Education Bureau Territory-wide System Assessment 2014 Secondary 3 Mathematics Marking Scheme

Transcription

1 9ME Education Bureau Territory-wide System Assessment 04 Secondary Mathematics Marking Scheme Note (for Section B and C of each sub-paper): *Mark for Answer: () The Mark for Answer may be given when there is a correct answer without any work shown. () If the work shown is incorrect, the Mark for Answer will not be given. () If the work shown is poorly presented but there is a correct answer, the Mark for Answer may be given. **Mark for Presentation: () If the work shown is correct but the answer is incorrect, the Mark for Presentation may be given. () If the work shown is incorrect, the Mark for Presentation will not be given. () If the numerical value of the answer is correct but not the approximate value as required by the question, the Mark for Presentation will not be given. (4) The Mark for Presentation may include overall work such as mathematical expressions, units, written explanations, use of symbols, etc. r.t. xxx means accept answers which can be rounded to xxx. Steps that may be skipped are shown in shade. Alternative suggested answers are shown in boxes. HKEAA 04

2 9ME Section A Sub-paper (9ME) ( mark each). B (9ME-). C. A 4. C. D 6. B (9ME4-6) 7. B 8. D (9ME-8) 9. C 0. A. C (9ME-). D. C 4. D. A 6. A (9ME4-6) 7. B 8. A 9. B 0. D (9ME-0) HKEAA 04

3 9ME Section B Sub-paper (9ME). (9ME4-) (i) 0. (ii) km. The number of female clerks in the company is S = 6. (9ME-) n 6. a ab 7. (9ME4-7) x x 8. ( x )( x ) y 4x i. 7 < 6 ii > 8.8 Must be all correct Must be all correct. x 7. (9ME-) x = 6 Unit may not be considered. (9ME-) Or other correct answers 4. (9ME4-4) (a) x = 4 (b) y = 0. x = (4a) (4b) Unit may not be considered Unit may not be considered HKEAA 04

4 9ME 6. DE 7. A, B Must be all correct 8. (9ME4-8) The coordinates of point P are Must be all correct ( 4, ). and in order 9. = 4.8 r.t. 4.8 Unit may not be considered 40. (9ME-40) (4) () () () 4. The modal class of the time for the 0 athletes to finish the race Must be all correct is min 9 min. HKEAA 04 4

5 9ME Section C Sub-paper (9ME) 4. Selling price = 400( + 40%) (4-) = 600 * (4-) The selling price of this painting is $ ** (4-) 4. The area of the sector 0 (4-) 60 = = 8.4 cm (corr. to the nearest 0. cm ) * (4-) ** (4-) 44. (a) r = 8 (44a-) 4. r = 9 (b) The circumference of the circle * (44a-) r.t. 8.4 cm = (9) (44b-) Correct method = 8 cm * (44b-) w (a) 8 w ** (44-) w * (4a) x (b) 4 (x ) x x 4 (4b-) Using ( x m ) n x m n x x 8 x * (4b-) Correct final answer (getting marks ) HKEAA 04

6 9ME 46. (9ME-4) 4 x + y = 0 x 0 y O 4 y 4 x * (46-) (46-) * (46-) Must be all correct In case the data in the above table is incorrect, students can still use the ordered pairs to draw a straight line. The line must pass through (0, ) and the range of x must include the values from to. Correct straight line (include: correct position, use ruler to draw the line, pass through the points and extend two ends of the line) If the data in the table is correct but not complete and the graph is correct, (0,, ) can be given. 47. (9ME-47) (Students must find the approximations for the prices of these items.) The total amount = = 000 Miss Lee can join the lucky draw. 0 0 No evidence of using estimation strategies nor giving reasonable justification 0 Partial evidence of using estimation strategies, but the solution is incomplete or contains errors Estimate with reasonable justification Exact calculation only The estimate is given only after exact calculation Use rounding up to estimate the prices One correct approximation only Estimate correctly, but the total amount is omitted Estimate correctly, but the total amount is less than $000 Correct method used, but minor errors occurred No need to consider unit/presentation Accept using instead of The conclusion must be correct and aligned with a reasonable explanation HKEAA 04 6

7 9ME 48. ABC = ADE (given) ACB = AED (given) BAC = DAE (common angle) ABC ~ ADE (AAA / equiangular) ABC = ADE (given) ACB = AED (given) ABC ~ ADE (AA) Marking Scheme: Case Any correct proof with correct reasons Case Any correct proof with poor presentation or without reason(s) Case Incomplete proof with any one correct statement and one corresponding reason Case 4 Incomplete proof 0 Or other correct proofs 49. (9ME-48) 0. (9ME-49) (a) The number of visitors of a country from 007 to 0 of visitors (million) Year T O Y B B T B O/O B B Y O O T/T O O O O Y/Y O Y Y T Y O Y Y * (49-) * (49-) * (0a) For the correct indication of all marks Correct broken line graph (including the points connected by line segments) Must be all correct (b) The probability that the two letters chosen are the same = 9 * (0b) HKEAA 04 7

