Version.0 General Certificate of Education (A-level) January 0 Mathematics MSB (Specification 6360) Statistics B Final Mark Scheme
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 events which all examiners participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every examiner understands and applies it in the same correct way. As preparation for standardisation each examiner analyses a number of students scripts: alternative answers not already covered by the mark scheme are discussed and legislated for. If, after the standardisation process, examiners encounter unusual answers which have not been raised 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 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 from: aqa.org.uk Copyright 0 AQA and its licensors. All rights reserved. Copyright AQA retains the copyright on all its publications. However, registered schools/colleges for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even for internal use within the centre. 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 3673) and a registered charity (registered charity number 07333). Registered address: AQA, Devas Street, Manchester 6EX.
Key to mark scheme abbreviations M mark is for method m or dm mark is dependent on one or more M marks and is for method A mark is dependent on M or m marks and is for accuracy B mark is independent of M or m marks and is for method and accuracy E mark is for explanation or ft or F follow through from previous incorrect result CAO correct answer only CSO correct solution only AWFW anything which falls within AWRT anything which rounds to ACF any correct form AG answer given SC special case OE or equivalent A, or (or 0) accuracy marks x EE deduct x marks for each error MS no method shown PI possibly implied SCA substantially correct approach c candidate sf significant figure(s) dp decimal place(s) o Method Shown Where the question specifically requires a particular method to be used, we must usually see evidence of use of this method for any marks to be awarded. Where the answer can be reasonably obtained without showing working and it is very unlikely that the correct answer can be obtained by using an incorrect method, we must award full marks. However, the obvious penalty to candidates showing no working is that incorrect answers, however close, earn no marks. Where a question asks the candidate to state or write down a result, no method need be shown for full marks. Where the permitted calculator has functions which reasonably allow the solution of the question directly, the correct answer without working earns full marks, unless it is given to less than the degree of accuracy accepted in the mark scheme, when it gains no marks. Otherwise we require evidence of a correct method for any marks to be awarded.
MSB (a).0 and. both (allow. 09 and. 9 ) (b) E X 0 (symmetry) Var X 0. 0 0. 0 00 sd X 00 0 3 A 3 For R then: Var a,a : E 0 X a a X iff a 0. 0, 0., 0. or their a = 0.09 to 0.0 used for 3 or 60 or 00 0.089 (3sf) A0 (c) P 0. 0 X 0. 03 0. 00 = 0. cao from correct value used 0. 03 Total 0. 0 oe 0. 03 0dx 0x 0. 0. 0
