Edexcel Math GCSE Mark Scheme June 2008 3H

Edexcel GCSE

Mathematics 2540

Paper 5540H/3H

Mark Scheme

Summer 2008

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NOTES ON MARKING PRINCIPLES

1 Types of markM marks: method marksA marks: accuracy marksB marks: unconditional accuracy marks (independent of M

marks)

2 Abbreviationscao – correct answer only ft – follow throughisw – ignore subsequent workingSC: special caseoe – or equivalent (and appropriate)dep – dependentindep - independent

3 No workingIf no working is shown then correct answers normally score

full marksIf no working is shown then incorrect (even though nearly correct) answers score no marks.

4 With workingIf there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme.If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. Send the response to review, and discuss each of these situations with your Team Leader.Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader.If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used.If there is no answer on the answer line then check the working for an obvious answer.

5 Follow through marksFollow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award.

Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.

6 Ignoring subsequent workIt is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg. incorrect cancelling of a fraction that would otherwise be correctIt is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect eg algebra.Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer.

7 ProbabilityProbability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks.If a probability answer is given on the answer line using both incorrect and correct notation, award the marks.If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.

8 Linear equationsFull marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded.

9 Parts of questionsUnless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another.

GCSE MATHEMATICS– JUNE 20085540H/3H - MARK SCHEME

PRE-STANDARDISATION VERSION

5540H/3HQuestion Working Answer Mark Notes1 (a) 24

3008

900 2

M1 for 24

8 oe or oe or 300 + 300 + 300

A1 for 900 (b) 180 2

M1 for use of or 1.5 or 120 + 60 or “120 8” 12

A1 for 180



5540H/3HQuestion Working Answer Mark Notes2 540

24 2160 10800 12960

5 4 0

11

0 8 02

22

01

6 04

9 6 0

10000 + 2000 + 800 160 = 12960

100 + 20 + 8 + 1.6 = 129.6

129.6(0) 3 M1 for a complete method with relative place value correct. Condone 1 multiplication error, addition not necessary.

OR

M1 for a complete grid. Condone 1 multiplication error, addition not necessary.

OR

M1 for sight of a complete partitioning method, condone 1 multiplication error. Final addition not necessary.

A1 for 129.6(0) caoA1 (dep on M1, but not previous A1) for correct placement of decimal point.

500 40 0

20 10000 800 0

4 2000 160 0

3 0.1 0.05

60 2 1 20

12 0.4 0.2 4



5540H/3HQuestion Working Answer Mark Notes3 2 378

3 14564 124555 023

2 3 = 23

3 M1 for using 2, 3, 4 and 5 as stemA1 for ordered stem and leaf diagram

B1 for key, e.g. 2 3 represents/means/= 23 (years)

4 (a) 1632 1 B1 for 1632 or 1632.0(b) 16.32 1 B1 for 16.32 cao(c) 3.4 1 B1 for 3.4 cao

5 (a) S 1 B1 for S cao(b) (2, 1, 3) 1 B1 for (2, 1, 3) cao

6 (a) (18 6) 4 3 2 M1 for 18 6 or 12 or 3 4 + 6A1 for 3 cao

(b) 2 B2 for (B1 for + a or +#6)

7

=

12 + 21 + 28 + 35

96 cm2 4M1 for or or or

M1 for attempt to add 5 facesA1 for 96 B1 (indep) for cm2



5540H/3HQuestion Working Answer Mark Notes8 6000 3 M1 for any two of 300, 10 or 0.5

A1 for or 300 20 or 600 10

A1 6000

9 1-h(0.1 + 0.2 + 0.3)

0.4 2 M1 for or 0.6 seen

A1 for 0.4

10 (a) 20pq 1 B1 for 20pq oe(b) d4 1 B1 for d4 cao(c) 2 M1 for or

A1 for cao(d) 2 M1 for 4n + 6 or 3n + 3

A1 for (e) 1 B1 for

(accept oe)(f) 1 B1 for

(accept oe)

11 Correct drawing 2 M1 for constructing arcs from each of the ends of the given lineA1 for a correct triangle with arcs within guidelinesSC: B1 for a correct triangle drawn within guidelines if M0 scored



