Set 4 Paper 1. Set 4 Paper 1. 1 Pearson Education Asia Limited Section A(1)

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Rodger Parsons
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1 Set Paper Set Paper Section A(). () ( ) ( ) 6 () x. x ( x ) x x x x x ( ) x x (). (a) x x 6 ( x 6) 5. (a) x + < (x 5) or x 6 x + < x or x x < or x x >.5 or x 999 < 999 is a solution of (*). () 6. Let x and be the nuber of pages of the dictionar and the nuber of pages of the fiction respectivel. x ( %)...() + x...() Fro (), x =....() B substituting () into (), we have.. B substituting = into (), we have x =.() = The difference between the nuber of pages of the dictionar and that of the fiction is. () 7. (a) Γ is the perpendicular bisector of AB. x x 6 ( x 6) ( x 6) ( x 6) [( x 6) ( x 6)][( x 6) ( x 6)] (x 6 6)(6 6) ( x )( ) (). The radius of the heisphere c 9 c The volue of the heisphere (9) c 6c The volue of the clinder (9) c 5 c The volue of the solid ( 6 5 ) c 7 c () AOB 6 (55 5) Let M be the id-point of AB. AB OM (propert of rhobus) OM 6cos OM MQ (propert of rhobus) The polar coordinates of Q (, 55 6) (6, 5) () Pearson Education Asia Liited 7

Solution Guide and Marking Schee. (a) In ABC and DEC, ABC DEC (given) ACB = DCE (coon ) BAC = EDC ( su of ) ABC~ DEC (AAA) 9. (a) Marking Schee: Case An correct proof with correct reasons.

2 Solution Guide and Marking Schee. (a) In ABC and DEC, ABC DEC (given) ACB = DCE (coon ) BAC = EDC ( su of ) ABC~ DEC (AAA) 9. (a) Marking Schee: Case An correct proof with correct reasons. Case An correct proof without reasons. ABC~ DEC DE DC (corr. sides, ~ s) AB AC DE c 5c (5 5) c DE 9 c DE CD (9 ) c 5 c CE EDC 9 (converse of Pth. theore) i.e. AF is parallel to ED. a a 7 The required ean kg 5 6kg Two of the newl added data are lower than 65 while the reaining two data are greater than 65. The required edian 65kg Section A(). (a) range = 9 ( 5b ) 5 9 b ean = ( a) a Standard deviation. (cor. to sig. fig.) () There are eploees with nubers of weekl working hours not exceeding. P(weekl working hours ). (a) B the converse of the factor theore, 5 f. (a) () 5 k 5 5k 5 k 9 -coordinate of A 5b 7 The required area ( b )[ ( 5b 7)] sq.units 5b 7b sq.units 5b 7b.5 5b 7b 5 (b 7b 5) () (b 5)( b b ) (b 5)( b )( b ) 5 b (rejected) or or Jason s clai is agreed. Let V c be the final volue of water in the vessel. c c V 5 V V 7 The final volue of water in the vessel is () + 7 c. () Pearson Education Asia Liited 7

Set Paper Let r c be the radius of the surface of water in the vessel before pouring extra water into the vessel. r () 7 r R c c H c c The wooden box and the vase are siilar figures.

3 Set Paper Let r c be the radius of the surface of water in the vessel before pouring extra water into the vessel. r () 7 r R c c H c c The wooden box and the vase are siilar figures. Height of thevase 6 and Height of thewooden box 6 Volue of thevase 6 Volue of thewooden box It is possible that the wooden box has a volue of 9.5 c and a base area of 6 c. () Let R c and H c be the radius of the water surface and the depth of water in the vessel after pouring extra water into the vessel respectivel. R H H.5R R H R (.5R) R 96 R 6 The area of the wet curved surface of the vessel (6) 6 [.5(6)] c 9.c 5c The area of the wet curved surface of the vessel is less than 5 c. Cath s clai is not agreed. (). (a) Let V k ka, where k, k. 6k k () 5 k k () B solving, we have k and k. The required volue 5 c If V 6, then A A 6 c 6 A A 9 A 6or (rejected) The required base area is 6 c. (). (a) AC = CE and AB = EB (given) CB AE (prop. of isos. ) i.e. CBA 9 AC is a diaeter of the circle. (converse of in sei-circle) () Coordinates of the centre of circle 6 6, (, ) Let (x, ) be the coordinates of C. AC is a diaeter of the circle. The centre is the id-point of AC. x i.e. and x 7 6 The coordinates of C (7, 6) AC [7 ( )] (6 ) AC = CE The coordinates of E (7, 6) (7, 6) Slope of the straight line passing through A and E 6 7 ( ) The required equation is 6 ( x 7) 6 x x 7 (7) Pearson Education Asia Liited 7

