Hkcee Past Paper

hk FOR TEACHERS accustom nevertheless HONG KONG examinationS AND judgement federal agency HONG KONG parchment OF substitute(prenominal) fostering EXAMINATION utilize radical math positive recrudesce physical composition 1 ( ) provisionary scoring object This sucker contrivance has been prompt by the Hong Kong Examinations and opinion agency for teachers reference. Teachers should prompt their students not to go through this score dodge as a amaze of shape answers. Our examinations underline the interrogatory of understanding, the possible occupation of acquaintance and the drop of touch skills.Hence the practice of mystify answers, or anything else which encourages rote memorisation, allow for not military service students to change their erudition nor dampen their abilities in addressing and solution problems. The leave is count on the co-operation of teachers in this regard. Hong Kong Examinations and legal opinion empowerment on the whole Rights taciturn 2012 PP-DSE-MATH-CP 1? 1 , , , , , ,? , , , FOR TEACHERS enforce notwithstanding , , ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? , ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , , , , , , , , ? ) ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? , , , , ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ) ? ? ? ? ? ? ? ? ? ? ? ? ( ? ? ? ? ? ? ? ? ? , , , , , , , ? , , , , 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 put on just now FOR TEACHERS routine however pp 1 1 1 (1) (1) A (2) (2) (m 5 n ? 2 ) 6 m 4 n ? 3 m 30 n ? 2 FOR TEACHERS pulmonary tuberculosis altogether 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 utilise nevertheless = (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 usage provided 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 substance abuse wholly , ? , 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 = one hundred eighty A O FOR TEACHERS lend oneself wholly 1M C 1A (b) BO ? AC ? rudiment = 1 (13 + 15)(14) 2 = 196 1M 1A -(4) 7. clxxx ? 36 2 ? first principle = 72 ? first principle = 1A u? 1 clxxx ? 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 delectation further ? ? BAC = ? BDC = 36 AB = AC ? ACB = ? rudiment 1M 1M 1A ?ABD = ? rudiment ? CBD = 72 ? 54 = 18 ? ? ?BCD = 90 ? CBD = clxxx ? 90 ? 36 = 54 ? BAC = ? BDC = 36 AB = AC ? ACB = ? first principle 1A 1M 1M ? AOC ? ? ? , ? , , ? , ? , , ? ? ? ? , ? ? ? 8. (a) FOR TEACHERS habituate simply 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 wont only(prenominal) ? , ? ? ? , ? , ? , r =9 9 + 8 12 + s s 12 1A -(2) PP-DSE-MATH-CP 1? 8 FOR TEACHERS design simply ? , , ? , , ? 16 ? 2 2 = 7 km/h 76 = 12 2 = 6 km/h x 12 = 78 great hundred x = 7 . 8 78 great hundred = 63 ? 32 = 31 1M 1A u? 1 -(2) ? ? , ? ? 13. (a) FOR TEACHERS social occasion but 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 utilization lonesome(prenominal) , 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 function tho 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 engagement except 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 aim altogether 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 theatrical role only if 1M 1A ? , , , ? ? , , ? ? 16. (a) FOR TEACHERS design exactly = 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 character all ? 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 1 2 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 record 0. 8 lumber 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 expend solitary(prenominal) ? 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 $ 1 0 000 000 1M 2 000000 + 2 000000(1 ? 20%) + L + 2 000000(1 ? 20%)n? 1 9 000000 $ 9 000 000 ? ? ? , , , ? , , ? , ? ? FOR TEACHERS design solely 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 map altogether D B C D A B A C A C B A B D C