GCSE Mathematics C (Graduated Assessment) Max Mark a* ......2011/06/02 · B282/01 Mathematics Terminal Paper (Higher) Raw 100 89 71 53 35 20 12 n/a n/a 0 UMS 400 360 320 280 240

For a description of how UMS marks are calculated see:www.ocr.org.uk/learners/ums_results.html

GCSE Mathematics C (Graduated Assessment)Max Mark a* a b c d e f g p u

B271/01 Mathematics Module Test M1 Raw 50 n/a n/a n/a n/a n/a n/a n/a 24 12 0UMS 59 n/a n/a n/a n/a n/a n/a n/a 40 20 0

B272/01 Mathematics Module Test M2 Raw 50 n/a n/a n/a n/a n/a n/a 35 20 13 0UMS 70 n/a n/a n/a n/a n/a n/a 60 40 30 0

Max Mark a* a b c d e f g uB273/01 Mathematics Module Test M3 Raw 50 n/a n/a n/a n/a n/a n/a 24 11 0

UMS 79 n/a n/a n/a n/a n/a n/a 60 40 0B274/01 Mathematics Module Test M4 Raw 50 n/a n/a n/a n/a n/a 36 22 13 0

UMS 90 n/a n/a n/a n/a n/a 80 60 50 0B275/01 Mathematics Module Test M5 Raw 50 n/a n/a n/a n/a n/a 24 12 n/a 0

UMS 99 n/a n/a n/a n/a n/a 80 60 n/a 0B276/01 Mathematics Module Test M6 Raw 50 n/a n/a n/a n/a 28 13 n/a n/a 0

UMS 119 n/a n/a n/a n/a 100 80 n/a n/a 0B277/01 Mathematics Module Test M7 Raw 50 n/a n/a n/a 30 16 n/a n/a n/a 0

UMS 139 n/a n/a n/a 120 100 n/a n/a n/a 0B278/01 Mathematics Module Test M8 Raw 50 n/a n/a 29 15 n/a n/a n/a n/a 0

UMS 159 n/a n/a 140 120 n/a n/a n/a n/a 0B279/01 Mathematics Module Test M9 Raw 50 n/a 27 13 n/a n/a n/a n/a n/a 0

UMS 179 n/a 160 140 n/a n/a n/a n/a n/a 0B280/01 Mathematics Module Test M10 Raw 50 32 17 n/a n/a n/a n/a n/a n/a 0

UMS 200 180 160 n/a n/a n/a n/a n/a n/a 0B281/01 Mathematics Terminal Paper (Foundation) Raw 100 n/a n/a n/a 71 58 45 32 19 0

UMS 279 n/a n/a n/a 240 200 160 120 80 0B282/01 Mathematics Terminal Paper (Higher) Raw 100 89 71 53 35 20 12 n/a n/a 0

UMS 400 360 320 280 240 200 180 n/a n/a 0

Unit level raw mark & UMS grade boundaries; specification level UMS grade boundaries - June 2010 series: GCSE 87

GCSE Mathematics C (Graduated Assessment) Max Mark A* A B C D E F G U

J517FMathematics C Foundation (Graduated Assessment) (Two Tier) (GCSE) UMS 800 n/a n/a n/a 460 380 300 220 140 0

J517HMathematics C Higher (Graduated Assessment) (Two Tier) (GCSE) UMS 800 700 620 540 460 380 300 n/a n/a 0

Oxford Cambridge and RSA Examinations

GCSE

Mathematics C (Graduated Assessment) General Certificate of Secondary Education B271

Module M1 (Sections A&B)

Mark Scheme for June 2010

OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a wide range of qualifications to meet the needs of pupils of all ages and abilities. OCR qualifications include AS/A Levels, Diplomas, GCSEs, OCR Nationals, Functional Skills, Key Skills, Entry Level qualifications, NVQs and vocational qualifications in areas such as IT, business, languages, teaching/training, administration and secretarial skills. It is also responsible for developing new specifications to meet national requirements and the needs of students and teachers. OCR is a not-for-profit organisation; any surplus made is invested back into the establishment to help towards the development of qualifications and support which keep pace with the changing needs of today’s society. This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which marks were awarded by Examiners. It does not indicate the details of the discussions which took place at an Examiners’ meeting before marking commenced. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes should be read in conjunction with the published question papers and the Report on the Examination. OCR will not enter into any discussion or correspondence in connection with this mark scheme. © OCR 2010 Any enquiries about publications should be addressed to: OCR Publications PO Box 5050 Annesley NOTTINGHAM NG15 0DL Telephone: 0870 770 6622 Facsimile: 01223 552610 E-mail: [email protected]

B271 Mark Scheme June 2010

1

Marking instructions 1. Mark strictly to the mark scheme. If in doubt, consult your team leader using the

messaging system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme (although

if this leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors. A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot be

awarded. W (workless) marks are independent of M (method) marks and are awarded for a correct

final answer or a correct intermediate stage. 5. Subject to 4, two situations may be indicated on the mark scheme conditioning the award of

A marks or independent marks: i. Correct answer correctly obtained (no symbol) ii. Follows correctly from a previous answer whether correct or not (“ft” on mark

scheme and on the annotations tool).