8 9ME Education Bureau Territory-wide System Assessment 04 Secondary Mathematics Marking Scheme Note (for Section B and C of each sub-paper): *Mark for Answer: () The Mark for Answer may be given when there is a correct answer without any work shown. () If the work shown is incorrect, the Mark for Answer will not be given. () If the work shown is poorly presented but there is a correct answer, the Mark for Answer may be given. **Mark for Presentation: () If the work shown is correct but the answer is incorrect, the Mark for Presentation may be given. () If the work shown is incorrect, the Mark for Presentation will not be given. () If the numerical value of the answer is correct but not the approximate value as required by the question, the Mark for Presentation will not be given. (4) The Mark for Presentation may include overall work such as mathematical expressions, units, written explanations, use of symbols, etc. r.t. xxx means accept answers which can be rounded to xxx. Steps that may be skipped are shown in shade. Alternative suggested answers are shown in boxes. HKEAA 04

9 9ME Section A Sub-paper (9ME) ( mark each). B (9ME-). A (9ME-). D 4. B. D 6. C 7. A 8. B 9. A 0. C (9ME4-0). C (9ME-). C. C (9ME-) 4. B. A 6. B 7. D 8. D (9ME4-8) 9. D 0. A HKEAA 04

10 9ME Section B Sub-paper (9ME). A 0 / 0 B 0 C 0. (9ME4-) 6. (9ME-) The rainfall in July : the rainfall in August = : 4 4. x = 4 y =. The value of the 0 th term of the sequence is (9ME4-6) h k 7. x x x 8. (9ME4-8) ( x )( x ) 9. (9ME-9) x = 0. 4a 4ab b. T = 0. The base radius of the cylinder is 6 cm.. (9ME-) Must be all correct Accept / :0.8 /.: 4 : / : 4 Must be all correct Or other correct answers 4. x = 84. (9ME4-) x = 9 Unit may not be considered Unit may not be considered HKEAA 04

11 9ME 6. (9ME-6) BAEH or its correct permutation BCEF or its correct permutation 7. x = 7 Unit may not be considered 8. The polar coordinates of point A are Must be all correct (, 0 ). and in order 9. AB = units 40. (9ME-40) (4) () () () 4. (9ME-40) The weighted mean mark of Alfred is 7.. HKEAA 04 4

12 9ME Section C Sub-paper (9ME) 4. The weight of copper = 0 (4-) = 44 kg * (4-) ** (4-) 4. Cost price = (9ME4-4) = $00 * (4-) Loss per cent = 00 00% (4-) The volume of the prism 4 = 6 = 0% * (4-) ** (4-4) (44-) = 6 cm * (44-) 4. Table of volunteering hours Frequency ** (44-) * (4-) Must be all correct Table of volunteering hours Frequency * (4-) Must be all correct HKEAA 04

13 9ME 46. (9ME4-46) x + y = 0 4 x 4 4 y The height of the wall (. 8 ) m = 4 m Acceptable range:. m to 4. m 4 O 4 y 4 x * (46-) (46-) * (46-) 0 0 No evidence of using estimation strategies nor giving reasonable justification 0 Partial evidence of using estimation strategies, but the solution is incomplete or contains errors Estimate with reasonable justification Must be all correct In case the data in the above table is incorrect, students can still use the ordered pairs to draw a straight line. The line must pass through (, 0) and the range of y must include the values from to. Correct straight line (include: correct position, use ruler to draw the line, pass through the points and extend two ends of the line) If the data in the table is correct but not complete and the graph is correct, (0,, ) can be given. Answer only, without any explanation The explanation is irrelevant or unreasonable Using reasonable estimation strategies, but the explanation is incomplete The explanation is reasonable, but the answer is not within the acceptable range The explanation is reasonable, but minor errors occurred The answer must be supported by reasonable explanation and within the acceptable range HKEAA 04 6

14 9ME 48. (9ME4-48) BCA + 4 = 80 BCA = BA = BC BAC = + + x = 80 x = 0 (48-) (48-) * (48-) ** (48-4) For BCA = BAC Can be absorbed BCA + 4 = 80 BCA = BA = BC BAC = + x = 4 x = 0 (48-) (48-) * (48-) ** (48-4) For BCA = BAC Can be absorbed (9ME4-49) 8 tan AC (49-) AC.8997 AC =. m ( corr. to d.p.) * (49-) r.t.. m The length of the shadow is. m. ** (49-) Mean height = 0 (0-) = 0 = = 47. cm * (0-) ** (0-) HKEAA 04 7

