Hkcee Past Paper

hk FOR TEACHERS habituate lonesome(prenominal) HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION physical exercise PAPER MATHEMATICS COMPULSORY PART PAPER 1 ( ) PROVISIONAL MARKING SCHEME This sucker purpose has been prepared by the Hong Kong Examinations and Assessment Authority for teachers reference. Teachers should remind their students NOT to regard this marking scheme as a set of model answers. Our examinations emphasise the testing of understanding, the practical application of knowledge and the mapping of processing skills.Hence the use of model answers, or anything else which encourages rote memorisation, will not help students to improve their scholarship nor develop their abilities in addressing and solving problems. The Authority is counting on the co-operation of teachers in this regard. Hong Kong Examinations and Assessment Authority entirely Rights Reserved 2012 PP-DSE-MATH-CP 1? 1 , , , , , ,? , , , FOR TEACHERS spend besides , , ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? , ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , , , , , , , , ? ) ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? , , , , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ) ? ? ? ? ? ? ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? , , , , , , , ? , , , , a. M A (u) 1 PP-DSE-MATH-CP 1? 2 8. 1. 3. 4. 7. 5. 2. 6. c. d. b. u-1 pp-1 M (1) 1 A (pp) M (2) u FOR TEACHERS USE whole FOR TEACHERS USE only(prenominal) pp 1 1 1 (1) (1) A (2) (2) (m 5 n ? 2 ) 6 m 4 n ? 3 m 30 n ? 2 FOR TEACHERS USE ONLY 1. = = m 4 n ? 3 m30 ? 4 n12 ? 3 1M 1M 1A -(3) m 26 = n9 2. 1M 1M 1A 3ab = 2b ? 5 2b ? 5 a= 3b 1M 1M 1A -(3) 3. (a) 9 x 2 ? 42 xy + 49 y 2 1A (b) 9 x 2 ? 42 xy + 49 y 2 ? 6 x + 14 y 1M 1A -(3) PP-DSE-MATH-CP 1? 3 FOR TEACHERS USE ONLY = (3x ? 7 y ) 2 ? 2(3x ? 7 y ) = (3x ? 7 y )(3 x ? 7 y ? 2) = (3x ? 7 y ) 2 ? 6 x + 14 y = (3x ? 7 y ) 2 5+b 3b 3b ? (5 + b) a= 3b 2b ? 5 a= 3b a = 1? ? 5+b = 3b 1? a 5 + b = 3b(1 ? a) ? 5+b = 3b 1? a 5 + b = 3b(1 ? a) 5 + b = 3b ? 3ab 3b(1 ? a) a 3b(1 ? a) a (a) ? ap = a p ? q a ? (ab) p = a pb p (a p )q = a pq ap 1 = q? p q a a ? ? ? ? 4. $x x (80%) = 360 (1 + 30%) 360(1. 