6. As a general principle, if two or more methods are offered, mark only the method that leads to the answer on the answer line. If two (or more) answers are offered, mark the poorer (poorest).

7. Always mark the greatest number of significant figures seen, even if this is then rounded or

truncated on the answer line, unless the question asks for a specific degree of accuracy. 8. i. Allow full marks if the correct answer is seen in the body and the answer given in

the answer space is a clear transcription error, unless the mark scheme says ‘mark final answer’ or ‘cao’.

ii. Allow full marks if the answer is missing but the correct answer is seen in the body. iii. Accuracy marks for an answer are lost if the correct answer is seen in the working but a completely different answer is seen in the answer space. Method marks would normally be given.

9. When the data of a question is consistently misread in such a way as not to alter the nature

or difficulty of the question, please follow the candidate’s work and allow follow through for A and W marks. Deduct 1 mark from any A or W marks earned and record this by using the MR annotation. M marks are not deducted for misreads.

10. For methods not provided for in the mark scheme give as far as possible equivalent marks

for equivalent work. If in doubt, consult your team leader. 11. For answers scoring no marks, you must either award NR (no response) or 0, as follows:

Award NR if:

• Nothing is written at all in the answer space • There is a comment which does not in any way relate to the question being

asked (“can’t do”, “don’t know”, etc.) • There is any sort of mark that is not an attempt at the question (a dash, a

question mark, etc.)

The hash key [#] on your keyboard will enter NR.


2

Award 0 if:

• There is any attempt that earns no credit. This could, for example, include the candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.

12. Where a follow through (ft) mark is indicated on the mark scheme for a particular part

question, you must ensure that you refer back to the answer of the previous part question if this is not shown within the image zone. You may find it easier to mark follow through questions candidate-by-candidate rather than question-by-question.

13. In cases where there is clear evidence that a calculator has been used in section A, mark

the script as normal then raise an exception (malpractice) in scoris. All suspected malpractice should be flagged using exceptions.

14. Anything in the mark scheme which is in square brackets [ … ] is not required for the mark

to be earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor. The following annotations are available:

and

Highlighter BOD Benefit of doubt FT Follows through ISW Ignore subsequent working (after correct answer obtained) M0, M1, M2 Method mark awarded 0, 1, 2 A1 Accuracy mark awarded 1 W1, W2 Workless mark awarded 1, 2 SC Special case ^ Omission MR Misread These should be used whenever appropriate during your marking. The A, M and W annotations must be used on your standardisation scripts for responses that are not awarded either 0 or full marks. It is vital that you annotate these scripts to show how the marks have been awarded. It is not mandatory to use annotations for any other marking, though you may wish to use them in some circumstances.

16. The comments box will be used by the Principal Examiner to explain his or her marking of the practice scripts for your information. Please refer to these comments when checking your practice scripts. Please do not type in the comments box yourself. Any questions or comments you have for your team leader should be communicated using the scoris messaging system, e-mail, or by telephone.

17. As far as possible you should mark roughly equal numbers of RIGs from sections A and B. It is helpful to mark some in each section as you go, rather than marking all RIGs in one section, then all RIGs from the other.


3

Abbreviations

The following abbreviations are commonly found in GCSE Mathematics mark schemes.

• Where you see oe in the mark scheme it means or equivalent.

• Where you see cao in the mark scheme it means correct answer only.

• Where you see soi in the mark scheme it means seen or implied.

• Where you see www in the mark scheme it means without wrong working.

• Where you see rot in the mark scheme it means rounded or truncated.

• Where you see seen in the mark scheme it means that you should award the mark if that number/expression is seen anywhere in the answer space, including on the answer line, even if it is not in the method leading to the final answer.

• Where you see figs 237, for example, this means any answer with only these digits. You

should ignore leading or trailing zeros and any decimal point e.g. 237000, 2·37, 2·370, 0·00237 would be acceptable but 23070 or 2374 would not.


4

Section A

1 (a) (i) Yoho or 337 1 NAMBI

(ii) Ural or 330

1

(b)

one thousand (and) five hundred (and) four or fifteen hundred and four

1 be liberal with spelling

(c) Correct 3 M1 for correct position of control block M2 for correct control block OR M1 for correct height or width

(d) 20 1

(e) (i) 28 to 32 2 M1 for 26 – 27 or 33 – 34 or for clear counting of squares with numbers

(ii) NAMBI (might be anywhere on paper)

1 must have arrowhead or some way of giving direction

(f) 80 4 to 6

1 1

condone repeats of “millions”

(g) (i) 25 (minutes)

1

(ii) 30 min or equivalent

1 half an hour

2 (a) 4

1 allow embedded or similar

(b) 5


(c) 8


3 (a) 20 or 30 etc

1

(b) 15 or 25 or 35 etc

1

4 (a) 28

1

(b) 5

1

(c) 6

1


5

5 (a) Even(s) (chance)

