2008 Mathematics. Standard Grade Credit. Finalised Marking Instructions

Transcription

1 008 Mathematics Standard Grade Credit Finalised Marking Instructions Scottish Qualifications Authority 008 The information in this publication may be reproduced to support SQA qualifications only on a non-commercial basis. If it is to be used for any other purposes written permission must be obtained from the Assessment Materials Team, Dalkeith. Where the publication includes materials from sources other than SQA (secondary copyright), this material should only be reproduced for the purposes of examination or assessment. If it needs to be reproduced for any other purpose it is the centre s responsibility to obtain the necessary copyright clearance. SQA s Assessment Materials Team at Dalkeith may be able to direct you to the secondary sources. These Marking Instructions have been prepared by Examination Teams for use by SQA Appointed Markers when marking External Course Assessments. This publication must not be reproduced for commercial or trade purposes.

2 Special Instructions The main principle in marking scripts is to give credit for the skills which have been demonstrated. Failure to have the correct method may not preclude a pupil gaining credit for the calculations involved or for the communication of the answer. Care should be taken to ensure that the mark for any question or part question is entered in the correct column, as indicated by the horizontal line. Where a candidate has scored zero marks for any question attempted, "0" should be shown against the answer in the appropriate column. It is of great importance that the utmost care should be exercised in adding up the marks. Where appropriate, all summations for totals and grand totals must be carefully checked. The answer to one part, correct or incorrect must be accepted as a basis for subsequent dependent parts of a question. Full marks in the dependent part is possible if it is of equivalent difficulty. 3 Do not penalise insignificant errors. An insignificant error is one which is significantly below the level of attainment being assessed. eg An error in the calculation of would not be penalised at Credit Level. 4 Working after a correct answer should only be taken into account if it provides firm evidence that the requirements of the question have not been met. 5 In certain cases an error will ease subsequent working. Full credit cannot be given for this subsequent work but partial credit may be given. 6 Accept answers arrived at by inspection or mentally, where it is possible for the answer to have been so obtained. 7 Do not penalise omission or misuse of units unless marks have been specifically allocated to units. Page

3 8 A wrong answer without working receives no credit unless specifically mentioned in the marking scheme. The rubric on the outside of the Papers emphasises that working must be shown. In general markers will only be able to give credit to partial answers if working is shown. However there may be a few questions where partially correct answers unsupported by working can still be given some credit. Any such instances will be stated in the marking scheme. 9 Acceptable alternative methods of solution can only be given the marks specified, ie a more sophisticated method cannot be given more marks. te that for some questions a method will be specified. 0 In general do not penalise the same error twice in the one question. Accept legitimate variations in numerical/algebraic questions. Do not penalise bad form eg sinx 0 = 0 5 = A transcription error is not normally penalised except where the question has been simplified as a result. Page 3

4 008 Mathematics SG Credit Level Paper Marking Instructions Award marks in whole numbers only Question Ans: 5.8 knowing correct order of operations must involve a multiplication followed by a subtraction carrying out both calculations 5.8 KU (i) for 5.8, with or without working award (ii) for 7., with or without working award (iii) for 8.4 ( ), with or without working award (iv) for.8 ( ), with or without working award (v) for ( ), with working award (vi) for a final answer of 8.9 award 0 Page 4

5 Ans: 5 ( 3)( x + 3 x ) beginning to factorise 5( x 9) factorised fully 5 ( x 3)( x + 3) KU (i) the st mark is available for 5( 9) x or ( 5 x 5)( x + 3) or ( x 3 )( 5x + 5) (ii) All 3 factors must be shown together to obtain the nd mark Page 5

6 3 Ans: H = W B beginning to rearrange W H = B completed rearrangement H = W B KU (i) (ii) for for W H =, with or without working award B W H =, with or without working award B (iii) the nd mark is for the square root of the candidate s expression for H Page 6

7 4 Ans: y = x + 8 gradient y-intercept 8 linear equation y = x + 8 3KU (i) for y = x + 8, with or without working 3 award 3 (ii) for y = x + c, with or without working award 3 (iii) for y = mx + 8, with or without working award 3 (iv) for an incorrect equation, the 3 rd mark can be awarded only if both gradient and y-intercept are consistent with stated values Page 7

8 5 Ans: 3 p + 5 p( p + 5) common denominator p( p + 5) or p + 5p simplified numerator 3 p + 5 KU (i) for wrong simplification beyond the correct answer award Page 8

9 6 (a) Ans: ( x + 8) expression ( x + 8) KU (b) Ans: 0.5x expression 0.5x KU (c) Ans: kilometres per hour equating the two distances ( x + 8) + 0.5x = 46 collecting like terms.5x = 30 x = 3RE (i) for answer of km/h without working award 3 Page 9

10 7 (a) Ans: 5 value 5 KU (b) Ans: x + 6 expression x + 6 RE (c) Ans: 7 x + 7 dealing with mean x + ( x + 5) rd term = x + 4 find term 7 x + 7 RE (i) for 7 x + 7, with or without working, award Page 0

11 8 (a) Ans: ( 0), ( 8, 0, ) coordinates of Q (, 0) coordinates of R ( 8, 0) KU (i) for and 8 award ) ) (ii) for ( 0, and ( 0, 8 award (b) Ans: 5 units axis of symmetry x = 5 finding height above x axis y = 9 5 units 3RE (i) for a final answer of 5, with or without working award 3 3 (ii) for a final answer of 9, with or without working award 3 Page