3) x= 0. 8 x = 585 FOR TEACHERS USE ONLY pp? 1 1M + 1M 1M+1M+1A 1A u? 1 = 1M+1M+1A 1M + 1M 1A u? 1 -(4) 5. x y pp? 1 ?x 4 ? = ? y 3 ? 7 x + 9 y = 11 ? 1A+1A 1A u? 1 x pp? 1 1A+1M+1A 1A y= u? 1 -(4) PP-DSE-MATH-CP 1? 4 FOR TEACHERS USE ONLY , ? , x= 4 5 1A 0. 8 4 5 ? ? ? 3x ? 7 x + 9 ? ? = 11 ? 4 ? 4 5 ? ? ? ? 3x ? 7 x + 9 ? ? = 11 ? 4 ? 4 x= 5 1M 0. 8 ? ? 360 (1 + 30%) 80% = $ 585 ? ? $ 585 x (80%) 360 (1 + 30%) 360 (1 + 30%) 80% ? ? ? ? , ? , , , ? x y 3x + 1M 4 7 x + 9 y = 11 6. (a) ? AOC = 337 ? 157 = 180 A O FOR TEACHERS USE ONLY 1M C 1A (b) BO ? AC ? ABC = 1 (13 + 15)(14) 2 = 196 1M 1A -(4) 7. 180 ? 36 2 ? ABC = 72 ? ABC = 1A u? 1 180 ? 36 2 ? ACB = 72 ? BCD = 90 ? ACB = ?ACD = 90 ? 72 = 18 ? ABD = ? ACD = 18 1A u? 1 -(4) PP-DSE-MATH-CP 1? 5 FOR TEACHERS USE ONLY ? ? BAC = ? BDC = 36 AB = AC ? ACB = ? ABC 1M 1M 1A ?ABD = ? ABC ? CBD = 72 ? 54 = 18 ? ? ?BCD = 90 ? CBD = 180 ? 90 ? 36 = 54 ? BAC = ? BDC = 36 AB = AC ? ACB = ? ABC 1A 1M 1M ? AOC ? ? ? , ? , , ? , ? , , ? ? ? ? , ? ? ? 8. (a) FOR TEACHERS USE ONLY 1A pp1 1A P pp1 (b) ( x , y) ( x ? 3) 2 + ( y ? 4) 2 = ( x ? 5) 2 + ( y ? (? 2)) 2 1M+1A 1A A? B ? ? 3 + 5 4 + (? 2) ? =? , ? 2 ? 2 ? = (4 , 1) 1M A? B? 4 ? (? 2) = 3? 5 = ? 3 1A 1A -(5) 9. (a) =5? 5 =0 2? 2 1M 1A = 5? 2 =3 (b) 1A 1A -(5) PP-DSE-MATH-CP 1? 6 FOR TEACHERS USE ONLY ? , ? ? ? , ? , ? , r =9 9 + 8 12 + s s 12 1A -(2) PP-DSE-MATH-CP 1? 8 FOR TEACHERS USE ONLY ? , , ? , , ? 16 ? 2 2 = 7 km/h 76 = 12 2 = 6 km/h x 12 = 78 120 x = 7 . 8 78 120 = 63 ? 32 = 31 1M 1A u? 1 -(2) ? ? , ? ? 13. (a) F OR TEACHERS USE ONLY pp? 1 n 6 3 = n 20 n = 40 1M k = 40 ? 6 ? 11 ? 5 ? 10 =8 (b) (i) 1M 1A -(3) 1M 1A u? 1 = (ii) m pp? 1 1M 1A -(4) PP-DSE-MATH-CP 1? 9 FOR TEACHERS USE ONLY , 5 + m (45)(2) = 40 + m 360 20 + 4m = 40 + m 3m = 20 20 3 5 (360) 40 = 45 5+m n+m ? ? ? ? 14. (a) ? BCD ? OA D FOR TEACHERS USE ONLY 2A -(2) 1M 1M (b) (i) (b) 1M AD CD ( 0 , 4) pp1 1M 1M (ii) AC OABC (3 , 2 ) OABC OABC k1 k2 ?0 + 0 + k1 (0) + k 2 (0) + k3 = 0 ? ? 2 2 ? 6 + 0 + k1 (6) + k 2 (0) + k3 = 0 ? 2 2 ? 0 + 4 + k1 (0) + k 2 (4) + k 3 = 0 ? 2 2 1M 1A -(7) OABC x + y ? 6x ? 4 y = 0 PP-DSE-MATH-CP 1? 10 FOR TEACHERS USE ONLY 2 2 k1 = ? 6 k 2 = ? 