1

(b) Unlikely

1

(c) Impossible

1

Section A Total: 25


6

Section B

6 1/4 or equivalent fraction

1 allow fraction written in words be liberal with spelling

7 all five others with no repeats or errors

2 W1 for one omission; condone repeats or errors

8 (a) 4.75 www 3 M1 for 72 – 15 or 57 seen M1 for “÷ 12” or digits “475” seen OR SC1 for (£)5 seen

(b) 74

1

(c) 3.5 to 4.0 35 to 40 cm mm

1 1

(d) (i) 30 to 35

1

(ii) NAMBI

1

9 (a) (2, 2) (4, 2) (6, 2)

2 W1 for two correct

(b) (i) (8, 2)

1

(ii) adding 2 to the first number oe 1 condone if example given, or if no reference made to “first number”, but must be “direction” + “number”

10 (a) (i) 1 1 allow repeat of “kg”

(ii) 50 www 3 M2 for (£)25 OR M1 for evidence of adding at least 6 bars M1 for “a total” × (£)2 OR SC1 for 48 or 52 seen

(b) (£)16.15 or (£)15.60 and “no”

3 M2 for (£)16.15 or (£)15.60 Or M1 for evidence of correct weight of boxes (4 & 6) or (8 & 2) OR SC1 for No + (£)24.48

(c) £3.90 www 3 M2 for figs “39” seen or 7.50 – 3.60 seen Or M1 for 10 × 36 or 0.75 or 75 or 3.6 or 360 seen or evidence of division (repeated subtraction)

Section B Total: 25

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GCSE






1

Marking instructions 1. Mark strictly to the mark scheme. If in doubt, consult your team leader using the messaging

system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme (although if this

leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors. A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot be

awarded. W (workless) marks are independent of M (method) marks and are awarded for a correct final

answer or a correct intermediate stage. 5. Subject to 4, two situations may be indicated on the mark scheme conditioning the award of A

marks or independent marks: i. Correct answer correctly obtained (no symbol) ii. Follows correctly from a previous answer whether correct or not (“ft” on mark




truncated on the answer line, unless the question asks for a specific degree of accuracy. 8. i. Allow full marks if the correct answer is seen in the body and the answer given in the

answer space is a clear transcription error, unless the mark scheme says ‘mark final answer’ or ‘cao’.


9. When the data of a question is consistently misread in such a way as not to alter the nature or

difficulty of the question, please follow the candidate’s work and allow follow through for A and W marks. Deduct 1 mark from any A or W marks earned and record this by using the MR annotation. M marks are not deducted for misreads.

10. For methods not provided for in the mark scheme give as far as possible equivalent marks for

equivalent work. If in doubt, consult your team leader. 11. For answers scoring no marks, you must either award NR (no response) or 0, as follows:

Award NR if:

• Nothing is written at all in the answer space • There is a comment which does not in any way relate to the question being asked

(“can’t do”, “don’t know”, etc.) • There is any sort of mark that is not an attempt at the question (a dash, a question

mark, etc.)



2

Award 0 if: • There is any attempt that earns no credit. This could, for example, include the

candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.

12. Where a follow through (ft) mark is indicated on the mark scheme for a particular part question,

you must ensure that you refer back to the answer of the previous part question if this is not shown within the image zone. You may find it easier to mark follow through questions candidate-by-candidate rather than question-by-question.

13. In cases where there is clear evidence that a calculator has been used in section A, mark the

script as normal then raise an exception (malpractice) in scoris. All suspected malpractice should be flagged using exceptions.

14. Anything in the mark scheme which is in square brackets [ … ] is not required for the mark to be

earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor. The following annotations are available:

and





3

Abbreviations








• Where you see figs 237, for example, this means any answer with only these digits. You should

ignore leading or trailing zeros and any decimal point e.g. 237000, 2·37, 2·370, 0·00237 would be acceptable but 23070 or 2374 would not.


4

Section A

1 (a) (i) 56

1

(ii) 22 500 2 M1 for figs 225 or attempt at subtraction seen

(b) 53·44 2 M1 for pence column correct (44) or pounds column (53)

(c) (i) 30

1

(ii) Carbohydrate starts at 55 not zero

1 it should be 25%; carbohydrate starts at 55% etc; see exemplars

(iii) 1/4 oe

1

(iv) 200

1

(d) 84 2 M1 for attempt at multiplication of 14 and 6

(e) (i) 5 2 W1 for 10 of the numbers listed in order 1 2 4 4 4 5 5 6 8 12 12

(ii) 4

1

(f) (i) south (S) north-east (NE)

1 1

(ii) clockwise

1

2 (a) (i) 118 to 122°

1

(ii) obtuse

1

(b) ∠ of 33 to 37° drawn 1

(c) acute reflex

1 1

3 (a) (i) 5

1

(ii) −3 oe

1

(b) multiply by 2

1 see exemplars

Section A Total: 25


5

Exemplar responses: 1(c)(ii) Response Mark Because she count from the beginning. 1 (min) Because Protein and Fat take most of it away 0 She is wrong because the bar is in the middle of 50 and 60. 0 Because it stops at 55 then goes to 80 if it was 80% Protein and Fat would not be there.

