Mark Scheme. Mathematics Specification A. General Certificate of Secondary Education. Paper 2 Higher examination - November series

Transcription

1 Version 1.0 abc General Certificate of Secondary Education Mathematics 3301 Specification A Paper Higher Mark Scheme 007 examination - November series

2 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 007 AQA and its licensors. All rights reserved. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). egistered address: AQA, Devas Street, Manchester 5 6EX. Dr Michael Cresswell, Director General. 3

3 Glossary for Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, for GCSE Mathematics papers, marks are awarded under various categories. M A B M dep B dep ft SC oe Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth. Or equivalent. Accept answers that are equivalent. 1 eg, accept 0.5 as well as

4 Paper H 1(a) 1.5 oe 1(b)(i) (b)(ii) 3.76, 3.8, 4 ft From any value 4 sf rounded to or 3 sf or any value greater than 3dp rounded to dp (a) 8x 8 = 1 + 3x Allow one sign or arithmetic error but not 8x 7 = 1 + 3x 8x 3x = x = 40 Allow one error (x =) 8 A1ft ft On one error SC 8x 7 = 1 + 3x leading to (x =) 3.8 oe (b) y 63 = 14 y (y =) 77 A1 7 = 11 3(a) Arc from P cutting road twice NB If end of road used only one arc may be seen Arcs on either side of line or same side above or below P Completion of perpendicular A1 SC only 3(b) 0.5 Their perpendicular inclusive A1 4 Trial above and correctly evaluated Trial below and correctly evaluated Testing a value that justifies 3.7 as answer ( inclusive) 4 7, , , , dep , Dependent on both M marks 3.7 A1 All values at least 1 dp rounded or truncated 3

5 seen 85% = or digits 85 oe 1% = (=147.) A A1 Digits 147 only implies Misread of 75%, say gives can score /3 6(a) 0 05 inclusive 6(b) 9 6(c) (= 7) ( 100) oe , 115.9, 160 A , 15.9, 16 (with working) A1 T&I at least to 15.9 accuracy seen 7(a) x + x 4x 8 Allow one arithmetic or sign error but must have x, two x terms and a constant term x x 8 A1 Allow non contradictory fw but do not award A1 If contradictory fw 7(b) m m + 3 Allow one arithmetic or sign error 4m + 13 or 13 4m A1 Allow non contradictory fw but do not award A1 If contradictory fw 8(a) (x =) 3 1 x + 1 = dep Must subtract squares and show intention to square root NB 3 1 is A1 4 with working 8(b) Sight of cos 18 cos 35 dep Any alternative method must have a complete scheme to get M 14.7 A1 15 with working NB Gradians

6 9 π to 15.1 A or 1000 Their 15. dep Their value 75 No with appropriate values eg, 13.3 and 15. or 1.9 (needed) or 75 and A1 No as 115 to > (a) A and D 10(b) B and C 10(c) B and C 11 Digits 85 cubed (0.614 ) Any power of 10 Their dep A1 NB Digits is M 1(a) x > 1(b) Fully correct B3 1 eeoo (allow solid or dashed lines) All lines correct, drawn dashed, marked 3 marks NB Solid lines should be considered incorrect for 1 mark loss 5

7 marked correct relative to two correct dashed lines 3 rd line incorrect or missing marks NB Solid lines should be considered incorrect for 1 mark loss All lines correct, drawn dashed, shaded in or out, not marked marks NB Solid lines should be considered incorrect for 1 mark loss 6

8 marked correct relative to one correct dashed line other lines incorrect or missing 1 mark NB Solid lines should be considered incorrect for 1 mark loss Two lines correct, drawn dashed, shaded in or out, not marked 1 mark NB Solid lines should be considered incorrect for 1 mark loss All lines correct, drawn dashed, no shading, not marked 1 mark NB Solid lines should be considered incorrect for 1 mark loss 7

9 13(a) 0.3, 0.3, 0.7, (b) (= 0.1) oe Multiplication of one of: Their green one of Their yellow 1 (Their yellow yellow) (Their green green) M 0.1 dep oe Addition of both their green yellow 0.4 A1ft oe ft Only if each pair of probs total 1 14(a).99(4) 10-3 or B Digits 994 or partial working or (b) 1 Their (a) Correct answer but not in SF eg, , 3 10 with working A AB = BC AM = MC (M midpoint of AC) Deduct for first non-reason only BM (common side) Congruent because of SSS oe Must mention 3 sides 15 Alt Angle BAM = Angle BCM (equal angles in isosceles triangle) Deduct for first non-reason only AM = MC (M midpoint of AC) BM (common side) or AB = BC Congruent because of SAS oe Must mention sides and included angle 8

10 16(a) (a 5) (a + 5) B For (4a 10)(a + 5) or (a 5)(4a + 10) or 8(a.5)(a +.5) 16(b) (6x 3)(x 5) or 3(x 1)(x 5) or (x 1)(6x 15), A1 Allow M if attempt made to split 1x or 4x into factors and 15 or 5 into factors and combine in brackets eg, 1x x 3 5 A1 If correct If factor of 3 cancelled ie, 4x 1x + 5 4x 1 A1 for top factorised to (x 1)(x 5) 3(x 1)(x + 1) or (6x 3)(x + 1) or (x 1)(6x +3) (x 1)(x + 1) x 5 A1 Allow non contradictory fw but do not x + 1 award A1 if contradicting fw 17(a) Attempt mf If correct 85, 1460, 1050, 1386, 948, 34 (=600) Their mf 40 dep Must divide by A1 Ignore rounding or truncation after correct answer but must see working for (b) 17 and / or 8 B Each value Correct bars width and height B 1 eeoo Correct heights 1.5, 1., 0.8 Gaps between bars 1 error 17(b)Alt Attempt to find area fd width ie, or and 8 A1 Calculation of at least fds ie, 5 0, 18 15, 1 15 Correct bars width and height A1 Correct heights 1.5, 1., 0.8 9

11 18 4 π 3 3 = k 1 π 6 8 M oe for both formula with correct values 3 3 (allow one error with radii) k = 8 3, 0.375, 37.5% A1 oe Values 113 to and 301 to for comparison 19(a) y = 3 x x + (3 x) = 5 x + 9 1x + 4x = 5 A1 x + 9 6x 6x + 4x = 5 19(b) (5x ± a)(x ± b) where ab = 4 ( 1 ± ( 1) Allow one error in use of formula from b, b, 4ac, a Do not accept wrong formula, wrong values, just dividing by or not dividing top line by a (5x )(x ) A1 1 ± or 1 ± 8 10 x = or 0.4 (or ) 5 A1 ft On 1 to and 0.4 ft On + 80 to.6966 and

12 0 P = 13 cos PQ = or oe For other angles 13 = cos Q PQ = 66 º A1 PQ = 34, QP = 79.7 or 80 Area = sin (Their 66) Dep oe For other angles to 51. A1 0 Alt P = 13 Use of Hero s formula (3 sides) 17.5 A1 (17.5)(4.4)(3.5)(9.5) Dep to 51. A g limit, A1 eg,.45,.85, For limit, A1 for at least correct Airport scales 9.95 minimum OK as 9.9 < 9.95 ft ft If they compare Their maximum total and airport scale minimum and reach a correct conclusion. P() + P( ) 1 P (no red) or 1 P (all blue) Must show all 3 probabilities A oe 5 A1 oe 50 decimals at least 3sf for answer

13 3 y = k 1 x 3 = k 8 y = k z = k/16 x 3 k = 3 z M k 1 = 4 1 A1 k 3 = 18 A k = 3 A1 A1 1