4 k3 = 0 ? ? ? ? , x + y + k1 x + k 2 y + k3 = 0 k3 2 2 ? ( x ? 3) 2 + ( y ? 2) 2 = 13 ? (3 ? 0) + (4 ? 2) 2 = 13 2 1A x 2 + y 2 ? 6x ? 4 y = 0 1M ? ? ? ? ? ? ? , , ? , ? ? , ? ? , ? , ) ( h 2 ? 24h + 80 = 0 h=4 h = 20 C 1A ( ) ? ? ? 12 ? h ? ? 2 2 ? 6 + 12 ? ? = 16 ? 45 ? 2 ? , ? ? ? C (0 , h) 16 ? CD ? ? ? = 45 ? AD ? 2 ? ? 15. (a) FOR TEACHERS USE ONLY s 36 ? 48 = ? 2 s s=6 1M 66 ? 48 6 =3 = 1A -(2) (b) 1 -(2) PP-DSE-MATH-CP 1? 11 FOR TEACHERS USE ONLY 1M 1A ? , , , ? ? , , ? ? 16. (a) FOR TEACHERS USE ONLY = 1M 1A = 1A -(2) 0. 112 (b) 1M 1A = = = 30 C4 1M 1A 1M 1A 1M 1A -(2) = 530 609 PP-DSE-MATH-CP 1? 12 FOR TEACHERS USE ONLY ? 18 12 11 10 ? ? 18 17 12 11 ? ? 18 ? ? 17 16 ? ? 12 ? = 4 ? ? + 6 ? ? + 4 ? ? ? ? ? ? ? 30 29 28 27 ? ? 30 29 28 27 ? ? 30 ? ? 29 28 ? ? 27 ? ? 68 ? 2 11 10 9 ? ? ? ? 609 ? 30 29 28 27 ? 530 = 609 = 1? 530 609 18 12 18 12 18 12 C1 C3 + C 2 C2 + C3 C1 530 609 ? = 1? 12 68 C4 ? 30 609 C 4 1 (a) p1 0. 870 3 0. 870 1 (a) p2 0. 870 14 0. 870 , ? ? 18 17 16 15 ? = ? ? ? 30 29 28 27 ? 68 = 609 1M 68 609 0. 112 ? r r ? 1 r ? 2 r ? 3 ? ? ? n n ? 1 n ? 2 n ? 3 ? ? ? ? 18 C4 30 C4 r 9 000 000 1 ? 0 . 8 (0. 8) n 0. 1 n log 0. 8 log 0. 1 n log 0. 1 log 0. 8 n 10. 31885116 11 n 1M 1A (ii) 1A (iii) = ( ( ) 1M )( ) 1M 1A (10) PP-DSE-MATH-CP 1? 16 FOR TEACHERS USE ONLY ? 2 000 000 (1 ? (0. 8) m ) 4 000 000 (1 ? (0. 64) m ) ? 0 m (0. 8) ? 1 0 m ? 2 000 000(1 ? (0. 8) m ) 4 000 000(1 ? (0. 64) m ) ? 1 ? 0 . 8 1 ? 0. 64 10 ? ? = 10 000 000 ? (1 ? (0. 8) m ) ? (1 ? (0. 64) m ) ? 9 ? ? 10 ? ? = 10 000 000 ? (1 ? (0. 8) m ) ? (1 ? (0. 8) 2m ) ? 9 ? ? 10 000 000 m 2 m = 10 ((0. 8) ) ? 9(0. 8) ? 1 9 10 000 000 = 10 (0. 8) m + 1 (0. 8) m ? 1 9 m (0. 8) m 0 (0. 8) m 1 1M 2 000000 + 2 000000(1 ? 20%) + 2 000000(1 ? 20%)2 + L 2 000 000 = 1 ? 0. = 10 000 000 $ 10 000 000 1M 2 000000 + 2 000000(1 ? 20%) + L + 2 000000(1 ? 20%)n? 1 9 000000 $ 9 000 000 ? ? ? , , , ? , , ? , ? ? FOR TEACHERS USE ONLY 1. 2. 3. 4. 5. A C A D D 31. 32. 33. 34. 35. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. C B D A B D A A B C D C A D C C B C D B D B A B C 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. FOR TEACHERS USE ONLY D B C D A B A C A C B A B D C