1

30% Protein, 25% Fat, 20% Water. 0 Because carbohydrate starts on 55% and finishes on 80%, so it can’t be. 1 Carbohydrates start at 40% and ends at 80% 0 It starts at 55 – 80 = 15% 1 isw She isn’t looking how much % of carbohydrates there is just where it stops 1 Carbohydrate does take up 0 to 80 0 It shows 30% to 80% 0 It does not start at 0 1 Protein and Fat make 55% so 45% is left. 0 Because 80% is nearly all the bar chart and 30% is Protein and Fat. 0 Exemplar responses: 3b

Response Mark Just double the number (and the last number is 120). 0 Double the number before. 1 Time it by 2 each time. 1 To find the next number you should add on 80. 0 You add the same number to get the next number in the sequence. 0 Add the same number twice. 0 It’s doubling in two’s 1 1 number add that same number. 0 First add 5, then add 10, then add 20 then add 40. 0 Double it. 1 By adding same number. 0 You add whatever the number you’re adding on to get the next number i.e 80 +80 =160

0

You add on the last number 1


6

Section B

4 (a)

4

1

8

5

6

3 oe

1 1 1

(b) (0)·75

1

5 correct reflection

2 W1 for 2 lines correct

6 cuboid pyramid cylinder cone sphere

3 W2 for 4 correct OR W1 for 3 correct

7 (a) R

1

(b) P

1

(c) Q

1

8 5

2 M1 for 20 ÷ 3.8 or 5.26… or 5 × 3.8 [= 19]

9 (a) Yellowknife

1

(b) 42

2 M1 for −15 and 27 identified

10 (a) 95

1

(b) 469

2 M1 for 213 and 256 identified

(c) 59

2 W1 for attempt at 118 ÷ 2

11 (a) 64

1

(b) 45

2 W1 for attempt to divide by 1.6

Section B Total: 25




GCSE






1

















Award NR if:






2

Award 0 if:








and





3

Abbreviations










Viewing tips for this paper In general, set your screen to ‘fit width.’ You may find it helpful to set to ‘fit height’ for the following questions: 5, 6a, 6b, 9a, 12a, 12bi, 13


4

Section A

1 (a) 1·28

1

(b) 7·2 1

(c) 1·3 1

(d) 18 2 M1 for 60 ÷ 10 × 3 or 6 seen or 180 seen

2 (a) 3 4 1

(b)

2

any orientation W1 for any 4 by 1 rectangle OR SC1 for two shaded squares separated by one unshaded with no outline of 4 by 1 rectangle drawn

161 oe 1 isw after

161 seen

3 (a)

(b) Yes because there 4 square

numbers but only 3 in the 5 times table

1 or correct comparison made see exemplars

4 (a) 10:45 oe 1 SC1 for 10:28

(b) 09:48 or 10:08 10:28

09:18 or 09:38 09:58

08:48 09:08 09:28

3 W1 for each ft arrival at Five Ways

5 10 × 6.20 0.2 × ‘their 62’ ‘their 62’ + ‘their 12·40’ 74·40

M1

M1 M1 A1

implied by 62 seen implied by 12.4 seen or any complete attempt at 20% of 62 for addition of two numbers, where one is from attempt at a percentage and one from attempted multiplication by 10 or W4 for 74.40 www or W3 for 74.4 www Alternative method M1 for 0.2 × 6.2 oe M1 for 6.20 + ‘their 1.24’ M1 for 10 × ‘their 7.44’ A1 for 74.40 OR M3 for 12 × 6.20


5

6 (a) Multiplied length in cm by 10 rather than 20 or 12 × 20 = 240 (m)

2 W1 for implying wrong scale factor used or 240 seen or 12cm or 12 squares seen see exemplars

(b) rectangle 5 cm by 3 cm drawn 2 W1 for rectangle with one dimension correct

7 (a) 24 1

(b) 15 2 M1 for 6 × 5 ÷ 2 oe or 30 seen

Section A Total: 25


6

Exemplar responses: 3(b) Comment Mark Yes, there’s more square numbers [more implies comparison] 1 Yes, more square numbers than numbers in the 5x table 1 Yes, only 3 counters that are in the 5x table but there are more square numbers 1 Yes, there is only 3 of the 5 times table and more square numbers 1 Yes, there is more square number [bod number not numbers] 1 Yes, thay are more square numbers then the 5 time table 1 Yes, there are only 3 numbers from the 5 times table than the squared numbers [3 is correct, trying to compare] 1

Yes, there are only 3 multiples of 5 [condone as ‘only’ just implies comparison without this it would not score] 1 BOD

Yes, there are only 3 numbers in the five times table [as above] 1 BOD Yes, they are three numbers what in the 5 time tables [no comparison] 0 Yes, there are only too numbers that are in the five times table [wrong statement] 0 Yes, there are many more square numbers than in the five times table [only one more, so implies they don’t understand] 0

