Hkcee Past Paper

hk FOR TEACHERS’ USE ONLY HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION PRACTICE PAPER MATHEMATICS COMPULSORY PART PAPER 1 ( ) PROVISIONAL MARKING SCHEME This marking scheme 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 use of processing skills.Hence the use of model answers, or anything else which encourages rote memorisation, will not help students to improve their learning 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 All Rights Reserved 2012 PP-DSE-MATH-CP 1? 1 Â © , , , , , ,? , , , FOR TEACHERS’ USE ONLY , , ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? , ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? : , , , , , , , , ? ) ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? , , , , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ; ? ; ? , ? ? ? ? ? ? ? ? ? ? ) ? ? ? ? ? ? ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? , , , , , , , ;? , , , , 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 ONLY FOR TEACHERS’ USE ONLY 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 = 337Â ° ? 157Â ° = 180Â ° A O FOR TEACHERS’ USE ONLY 1M C 1A (b) BO ? AC ? ABC = 1 (13 + 15)(14) 2 = 196 1M 1A ———-(4) 7. 180Â ° ? 36Â ° 2 ? ABC = 72Â ° ? ABC = 1A u? 1 180Â ° ? 36Â ° 2 ? ACB = 72Â ° ? BCD = 90Â ° ? ACB = ?ACD = 90Â ° ? 72Â ° = 18Â ° ? ABD = ? ACD = 18Â ° 1A u? 1 ———-(4) PP-DSE-MATH-CP 1? 5 FOR TEACHERS’ USE ONLY ? ? BAC = ? BDC = 36Â ° AB = AC ? ACB = ? ABC 1M 1M 1A ?ABD = ? ABC ? CBD = 72Â ° ? 54Â ° = 18Â ° ? ? ?BCD = 90Â ° ? CBD = 180Â ° ? 90Â ° ? 36Â ° = 54Â ° ? BAC = ? BDC = 36Â ° AB = AC ? ACB = ? ABC 1A 1M 1M ? AOC ? ? ? , ? , , ? , ? , , ? ? ? ? , ? ? ? 8. (a) FOR TEACHERS’ USE ONLY 1A pp–1 1A P pp–1 (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 7>6 = 12 2 = 6 km/h x 12 = 78 120 x = 7 . 8 78 : 120 = 63 ? 32 = 31 1M 1A u? 1 ———-(2) ? ? , ? ? 13. (a) FOR 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 (360Â °) 40 = 45Â ° 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) pp–1 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 FO R 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