5540H/3HQuestion Working Answer Mark Notes12 –2, –1, 0, 1, 2 2 B2 for –2, –1, 0, 1, 2 cao

(B1 for 4 correct and not more than one incorrect value or all 5 correct and not more than one extra incorrect value)

13 (a) 1B1 for or 0.25 or 4–1

(b)

or

or2.8-1.75

3 M1 for attempt to convert to fraction with common denominator, e.g. two fractions denominator 20

A1 correct conversion: and oe, or or oe

A1 for or

OR

attempts to convert to decimals: must be exactM1 for 0.8 0.75 (or 2.8 1.75)A2 for 1.05(A1 for 0.05)

(c) Reason 1 B1 for ‘1/3 = 0.3 recurring, which is not equal to 0.3’ oe



5540H/3HQuestion Working Answer Mark Notes

14 (a) Triangle A Triangle with vertices (-1,5),

(-1,3), (3,3)

2 B2 for triangle with vertices (–1, 5), (–1, 3), (3, 3)(B1 for triangle with correct orientation)

(b) Triangle B Triangle with vertices (1,-2),

(5,-2), (5,-4)

1 B1 for triangle with vertices (1, –2), (5, –2), (5, –4)

(c) Triangle C Triangle with vertices (1,1.5),

(2,4), (1,4)

2 B2 for triangle with vertices (1, 1.5), (2, 4), (1, 4)(B1 for any two of the vertices (1, 1.5), (2, 4), (1, 4) )

15 (a) 2 B2 for

(B1 for seen)(b) 1 B1 for

16 (a) Complete box plot MedianHighest mark

2 B1 line drawn at 30B1 whisker drawn to 55

(b) Complete table 10 1 B1 for 10 cao

17 (a) 64000 1 B1 for 64000 (b) 3.9 10–3 1 B1 for 3.9 10–3 (c) 2.5 106 1 B1 for 2.5 106



5540H/3HQuestion Working Answer Mark Notes18 (a)(i) 2 70 140 2 B1 for 140 cao

(ii) Reason B1 for ‘angle at centre is twice angle at circumference’(b)(i)

180 – 70 or 110 2 B1 for 110 cao

(ii) Reason B1 for ‘opposites angles in a cyclic quadrilateral sum to 180 degrees’ or (if using BOD=220) ‘angle at centre is twice angle at circumference’

19 e.g. adding equations leads to 3x = 9

substitute x = 3 into eqn(1) leads to 3y = 6

3 M1 for adding equations or for coefficients of x the same followed by subtracting the equations, condone one arithmetical errorM1 (dep) for substituting found value in one equationA1 cao(SC: B1 for one correct answer only if Ms not awarded)

20 (a) 7, 2, 2 2 B2 all three correct(B1 for any one or two correct)

(b) y

x

2 B1 ft points plotted correctly 2 mmB1 for smooth curve drawn through their points provided B1 awarded in (a).




21 (a) 0.2 and 0.4, 0.4 2 B1 for 0.2 on LH branchB1 for 0.4 on both RH branches

(b) 0.48 2 M1 for A1 for 0.48 oe

(c) 0.44 3 M1 for 0.8’0.4’ or 0.20.6M1 for A1 for 0.44 oe

22 4 M1 for M1 for M1 for

A1 for cao

23 (a) 1 B1 for cao

(b) 2 M1 for or three of 2, , , 3A1 for cao[SC: B1 for or if M0 scored]




24 (a) 320 2M1 for

A1 for 320 cao(b) 75 2

M1 for

A1 for 75 cao

25 (a)(i)a

2B1 for a oe

(ii)a c B1 for a c oe

(b) = a c

= (a c)

2 B1 for = a c oe

B1 for oe

26 3M1 for = “volume of cone” or = “volume of

cylinder”M1 (dep) for a case of attempt to isolate h

A1 for cao

27 (i) (4, 3) 2 B1 for (4, 3)(ii) (2, 6) B1 for (2, 6)




28 3B3 for

(otherwise award B1 for and/or B1 for

seen)

Documents

Edexcel Math GCSE Mark Scheme June 2008 3H