Yes, there are 13 counters and only 3 are in the 5 times table [13 is wrong] 0 Yes, it has 16 numbers and you are having 5 two times [doesn’t understand 5x table] 0 Yes, there are only 3 numbers in the 5 times table, but there are a lot of numbers that can be squared [not talking about square numbers] 0

Yes, because there are not many numbers in the 5 times table 0 Yes, there are more than 5s in the bag 0 No, there are more square numbers than numbers in the 5 times table [No – so award 0] 0

No, because there is only 3 numbers out of the 5 times table [No – so award 0] 0 Exemplar responses: 6(a) Response Mark Because it 1cm to every 20m and the total is 240m. [identified scale and correct length] 2 Because there are 12 squares 12 x 20 = 240 [correct calculation shown] 2 Because it is double not 120 = 240 [indicates what needs to be done to get right answer, and gives right answer]

2

1cm is 20, 12 cm is 240 2 Because there are 12 blocks and 12 × 20 = 240 2 He measured the width not the length [120 is correct ‘real width’] 2 Lian is wrong because it is 12cm long not 6. [stated correctly what error was – showing understanding of scale]

2

He might as well have done 1cm to 10 cm he only did half the length [scale wrong - if it had 1cm to 10m scores 2]

1

Because on the diagram it shows 240 m. [needs to show where 240 comes from for 2] 1 Its 240 m. 1 He’s wrong because he only timesed by 10. [not indicated what he should have done] 1 Because it should be twice the size [bod for mention of twice] 1 Because it is 1cm to 20m there 12 squares, that comes to 160 [bod mark is for identifying 12 squares, error in calc so not worth 2]

1

Because it is 12cm long 1 Lian has only calculated half of the field [bod for mention of half] 1 Because all he done was add the squares and x by 10 [implies chosen wrong scale factor]

1

Because there are only 12 squares going along instead of 20 [although 20 is wrong 12 squares is seen so 1 mark]

1


7

Because it is only 12m long. [m not cm so 0] 0 Because the scale is only 1cm to 20m [not sufficient to simply restate scale] 0 The answer is 224, you times the squares by 2 [2 errors, so 0] 0 He is wrong because it is shorter than 120m 0 It is bigger 0 Because 1m is 5 cms & one square of the playfield is 10 cm 0 Because the scale is 1cm to 20cm 0 A playing field is longer than 120m 0 Liam has timed the length 20m by 10 0


8

Section B

8 (a) hours kilometres kilograms

1 1 1

(b) 1/4 oe fraction

1

(c) 1500 1

9 (a) (i) Linear vertical scale to at least 7 Horizontal axis numbered correctly, both axes labelled and bars equal width All bars correct height 1, 4, 7, 6, 5, 2

W1

W1

W2

numbers by gridlines, not in gaps W1 for 4 bars correct height or 6 correct heights, in any order

(ii) 2 1

(b) 2·6 3 M1 for attempt to add soi by 24 to 28 seen M1dep for division by 10 seen OR SC2 for answer 23·3

10 (a) 11 1

(b) 6 1

(c) 17 1

11 (a) 2·56 1

(b) 10·2

2 M1 for 6·8 or 1·5 seen

12 (a) 55 2 M1 for 40 × 100 or 30 × 50 or 0·4 × 100 or 0·3 × 50 or 4000 or 1500 or 15 or £40 seen

(b) (i) 6·5 – 7·5 1

(ii) 54 – 56 1

13 C D

1 1

Section B Total: 25




GCSE






1

















Award NR if:






2

Award 0 if:








and





3

Abbreviations











4

Section A

1 (a) 14 cao

1

(b) 9 cao

1

(c) 5 cao

1

2 (a) 0·075, 0·507, 0·57

1

(b) 57/100 oe fraction

1

(c) 40

1

3 (a) triangle with vertices at (4, 1)(5, 1) and (5, 3)

2 SC1 for a reflection in other x = k or reflection in y = 3

(b) (i) (−2, 1) plotted

1

(ii) (3, 1) or (−7, 1) plotted or ft their R to make parallelogram

1

(iii) (3, 1) or (−7, 1) or coordinates of their S

1

4

(a)

20x 1 condone x × 20, 20 × x or x20

(b) y + 4 or 4 + y

1

5 (a) comparison of 1/2 and 1/6 eg ‘it isn’t as much as 50-50 since there are 6 faces and only one gives a six’

1 must refer to 6 faces or numbers and 1 eg 1/6, 1 out of 6 oe or identifies one 6 or one of each number or five other numbers or not three sixes see exemplars

(b) probabilities should be fractions / decimals / %

1

just one of these is sufficient eg it should be ½ oe not 1 out of 2 see exemplars


5

6 (a) (i) 71·64 2 M1 for valid strategy seen eg long

multiplication attempted or 36 × £2 − 36p or repeated addition

(ii) 16 3 M2 for a correct strategy used, eg short division or chunking or repeated addition or multiples – must be using correct numbers in ‘chunks’ etc to earn M2 Or M1 for 288 ÷ 18 seen OR M1 for 288/18 = 144/9 M1 for partially correct attempt at division of 144 by 9

