AQA GCE Mark Scheme June 2005 - Mr Barton Maths

Version : 1.0: 0206

abc General Certificate of Education

Mathematics 6360 MD01 Discrete 1

Mark Scheme 2005 examination – June series 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.

Copyright 2005© AQA and its licensors. All rights reserved.

MD01 - AQA GCE Mark Scheme, 2005 June series

Key to mark scheme and abbreviations used in marking M m or dM A B E

or ft or F CAO CSO AWFW AWRT ACF AG SC OE A2,1 –x EE NMS PI SCA

mark is for method mark is dependent on one or more M marks and is for method mark is dependent on M or m marks and is for accuracy mark is independent of M or m marks and is for method and accuracy mark is for explanation

follow through from previous incorrect result correct answer only correct solution only anything which falls within anything which rounds to any correct form answer given special case OE 2 or 1 (or 0) accuracy marks deduct x marks for each error no method shown possibly implied substantially correct approach

MC MR RA FW ISW FIW BOD WR FB NOS G c sf dp

mis-copy mis-read required accuracy further work ignore subsequent work from incorrect work given benefit of doubt work replaced by candidate formulae book not on scheme graph candidate significant figure(s) decimal place(s)

Application of Mark Scheme No method shown: Correct answer without working Incorrect answer without working

mark as in scheme zero marks unless specified otherwise

More than one method / choice of solution: 2 or more complete attempts, neither/none crossed out 1 complete and 1 partial attempt, neither crossed out

mark both/all fully and award the mean mark rounded down award credit for the complete solution only

Crossed out work

do not mark unless it has not been replaced

Alternative solution using a correct or partially correct method

award method and accuracy marks as appropriate

2

AQA GCE Mark Scheme 2005 June series – MD01

MD01 Q

Solution

Marks

Total

Comments

1(a) 23

3

17

4

6

19

14

3

3

23

17

4

6

19

14

3

3

17

23

4

6

19

14

3

3

4

17

23

6

19

14

3

3

4

6

17

23

19

14

3

3

4

6

17

19

23

14

3

3

4

6

14

17

19

23

3

3

3

4

6

14

17

19

23

M1 A1 m1 A1

A1

Total

SCA 1st pass 2nd pass 3rd pass

5

All correct

5

2(a)

M1 A1

(b) Initially KP, MJ, NA Paths G → A→ N → F

S →J →M →R Match GA, NF, SJ, MR, KP Or GP, KF , MR, SJ , NA

2

Bipartite graph

B1

Starting with G, F, S, R

M1 A1 M1 A1

1st pass path starting G,F

B1

Total

6

8

3

2nd pass path starting S,R Or G → P→K →F Or S → A→ N → F G → A→ S → J → M → R


MD01 (cont) Q

Solution

Marks

Total

Comments

3(a)

AB AC BD CE EF FI HI IK HG HJ

or 20 25 30 35 40 35 30 35 40 45

M1 B1 A1 A1

(b) 335

SCA 10 edges BD third CE fourth

A1

5

B1

1

All correct

(c)

B1 M1 A1

(d) Add AE Delete CE

Extra

+40 –35

M1

+5

A1 Total

10 edges 3

Adding AE, deleting CE/CA 2 11

4

15 with no working ( M1, A0 )


MD01 (cont) Q 4(a)(i) 21 (ii) 6 (iii) 7

Solution

(b)(i) All vertices are even (ii) n odd

Marks

Total

B1 B1 B1

1 1 1

E1 E1

1 1

Comments

OE

(c)

M1 A1

Total 5(a)(i)

X 2 5 4.1 4.001

(ii)

K

Graph with 6 vertices 2

7

Y

1 2 3 4

5 4.1 4.001

X

K

−6 −4.33 ( 3) −4.01( 3)

1 2 3

−4.000

4

M1 A1 A1 A1

Y −4.33 ( 3) −4.01( 3) −4.000

A1 A1 A1

(b) Continuous loop

B1 Total

5

4

SCA (either part) Y=5 Y = 4.1 All correct

3

Y = – 4.33 (…) Can be fractions Y = – 4.01 (…) All correct

1 8


MD01 (cont) Q 6(a)(i)

(ii)

Solution

S →R→M →B→L→S 15 55 25 50 = 165

Marks

M1

20

A1

S →R→L→B→M →S 15

25

50

25

Total

90

= 205

Comments

Adding 5 numbers 2

M1

Tour

M1 A1 B1

Visits all vertices Correct order 4

(b)

Choose 25, 50 (or BM, BL) Total 165

M1

SCA ( mst and 2 edges )

m1

3 edges

A1

Correct mst

m1 A1

5

(c)

B1F

E1

Total

ft if M1 awarded in (b)

2

13

6

Either


MD01 (cont) Q

Solution

Marks

Total

Comments

If reverse M1 SCA M1 2 values at W A1 both correct M1 2 values at R A1 all correct B1 400

7(a)

M1

SCA

A1

2 correct values at G

M1

2 values at C

M1

2 values at T

A1

All correct 400 at L

A1

6

(ii) R S G W M C L

B1

1

(b) Possible R C L = 410 R S G W T L = 415 Extra time = 10 minutes

M1

Considering both routes

A1

410 and 415

RCL

B1 Total

7

3 10


MD01 (cont) Q

Marks

Total

8(a) Milky 12 x + 18 y ≤ 600 ⇒ 2 x + 3 y ≤ 100

B1

1

x ≥ 15, y ≥ 15 x + y ≥ 35 20x + 10y ≤ 600 ( P = ) 1.5x + y

B1 B1 B1 B1

(b)

Solution

Comments

OE

4

(c)

B1 B1 ×3 B1 B1

6

G

(d) Considering one of their extreme points

P = 50

M1 A1

Total Total

2 13 75

8

x ≥ 15, y ≥ 15 Other 3 lines Feasible Region Objective Line