15 9ME Education Bureau Territory-wide System Assessment 04 Secondary Mathematics Marking Scheme Note (for Section B and C of each sub-paper): *Mark for Answer: () The Mark for Answer may be given when there is a correct answer without any work shown. () If the work shown is incorrect, the Mark for Answer will not be given. () If the work shown is poorly presented but there is a correct answer, the Mark for Answer may be given. **Mark for Presentation: () If the work shown is correct but the answer is incorrect, the Mark for Presentation may be given. () If the work shown is incorrect, the Mark for Presentation will not be given. () If the numerical value of the answer is correct but not the approximate value as required by the question, the Mark for Presentation will not be given. (4) The Mark for Presentation may include overall work such as mathematical expressions, units, written explanations, use of symbols, etc. r.t. xxx means accept answers which can be rounded to xxx. Steps that may be skipped are shown in shade. Alternative suggested answers are shown in boxes. HKEAA 04

16 9ME Section A Sub-paper (9ME) ( mark each). A. A (9ME-). A 4. C (9ME4-4). D 6. B 7. C 8. D (9ME-8) 9. A 0. D. A. B. C (9ME-) 4. C (9ME4-4). B 6. D 7. B 8. B 9. C 0. D (9ME-0) HKEAA 04

17 9ME Section B Sub-paper (9ME) (9ME-) The rainfall in July : the rainfall in August = : 4 4. (9ME4-4) The machine can produce 080 bottles of sauce in one hour.. (9ME-) n 6. x x 6x 7. x ( x ) 8. x x 9. (9ME-9) x = 0. (9ME4-) x 6. The volume of the cone is 00 cm.. FGH FHG GFH GHF HFG HGF. Figure T and Figure A have the same 4. (a) x = 70. (9ME-) x = 6 number of axes of symmetry. (b) y = 6. (9ME-6) BAEH or its correct permutation BCEF or its correct permutation 7. (9ME4-7) AC = 4 cm 8. x = 9. (a) There are students in A. (b) The least lunch expense of A students (c) last Friday was $. 6 students spent more than $4 on their lunch last Friday. Accept / :0.8 /.: 4 : / : 4 Must be all correct * (9a) * (9b) * (9c) 40. (9ME-4) The weighted mean mark of Alfred is 7.. Must be all correct Unit may not be considered Unit may not be considered Unit may not be considered HKEAA 04

18 9ME Section C Sub-paper (9ME) 4. Amount = 000 ( %) (4-) = $0 Interest = $0 * (4-) * (4-) ** (4-4) 4. The length of AB 0 = (6) (4-) =.4 cm (corr. to sig. fig.) * (4-) 4. The surface area of the sphere 44. ** (4-) = 4 8 (4-) cm r.t..4 cm = 804 cm (corr. to the nearest cm ) * (4-) r.t. 804 cm x y x y 0 0 Substitute () into (): y y 0 0 y 7 Substitute y 7 into () x (7) x 7...()...() ** (4-) (44-) * (44-) (44-) * (44-4) Correct method (eliminating one of the variables) Correct value of y (or x) Correct method Both values are correct HKEAA 04 4

19 9ME 4. (9ME-46) x + y = 0 4 x 0 y DAE = 80 ( sum of ) DAE = 6 CDF = DAE = 6 AB // DF (corr. s equal) 4 O 4 y 4 x * (4-) (4-) * (4-) Must be all correct In case the data in the above table is incorrect, students can still use the ordered pairs to draw a straight line. The line must pass through (0, ) and the range of x must include the values from to. Correct straight line (include: correct position, use ruler to draw the line, pass through the points and extend two ends of the line) If the data in the table is correct but not complete and the graph is correct, (0,, ) can be given. EDF = 80 EDF = 80 AED = EDF = 80 (adj. s on a st. line) AB // DF (alt. s equal) Marking Scheme: Case Any correct proof with correct reasons Case Any correct proof with poor presentation or without reason(s) Case Incomplete proof with any one correct statement and one corresponding reason Case 4 Incomplete proof 0 HKEAA 04

20 9ME 47. (9ME-47) (Students must find the approximations 0 0 No Exact calculation only for the prices of these items.) evidence of using The estimate is given only estimation after exact calculation The total amount strategies nor Use rounding up to = giving reasonable estimate the prices justification = Partial One correct approximation evidence of using only Miss Lee can join the lucky draw. estimation Estimate correctly, but the strategies, but the total amount is omitted solution is Estimate correctly, but the incomplete or total amount is less than contains errors $000 Correct method used, but minor errors occurred Estimate No need to consider with reasonable unit/presentation justification Accept using instead of The conclusion must be correct and aligned with a reasonable explanation HKEAA 04 6