MSB (cont) (a)(i) H 0: 6. H : 6. (both) z calc 6. 0 6. 7. 6. 9 A z crit. 96 or (shown in / implied by diagram) Alternative: P X 6. 0 P Z. 9 0. 977 0. 073 0. 0 Accept H0 Use of t max(a) Accept H0 Adep dep() but not A (ii) Insufficient / o evidence (at % level) to suggest /show mean (age has) changed (from 6. years.) Mean (age) has not changed at % level (of significance) Edep 6 6. 3 7. 38. 9 > none under the age of years. Very unlikely any members < yrs. If incorrect or no hypothesis then B0 max(a) i.e. final AdepEdep not available dep(adep) 6. z. 8 7. P Z. 8 0 none aged under included (b)(i) y 70 y 8. n y y 88. 8 0 n s. ( s. 83 ) 7. 3 or. 7 iff used below t. 796 crit 90% CI for : s 8.. 796 8.. 68 7. 03, 9. 97 Ignore signs for t crit If z used then max(b0m0a0) their y their y their s t OR their t 7. 0, 60. 0 A (ii) upper limit < 6. recruitment drive lowered the average age of the club membership ft Total 3 Must refer to 6. (on their CI)
MSB (cont) 3(a)(i) mp ; mq ; np ; nq any one correct Ei B, B all correct (simplified) (ii) mp mq np nq Ei i m p q n p q (oe) m n = = m n = (since p + q = m + n = ) Mdep Adep 3 i E i mp mq np nq m p q n p q = (or use of unsimplified forms) = p qm n (AG) = = (b) H0 : o association between Andy's results and wind conditions E : i 7.8.8 33 9.8 7.8 7 7 3 0 0 E 0.. 3 i i X 0. 300 0. 36 0. 863 0. 6883 =.93 0%. 706 Accept H0 A Adep Attempt E s Yates correction attempted Final column attempted awrt correct value of dep ( for H 0 ) only (allow.7) o association (between Andy s results and wind conditions) Edep 8 Total 3 Appropriate conclusion dep( for H ; final column;. 706 ) 0 0% (a)(ii) An example of unsimplified values mp derived from a : mp mp b m ; c p ; mp d n (oe) n
MSB (cont) (a)(i) Poisson (ii) X X E 3 3 Var 3 9 oe (allow 3 ) (iii) e P X x e P X x x! x x! x (b)(i) car 00 / hour coach x e x x! x e x x! P X x x 0 / hour vehicle 0 / hour 8. / min P V 0 0. 630 0. 37 (ii) car 836 / hour coach / hour vehicle 88 / hour =. 3 / min V V,,, P 3 P 0 3 Mdep Adep 3 A 3 dep() AG for 8. stated / used special case: 0 M0A0 0. 8 or 0. for.3 stated /used 3. 3. 3. 3. 3 e 6. 3 e 60. 983 0. 000376 to 0. 000373 All terms required for any 0 M0 for use of normal approximation 0. 00037 (sf) Adep 3 dep Total
MSB (cont) (a) P n n Outcome H 0. ( ) TH 0. ( ) 3 TTH 0. ( 8 ) TTTH 0.06 ( 6 ) TTTTA 0.06 ( 6 ) B, for one correct entry for n =,, B for all 3 correct Can be implied by correct E (b) E 3 8 6 6 3 3 8 6 6 6 (.937) 6 m Outcome PM m H TH 3 3 6 3 TTH TTTH 3 3 3 9 6 7 6 A TTTTA 3 8 6 B3,, 3 n n n P n (all terms attempted /seen/ implied) (awfw.93 to.9) (given) (given) ( any one correct) (B any correct) (B3 all 3 correct) (c)(i) P J,R: P, 8 (oe) 3 3 P, 6 6 (oe) 9 9 P3,3 8 6 (oe) 7 7 P, 6 6 096 (oe) 8 8 P, (oe) 6 6 096 n p Pn,n n p (0.8) 0 (ii) 803 3 0 0 + 3 0 X X X P P P 3 0. 0 (3dp) A A m A Mdep A Total 6 e.g 0. attempt at any Pn,n any correct to 3sf all correct to 3sf n n P n,n with all values attempted (awfw 0. to 0.7) (either term with their p used) ( 0 p ) (second term with their p used) ( 0 p ) dep () (allow 0.9; 0.; 0.)
MSB (cont) 6(a) B for st. line from, 0. to, 0. 3 B, st. line (m > 0) from x = to x =. 0 3 (b) E X x x 7 dx 0 3 x 7x 0 3 7 7 0 3 3 3 A A 3 Ignore limits Ignore limits cao (accept 3. 33 7 or oe exact) (c) x F x x 7 dx 0 x 7x 0 80 x x 80 x x 80 x x (d)(i) P. X. F. F. (ii) F m x 9. 3. 7.. 80 (0.) 80 0 A Adep Adep A F x x 7 dx 0 0 x 7x c (A) 80 0 7 F 0 c 80 0 80 or [use of F() = ] F(x) 80 x x F x x x (AG) 80 Trapezium Rule 3 9 80 80 = 80 0 m 0 x 7 dx 0. () (e) m m 80 80 m m 0 m m 0 Adep 3 96 0 0. 396 m 0. 396 m (since m > ) A m 3. 98 (3dp) Total 6 TOTAL 7 Correct equation formed AG Correct attempt at solving quadratic (by formula, oe). cao