(b) (i) 110

1

(ii) toast 1 (iii) 30

1

(iv) 140

2 M1 for at least one of 130 and 270 soi allow SC1 for 180 (using 2008 figures)

Section A Total: 25


6

Exemplar responses for 5(a) Response Mark Because there is 5 other numbers to roll 1 Because there is only 2/12 chance of getting a six 1 Because it’s 1 out of 6 1 The dice has 5 other possibilities to land on. 1 Because there are 5 other numbers on the dice and it is 1 out of 6 chance 1 Because the dice has only 1 side that has a six on it 1 Because the chance of getting a six is 1/6 so 50-50 is wrong 1 Because there is only 1 six 1 Because there are not 3 sixes on a dice 1 Because it is a six sided dice and there is one six 1 Because there is only one side with six dots on it 1 ‘cos it wood be 1 in 6 chance that he wood get 6 1 Getting a six and not getting a six are not equally likely 1 Because it’s very unlikely you can get a six on a six sided dice. 0 Because there is six numbers on the dice not two 0 There are six sides not two 0 There is not an even number to get a 50-50 chance. 0 Because there are 1 to 6 numbers and he thinks there is just 1 number 0 Because there are more than one number 0 Because on a dice there are 6 numbers 0 Because if it were 50-50 there would be half one number and the other half another but there is six numbers on a dice

0

Because the dice is six sided not two-sided 0 Because 50-50 means half a chance and there is 6 numbers so it can’t be 50-50

0

Exemplar responses for 5(b) Response Mark Is 1 out of 2 but she could have said half 1 Because the chance of getting an even number is 50% 1 It should be 3/6 1 It is not written as a fraction 1 You write it as a fraction 1/3 1 It is not written as a fraction 1 She could have made it more sense e.g. 50% 1 There is 3 even numbers and it’s out of 6 so the chance would be 3/6 1 He should say 3 out of 6 0 There are 3 even numbers out of 6 0 There are more than two even numbers 0 There is 3 even and 3 odd numbers 0 She should have said 50-50 0 There are 3 even numbers on the dice so it would be 1/3 0 There is the same amount of even numbers as odd numbers 0 The probability is 3 out of 6 chances 0 There is 6 chances not 2 0 As there’s not 2 numbers- it is a 50-50 chance 0 It wouldn’t be 1 out of 2. it would be written as 1:2 0 Because the probability on a die would be 3 out of 6 0 It is 3 in 6 chance 0 Not enough information 0


7

Section B

7 (a) 10 50 250

2 W1 if one error, ft from their error

(b) 30 5 rows and 6 columns

1 1

or nos. of rows and cols go up by one each time or you add on an extra 2 more each time or + 4 + 6 + 8 + 10 condone 5 × 6

8 (a) (i) 95 - 97

1

(ii) 1 ¼ or 1.25 or 75 mins or 1h 15m

1 allow 1:15 but 0 for 1:25 or 1.15 or other confusion with decimal hours and minutes

(iii) B to C because steepest oe

1

(b) 42

2 M1 for 126 ÷ 3

(c) 6·5 www 3 M1 for 39 or addition of correct 6 numbers M1 for their sum ÷ 6 OR SC2 for 32·3(3…) [from 3 + 8 + …+ 8 ÷ 6]

(d) 8 to 10 inclusive

1

(e) 7 × 80 [= 560] 1050 − their 560 490

M1 M1 A1

W3 for 490 www

9 22·4 cm2

2

1

M1 for 3·5 × 6·4 or 35 x 64 or figs 224 or 112/5 condone ‘square centimetres’ or ‘cm sq’ etc

10 124 73

1 2

M1 for 360 – (210 + 77) oe

11 correct trial 19 × 24 = 456 19

M2

W1

or for two correct trials in the range 11-25 with second one closer to 456 OR M1 for correct trial of 11 - 18 inclusive M1 for a trial of 20 - 25 inclusive if answer line blank, allow indicated in table eg as last trial

Section B Total: 25




GCSE






1

















Award NR if:






2

Award 0 if:








and





3

Abbreviations











4

Section A

1 (a) 200 cao

1

(b) 300 or 310 × their 200 60 000 – 62 000

1 1

if 0 scored, SC1 for (200 or 190 or 194) × (300 or 310 or 307)

2 (a) (i)

4

1 =

12

3

or 3

1 =

12

4

1 either pairing correct

(ii)

5

1 cao

1

(b) £3(.00) isw 2 M1 for (£)1.5(0) OR 150p seen

or 20100

15 × oe

after £3, ignore further attempt to add (or subtract from) £15 If 0 scored, SC1 for 18 only

3 (a) 20 1

(b) No and statement referring to number of words on line (and not frequency)

1 see exemplars W0 for answer starting with Yes

(c) one statement comparing modes one statement comparing ranges

1ft

1

see exemplars not simply restating values may use V’s mode = 6, even if refuted in (b), or their mode stated in (b) if one statement is the converse of the other, mark only one eg D has smaller writing V has bigger writing W0 for contradictory statements (even given as two separate parts)