21 9ME 48. (9ME-49) The number of visitors of a country from 007 to 0 * (48-) For the correct indication of all 0 marks of visitors (million) 0 0 * (48-) Correct broken line graph (including the points connected by line segments) Year 49. (9ME-0) (a) T O Y B B T B O/O B B Y O O T/T O O O O Y/Y O Y Y T Y O Y Y * (49a) Must be all correct (b) The probability that the two letters chosen are the same = 9 * (49b) HKEAA 04 7

22 9ME4 Education Bureau Territory-wide System Assessment 04 Secondary Mathematics Marking Scheme Note (for Section B and C of each sub-paper): *Mark for Answer: () The Mark for Answer may be given when there is a correct answer without any work shown. () If the work shown is incorrect, the Mark for Answer will not be given. () If the work shown is poorly presented but there is a correct answer, the Mark for Answer may be given. **Mark for Presentation: () If the work shown is correct but the answer is incorrect, the Mark for Presentation may be given. () If the work shown is incorrect, the Mark for Presentation will not be given. () If the numerical value of the answer is correct but not the approximate value as required by the question, the Mark for Presentation will not be given. (4) The Mark for Presentation may include overall work such as mathematical expressions, units, written explanations, use of symbols, etc. r.t. xxx means accept answers which can be rounded to xxx. Steps that may be skipped are shown in shade. Alternative suggested answers are shown in boxes. HKEAA 04

23 9ME4 Section A Sub-paper 4 (9ME4) ( mark each). D. C. A 4. C (9ME-4). A 6. B (9ME-6) 7. B 8. A 9. B 0. C (9ME-0). D. B. D 4. C (9ME-4). D 6. A (9ME-6) 7. C 8. D (9ME-8) 9. A 0. B HKEAA 04

24 9ME4 Section B Sub-paper 4 (9ME4). (9ME-). (9ME-). (i) 0 (ii) 4 Must be all correct 6 0 Acceptable range: 0. < < (9ME-4) The machine can produce 080 bottles of sauce in one hour.. The coefficient of y 6 is. 6. (9ME-6) 7. (9ME-7) 8. (9ME-8) h k x x ( x )( x ) 9. 9y 0.. (9ME-0) D C 9 x 6 - Putting D on one side - Or equivalent. P, R Must be all correct. The cross-section is a rectangle 4. (a) x = 4 (4a) (9ME-4). (9ME-) (b) y = 0 (4b) x = 9 6. EAD DAE FBC CBF Unit may not be considered Unit may not be considered HKEAA 04

25 9ME4 7. (9ME-7) AC = 4 cm 8. (9ME-8) The coordinates of point P are ( 4, ). Must be all correct and in order 9. x = 4. r.t The number of qualified boys is The required empirical probability 7 Or 0.07 = 00 HKEAA 04 4

26 9ME4 Section C Sub-paper 4 (9ME4) 4. (9ME-4) Cost price = = $00 * (4-) Loss per cent = 00 00% (4-) 00 = 0% * (4-) ** (4-4) 4. Interest = 00 % 4 (4-) = $40 * (4-) Amount = = $90 * (4-) ** (4-4) 44. The present value of the crystal = 700 ( 0%) (44-) = $847 * (44-) ** (44-) The present value of the crystal is $847. (44-) * (44-) ** (44-) Correct method (multiply. two times) 4. The volume of the pyramid (4-) = 6 = 44 cm * (4-) ** (4-) HKEAA 04

27 9ME4 46. (9ME-46) x + y = 0 4 x 4 4 y 0 4 O 4 y 4 x * (46-) (46-) * (46-) Must be all correct In case the data in the above table is incorrect, students can still use the ordered pairs to draw a straight line. The line must pass through (, 0) and the range of y must include the values from to. Correct straight line (include: correct position, use ruler to draw the line, pass through the points and extend two ends of the line) If the data in the table is correct but not complete and the graph is correct, (0,, ) can be given. 47. The mode of a set of data is the datum with the highest frequency, but it does not imply that the number of appearances of the datum must be more than half of the total. (47-) Reasonable Explanation Of these tests, Michael got full mark in only of them. Therefore, he did not get full marks in more than half of the tests. (47-) Reasonable Explanation Michael s saying is misleading. (47-) Reasonable attempt to explain HKEAA 04 6

28 9ME4 48. (9ME-48) BCA + 4 = 80 BCA = BA = BC BAC = + + x = 80 x = 0 (48-) (48-) * (48-) ** (48-4) For BCA = BAC Can be absorbed BCA + 4 = 80 BCA = BA = BC BAC = + x = 4 x = 0 (48-) (48-) * (48-) ** (48-4) For BCA = BAC Can be absorbed 49. (9ME-0) Mean height = = = 0 (49-) = 47. cm * (49-) ** (49-) HKEAA 04 7