12 9 Ans: 7 m correct index m 7 m KU Page

13 0 (a) Ans: ( 0, ) coordinates of C ( 0,) KU ( ) (i) accept an answer of y = (b) Ans: a = 4 method 6 = a processing a = 4 KU (i) for a = 4, with or without working award Page 3

14 Ans: 3 method AC + ( 3 ) = ( 50) 8 simplification of a surd 3 3KU (i) for a final answer of 8 with working award 3 (ii) the 3 rd mark is available for the simplification of 8, 3 or 50 (iii) 8 without working cannot be awarded the first marks Page 4

15 Ans: a = 5, b = 7 valid strategy either ax ax or a + b processing a = 5 b = 7 3KU (i) for a = 5, with or without working, award the first two marks Page 5

16 3 algebraic method Ans: x = 3 strategy processing 7 + x 4 + x 7 + x 4 + x = 3 x = 3 3RE numerical method Ans: x = 3 strategy processing adding the same number to numerator and denominator further fractions x = 3 3RE numerical method Ans: x = 3 strategy processing listing at least 3 fractions equivalent to 3 4 selecting x = 3 3RE (i) for x = 3 without working award [END OF PAPER MARKING INSTRUCTIONS] KU 7 marks RE marks 3 Page 6

17 008 Mathematics SG Credit Level Paper Marking Instructions Award marks in whole numbers only Question Ans: tonnes multiplying factor.08 power of (unrounded) (rounded) KU (i) for 5 900, with or without working award (ii) for , with or without working (.8 ) 3 (iii) for 3 700, with or without working ( 0.9 ) award 4 3 award 4 3 (iv) for any other final answers, an unrounded solution must be stated to access the 3 rd and 4 th marks (v) candidates using simple interest may only be awarded the last mark = (( ) ) Page 7

18 (a) Ans: 34, 9 median 34 mode 9 KU (b) Ans: 30 probability or equivalent 30 KU (i) for median = 9 and mode = 34 award Page 8

19 3 Ans: 56.5 valid strategy 80% = 45 processing 00 % = KU (i) for 56.5, with or without working award 3 3 (ii) for (0% = 45), with working award 3 (iii) for 36 (80% of 45), with or without working award 3 0 (iv) for 54 (0% of 45), with or without working award 3 0 (v) Caution: Some candidates state 80% = 45 but continue as in notes (iii) or (iv). In these cases, the st mark is still available Page 9

20 4 (a) Ans: x + y = 60 equation x + y = 60 KU (b) Ans: 50 x + 0 y = 740 equation 50 x + 0y = 740 KU (c) Ans: 8 fifty pence coins evidence of scaling 0 x + 0y = 00 or equivalent processing 30 x = 540 or equivalent value of x 8 3RE (i) for 8 without working award 3 0 (ii) for 8 and 4 verified in both equations award 3 Page 0

21 5 (a) Ans: 65 method OP = or 8.06 RE (b) Ans: 40 method PT = ( 65) 5 40 or 6.3 RE (i) the wrong form of Pythagoras should not be penalised in part (b), if already penalised in part (a) Page

22 6 Ans: no, the boat is not beyond the horizon, with numerical comparison variation statement d h variation equation d = k h evaluating k k = 3. 5 method to enable comparison answer and justification visible distance =.4 or height should be 3.7 or k 0 = 3. 6 from 40 no, with numerical comparison 5RE Page

23 each mark 7 Ans: 5.6 m method BC = 3.3 strategy use of cosine rule substitution AC = cos RE (i) (ii) accept solutions in radians or gradians for any attempt involving Pythagoras or sine rule, only the st mark is available Page 3

24 8 (a) Ans: 6.9 m valid strategy substitution ab sin C 5 8 sin KU (i) evidence for the st mark may be implicit in the substitution (b) Ans: RE Page 4

25 9 (a) Ans: KU (b) Ans: 45.8 cm correct ratio or 5 processing 50 0 = 360 πr 0 = 88 5 processing r = 50 π 88 r = π RE (i) a calculation using πr ( which leads to r = 9. 57) cannot be awarded the mark Page 5

26 0 (a) Ans: KU (b) Ans: C = 5d + 0.m 4 starting formula 5d continuation 0.m formula C = 5d + 0.m 4 or ( 00) C = 5d + 0. m 3RE Page 6

27 (a) Ans: answer KU (b) Ans: proof forming equation 55 = n ( n ) rearranging n n 0 = 0 RE 55 = n n 0 = n n (i) for a solution of 55 = n ( n ) n n 0 = 0 award (c) Ans: factorising ( n + 0 )( n ) = 0 solving equation -0 and selecting valid solution 3RE (i) for an answer of without working award 3 0 Page 7

28 (a) Ans: 78.7, 58.7 equation tan x = 5 first solution 78.7 second solution 58.7 (first solution + 80) 3RE (i) for answers of 90 or 70, only the st mark is available (b) Ans: RE (i) the solution must be consistent with a solution in part (a) (ii) for 450, following from 90, 70 in part (a) award KU 8 marks RE 33 marks [END OF PAPER MARKING INSTRUCTIONS] Final KU 45 Totals RE 45 Page 8