General Certificate of Secondary Education June Mathematics (Linear) B 4365 Paper 2 Higher Tier. Final. Mark Scheme

Transcription

1 General Certificate of Secondary Education June 0 Mathematics (Linear) B 4365 Paper Higher Tier Final Mark Scheme

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 students responses to questions and that every examiner understands and applies it in the same crect way. As preparation f the standardisation meeting each examiner analyses a number of students scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated f. 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 wking document, in many cases further developed and expanded on the basis of students 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 0 AQA and its licenss. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered schools/colleges f AQA are permitted to copy material from this booklet f their own internal use, with the following imptant exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even f internal use within the school/college. Set and published by the Assessment and Qualifications Alliance. 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 ). Registered address: AQA, Devas Street, Manchester 5 6EX

3 Glossary f Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, f GCSE Mathematics papers, marks are awarded under various categies. M M dep A B B dep Q ft SC Method marks are awarded f a crect method which could lead to a crect answer. A method mark which is dependent on a previous method mark being awarded. Accuracy marks are awarded when following on from a crect method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. A mark that can only be awarded if a previous independent mark has been awarded. This mark is f quality of written communication. Further details of how to apply it will be in the mark scheme. Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation which has some mathematical wth. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as [a, b] Accept values between a and b inclusive.

4 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final (7.) x 6 = (their 3.) 4 dep 4x = x = A SC SC their hours 36 (minutes) A miles to go 67.6 (mph) h 30.5 h 50 (minutes) (not 9.0) B.5 h No A 47 B May be seen on diagram 3(a) Cresponding Q eg (y is) alternate and x is opposite Check part (b) Strand (i) 3(b) 47 Bft Alternate (vertically) opposite Q May be seen on diagram ft their (a) eg x is cresponding and y is opposite Strand (i) (x ) (x ) ( ) ( 00) x 600 ( 00) A 45 their and 540 and Hire Deal A their 60 9 their and 54 and Hire Deal 4

5 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final 5 5 ( ) (3 3 + ) ( ) 705 A 6(a) x + x = 360 x + 6 = 360 x + x = x = (=0) and their 0 6 (=9) dep their 9 (x =) 46 A Answer may be on diagram 6(b) Yes and = = 0 Bft ft reason from their x (5) A 34.7 Bft ft their answer if me dp seen SC f 34.7 coming from premature rounding approximation seen x (= 0) 3x 7 = 0 4 3x = x = 0 + 3x = This mark is f separating terms in their equation 4 Aft ft if M0 M0 9 Lists at least 3 crect combinations seen ()A3, ()A4, ()B3, ()B4, ()C3, ()C4 3 Lists chooses all 6 crect combinations 3 6 seen 3 Seen implied eg 6 lines drawn from letters to numbers on diagram A 3, A 4,B 3 etc 6 A 5

6 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final Crect trial such that root < trial 5 eg = 5 (too big) Obtains 3 < x 5 better (need not be stated) 3 < trial < st trial Improved crect trial 3 < trial < root eg = 3.(3 ) 3.4 (too small) ( ) 35.9 Obtains 3. x 3.9 better A (5 ) (4 ) (6 ) (665) Tests 3.5 ( 3.4) and concludes 3. Q (0304) Using dp to ensure dp Strand (ii) (AC =) (=490) A = tan - 3 ( ) C = tan - 3 ( ) their 490 dep eg 3 sin cos cos sin (...) 39 A Suitable question with time frame B Suitable response section B No gaps, no overlap and final categy openended 3(a) 3x x x 3 x 7 A 3(b) y 6 B 6

7 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final Crect heights plotted shown B 4 Fully crect frequency polygon B Midpoints used and straight lines intended to join them Allow midpoints to be at [4.5, 6] [34.5, 36] etc SC f one height plotted increctly but midpoints used in an otherwise crect frequency polygon Equates two sides 5w = 3w + 3 3w + 3 = w + 6 5w = w + 6 Collects like terms 5w 3w = 3 dep 3w w = 6 3 5w w = 6 5 (w =).5 A Wks out that all sides are 7.5 solves another pair to get (w =).5 A Must have 3 rd side = 7.5 and one side using their equation = 7.5 as a minimum 6 Crect cubing of any integer [5, 30] Note: 5 3 = = = = = = A SC f 3 (= 53) their (%) (%) dep 00 00(%) (6..) A (a) r + r B their ( r + r) =.6 Bft ft their fmula from (a) f an increct fmula that is given in (a) Allow = 3.4 better throughout (b) r( + ) =.6 (r =).6 ( + ) A.6.3 Bft Accept..5 if r used.7.7 if r used if r used 7

8 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final 9(a) Fully crect box plot B B f three four five crect plots 0, 50, 30, 390, 470 9(b) No change Increase Increase B B B 0(a), 3, 5 B B f crect 0(b) Axes drawn and labelled Points plotted Bft ft 5 points B B f x-axis from to (minimum) B f y-axis from 3 to 5 (minimum) Condone one missing x y label Smooth curve through their 5 points Bft Must be a U shape Possible weight given f one of Amy s fish [6.75, 6.) [4.5, 4.3) [5.5, 5.) Any Amy weight could go down ( Kate up) by 0.05 Possible weight given f one of Kate s fish (.,.5] (3.4, 3.45] (4.5, 4.55] Any 3 Amy weights could go down ( Kate up) by of these allowed values = = 6.5 Totals showing possible Must have total f Kate > total f Amy A Amy = [6.5, 6.3) Kate = (6., 6.5].5 3 seen seen as a scale fact.5.5 dep : : tan C = 36 EC = = EC CE = tan (their 36) A 6.5(...) 5.5(...) ( + ) their 5.5 their 99 ( + ) their ED their 6.5 their ED + x their ED 4

9 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final 55 A 3 Lists outcomes, 4 4,, 5 5,, 6 and/ 6,, 4 4,, 5 5,, 6 6, Even dice 3 odd dice 3 odd dice even dice One of: P(both even) = = One of : A (both even) has outcomes B (both odd) has outcome C (one odd one even) has 3 outcomes dep P(both odd) = = 3 6 P(odd and even any der) 3 = + = B, A, C A All three shown and crect and BAC 6x 5xy + xy 5y 3 terms crect 4 6x 5xy + xy 5y 6x 3xy 5y A ft ft from four terms A 5 (x =) (x =) () 4(6)( 5) (6) () 4(6)( 5) (6) 0.76 and.09 A A (x =) Allow one err their (a) (7 ) their their (5 ) A Must have come from use of volume of a sphere fmula B ft ft any crectly rounded down number 9

10 AQA GCSE Mathematics Linear (B) 4365/ Paper Higher Tier /June 0 / Final 6(b) 500 their their A ft their 0 x 0 x 4 from (a) 5 4 (3n )(n ) (3n + )n n(n ) as denominat on LHS 7 (3n )(n ) (3n + )n dep 3n 6n n + 3n n 3n 6n n + and 3n n dep dep on first only A Crect common denominats must be used f 4 marks to be awarded 4 x (..) 0.4(4 ) 0.09(0909 ) (3 ) better A If replacement used award SC f 3 SC f Choose st counter in ways Choose nd counter in ways (any of the other two colours) Alt 96 A 3 0