4 (a) (i) a + b 1 no extras

(ii) 4b – a oe 2 no extras W1 for 4b or –a oe seen condone extras only for maximum W1

(b) 15 2 W1 for 24 − 9 seen


5

5 (a) Complete triangle joined to ends of

line (±2 mm) with arcs shown 2 M1 for at least one arc of radius 8 cm

(±2mm) from end of given line

(b) (i) the angles are not 90° 1 the angles in a triangle are 60° so some are 60° and some are 120° the angles of the quadrilateral are not all the same size see exemplars

(ii) rhombus cao 1

(iii) 2 cao 1

6 (a) (SA) AS, SH, HS, AH, HA. 2 W1 for 3 correct (even if repeats or errors also shown)

(b)

6

1

1ft ft

6

1

their

(c)

6

4 or

3

2

1ft strict follow from (a)

6

4

theirtheir

W0 if 9

6seen

Section A Total: 25


6

Exemplar responses for 3(a) Response Mark No and there never was even 6 words on a line. 1 Mentions words on line No and the mode would be 12 1 Give correct answer (for words on line) No and 6 doesn’t occur 1 Since 6 words on line does not appear

assume reference to words on line. No and 6 isn’t one of the numbers on a line 1 References words on line No and That is the frequency 1 No there was only 1, 6 and that was the frequency

1 Distinguishes from frequency

No and mode is the number most frequently used.

0 Defines mode

No and number 6 isn’t common number in the results table

0 Implies frequency

No and 6 doesn’t occur the most. 0 Implies frequency No and Most of them aren’t 6 0 Implies frequencies considered No and 6 is no the most number that occurs – 2 is 0 Implies frequencies considered Yes and anything 0 Exemplar responses for 3(a) Response [Deepika or she, Vipin or he in statements] Mark Deepika has a smaller range 1 D’s range is 1 less 1 D’s writing is more consistent 1 Vipin has a larger range 1 Their ranges are very close (similar) 1 The ranges are similar 1 Deepika has smaller writing (than Vipin) 1 Deepika has a bigger mode (than Vipin) 1 Deepika gets more words on a line (than Vipin) 1 Deepika wrote more words. 1 She has much smaller writing than Vipin’s 1 The mode of Deepika is bigger/larger than Vipin’s mode by 10. (ft from mode = 6, even if they have said 6 is wrong in part b)

1

Vipin has bigger writing (than Deepika) 1 Vipin gets fewer (less) words on a line (than Deepika) 1 She writes more words on a line compared to him. 1 Hers may be smaller writing 1 She had more words on the lines. 1 The range of Vipin’s results are bigger than Deepika because it is 6-1=5 for Vipin and only 4 for Deepika (Calculation for range from frequencies)

0

Her mode is better 0 D’s writing was bigger than V’s because her mode is bigger. (contradictory?) 0 D writes longer sentences than V 0 She also has written more lines. 0 The size or their writing were different 0 The amount of words on their lines were different. 0 The range is around the same so the number of words must have been simler to Vipins. 0 Deepika’s range is 4 and Vipin’s (his) is 5 0 Deepika’s mode is 16 and Vipin’s is 12 0 Wrote more words (Does not say who) 0 Higher frequency 0


7

Exemplar responses for 5(b)(i) Comment Mark A square has 4 lines of symmetry, this only has 2 1 a square has 4 90 degree angle also know as right angles. (implies “this has not”) 1 She is wrong because a square has 4 lines of symmetry not 2. 1 Because a square has more lines of symmetry. (implies “than 2”) 1 This cannot be a square because there is know right angles 1 It is not a square because the angles are not all the same size. 1 The angles are different (Just about!!) 1 A square has 4 angles of 90o and this only has 2 (contradiction) 0 She is wrong because it isn’t at a 90 degree angle like a square. (Implies tilted) 0


8

Section B

7 (a) −1, 2

1

(b)

1ft

1dep

their 3 points plotted correctly ±½ square Correct line at least from 2 ≤ x ≤ 8 ±½ square

8 (a) 80 1

(b) 4 2 M1 for 12 = 3x or reverse flow chart correct 11 → +1 → ÷ 3

9 25.7 to 34.6 inclusive 2 W1 for 2·3 to 3·2 or 4.6 to 6.4 in working (as lengths)

10 (a) Spinnaker 1

(b) 168 000 2 M1 for 800 000 × 0·21

or 21100

000800 × oe

or360

000800 × (73° to 77°)

or figs 168

11 (a)

2 W1 for any figure with order 3 using other than 2 additional lines or if one line extends beyond half way to next dot or correct shape with 1, 2 or 3 axes of symmetry included If 0 scored, SC1 for correct shape but with vertices up to half a line space to next dot.

