) is divided by, the remainder is is a factor of g( ) g( ) f ( ) ( )( ) M ( )( )( ) + or or for all correct (5) -LSC-F6-MOCK-MATH-CP -MS 5 5

6 . (a) Slope of L 7 M Let m be the slope of L. m m The equation of L is y 7 y 7 + y + 9 A (,) + y 9 or equivalent y B (,7) L L L Sub y into L Thus, the coordinates of C are ( 7, ). (c) Let the coordinates of D be (,). ( ) ( 7 ) 4 ( 7 ) ( 7 ) M for A 4 A ( + ) 5 ( 7 ) 5 ( ) Thus, the coordinates of D are ( 5, ). The equation of BD is y y 7 5 ( ) ( y ) y+ 5+ y or equivalent -LSC-F6-MOCK-MATH-CP -MS 6 6

7 Area of ΔABD : Area of Δ CBD 4 : AD : DC 4: M The coordinates of D + 7 4, + 4 ( 5,) The equation of BD is y y 7 5 ( ) ( y ) y+ 5+ y or equivalent (6) -LSC-F6-MOCK-MATH-CP -MS 7 7

8 4. (a) Let y r tan + scos, where r and s are pp for undefined symbols non-zero constants. Since, y r tan + scos ( ) s( ) r + either one s Since, 4 y 4 r tan + scos r 4 4 r tan cos M y When 48, y tan 48 cos (c) When y, tan cos tan cos sin cos cos M for sin tan cos 4 sin cos cos ( ) cos cos cos cos cos cos 4 for 4 4 cos + 5cos ( )( ) cos cos + cos or cos cos or cos (rejected) sin cos 45, 5, 5 or 5 u for missing unit (7) -LSC-F6-MOCK-MATH-CP -MS 8 8

9 5. (a) r h 6 tan r h r: h : (or :) The volume of the hemisphere 4 r cm π M π r cm The volume of the cone r hcm π M The required ratio : π r π r h r: h : (or :) h cm 6 r cm (c) The volume of the hemisphere 9( + ) π cm M + 8π cm u for missing unit π r r 7 8 π r u for having unit (8) -LSC-F6-MOCK-MATH-CP -MS 9 9