4 Solution Guide and Marking Schee Section B 5. (a) Let t s be the result of Victor in the 5 Breaststroke event. t..5. t.5 The result of Victor in the 5 Breaststroke event is.5 s. () The standard score of Victor in the Freestle event Relative to other athletes, Victor perfors better in the Freestle event than in the 5 Breaststroke event. Victor s clai is incorrect. 6. (a) P(Bill gets his own present but Ada does not)!! 5 7. (a) P(Bill gets his own present Ada does not) 5 9 9!! f ( x) x x 6 ( x 96x) 6 ( x 96x ) 6 ( x ) 9 The coordinates of the vertex are (, 9). () () () () The -axis is the axis of setr of the graph of = g(x). The vertex of the graph of = g(x) lies on the -axis. g ( x) f ( x ) + x 9 () (c) h( x) f ( x) The graph of h(x) can be obtained b reflecting the graph of f (x) about the x-axis first, followed b reflecting the resulting iage about the -axis. (or in reverse order) +. (a) (i) Alternative Solution h ( x) f ( x 96) The graph of h(x) can be obtained b reflecting the graph of f (x) about the x-axis first, followed b translating the resulting iage to the right b 96 units. (or in reverse order) + cosvab VAB (cor.to sig.fig.) Let X be the foot of the perpendicular fro V to AB. () VX c 9 c Suppose that VY is the height of the praid. Consider VXY, cosvxy 9 VXY (cor.to sig.fig.) The angle between the planes VAB and ABCD is 6.. () Let M and N be the feet of the perpendicular fro E to AB and CD respectivel, and AE = x c. Then ME xsin MEN ( su of ).99 Consider EMN, b the sine forula sinmen sinenm MN EM sin.99 sin xsin5.755 x (cor.to sig.fig.) AE 6.97c Area of all lateral faces of VABCD sin5.755 c.9999c.9996c Pearson Education Asia Liited 7

5 Set Paper 9. (a) Area of the surfaces covered with crea after cutting sin c c The percentage of reoved crea % % % Saantha s clai is agreed. x( t) A n 5 k k kt k k The aount of drug reaining iediatel before the nth injection... ( n) ( n) ters ( n)... () ( n) [ ] ( n ) ( ) n ( n) 5 ( n) 5 ( n) 5 Take coon logarith on both sides, we have ( n) log log5 ( n ) log log5 ( n ) log5 log log5 n log n.995 The aount of drug reaining iediatel before the th injection will be ore than µg. The least nuber of injections such that the aount of drug reaining in the blood strea of Leo will alwas be ore than µg is. (c) The aount of drug reaining for treatent A iediatel before the ( + )th injection...() The aount of drug reaining for treatent B at the sae tie () 6 () () 6 ters () 6 [ 6...()... 6 () 6 Dr Chan s clai is correct. ] () 5 Pearson Education Asia Liited 7

Set 6 Paper 1. Set 6 Paper 1. 1 Pearson Education Asia Limited Section A(1) (Pyth. Theorem) (b) 24units Area of OPQ. a b (4)

Set 6 Paper 1. Set 6 Paper 1. 1 Pearson Education Asia Limited Section A(1) (Pyth. Theorem) (b) 24units Area of OPQ. a b (4) Set Paper Set Paper Section A().. a b a b 8 ( a b) a b ( 8) a b a b a b k k k h k. The weight of Sam 5kg( %) 5kg The weight of Benny 5kg( %). 5. (a).85kg 5kg Benny is the heaviest one among them, his claim