(b) 60° cao 1

-1 0 1 2 3 4 5 6 7 8

-3

-2

-1

0

1

2

3


9

12 (a) (i) 125 1

(ii) 3.2 2 W1 for 3.1(6…..…) seen or answer 3.20(000000)

(b) (i) 125 1

(ii) 55 3ft W2 for 180 seen Or W1 for 6, 5 and 6 seen M1 180 – their (b)(i) Alternative method (adding layers) W1 for 30 seen W1 for 25 seen M1 for their 30 + their 25 If 0 scored, SC1 for 50 or 60 as answer

13 (a) (i) 4507 1

(ii) −18 1

(b)

3

2

2 condone

3

2 and

6

4 on answer line

W1 for 6

4 isw

SC1 for 2

3

Section B Total: 25



GCSE



General Certificate of Secondary Education B276

Mathematics C (Graduated Assessment)





messaging system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme

(although if this leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors.

A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot be awarded. W (workless) marks are independent of M (method) marks and are awarded for a correct final answer or a correct intermediate stage.

5. Subject to 4, two situations may be indicated on the mark scheme conditioning the award

of A marks or independent marks: i. Correct answer correctly obtained (no symbol) ii. Follows correctly from a previous answer whether correct or not (“ft” on mark scheme

and on the annotations tool). 6. As a general principle, if two or more methods are offered, mark only the method that

leads to the answer on the answer line. If two (or more) answers are offered, mark the poorer (poorest).




ii. Allow full marks if the answer is missing but the correct answer is seen in the body. iii. Accuracy marks for an answer are lost if the correct answer is seen in the working

but a completely different answer is seen in the answer space. Method marks would normally be given.

9. When the data of a question is consistently misread in such a way as not to alter the

nature or difficulty of the question, please follow the candidate’s work and allow follow through for A and W marks. Deduct 1 mark from any A or W marks earned and record this by using the MR annotation. M marks are not deducted for misreads.



Award NR if: Nothing is written at all in the answer space There is a comment which does not in any way relate to the question being asked (“can’t do”, “don’t know”, etc.) There is any sort of mark that is not an attempt at the question (a dash, a question mark, etc.) The hash key [#] on your keyboard will enter NR.

1


2

Award 0 if: There is any attempt that earns no credit. This could, for example, include the candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.






to be earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor.

The following annotations are available: and


16. The comments box will be used by the Principal Examiner to explain his or her marking of

the practice scripts for your information. Please refer to these comments when checking your practice scripts. Please do not type in the comments box yourself. Any questions or comments you have for your team leader should be communicated using the scoris messaging system, e-mail, or by telephone.

17. As far as possible you should mark roughly equal numbers of RIGs from sections A and B.

It is helpful to mark some in each section as you go, rather than marking all RIGs in one section, then all RIGs from the other.


Abbreviations

The following abbreviations are commonly found in GCSE Mathematics mark schemes. Where you see oe in the mark scheme it means or equivalent. Where you see cao in the mark scheme it means correct answer only. Where you see soi in the mark scheme it means seen or implied. Where you see www in the mark scheme it means without wrong working. Where you see rot in the mark scheme it means rounded or truncated. Where you see seen in the mark scheme it means that you should award the mark if that

number/expression is seen anywhere in the answer space, including on the answer line, even if it is not in the method leading to the final answer.

Where you see figs 237, for example, this means any answer with only these digits. You

should ignore leading or trailing zeros and any decimal point eg 237000, 2·37, 2·370, 0·00237 would be acceptable but 23070 or 2374 would not.

3


Section A 1 (a) correct reflection

1 points at (2, ─1), (5, ─1) and (2, ─5)

allow ± 2 mm but mark intention

(b) correct rotation 3 points at (─1, 2), (─1, 5) and (─5, 2) W2 for ‘correct’ rotation except in the wrong direction ie (1, ─2), ( 1, ─5), (5, ─2) Or W1 for correct rotation using the wrong centre

2 (a) (0)·875

2 M1 for the division 7 ÷ 8 or (0)·125 seen or figs 875 seen

(b) 1/10

2 M1 for 20

2oe

or 4512

or for their proper fraction correctly and fully simplified

3 (a) —10

1

(b) 15 www

2 M1 for 16 – 1 seen or 11 coming from use of 23 = 6 eg 2 × 23 – 1 = 12 −1 = 11 W1 for 8 seen

4

(a) 5

3 oe

1

(b) 0·15

2 M1 for 1 - 0·3 - 0·1 - 0·45 soi or figs 15, 85 or an answer of 0·51

5 (a) Colin (or 10) and you multiply (or times) first

1 allow the correct working eg 2 × 3 = 6 and 6 + 4 or just 4 + 6

(b) 72

2 M1 for 8 or 9 seen

4


6 (a) 4

30 oe www isw

2 M1 for 4x = 27 + 3 or better

or 4bx from 4x = b

or if correct answer not seen award W1 for 7·2

(b) 7 www 3 If 7 not found, award a maximum of 2 marks from the following: M1 for khxx 35 or better

M1 for 1125 hxkx or better

W1 for abx from ax = b

7 15 www 3 M1 for 48 ÷ (5 + 1) or better soi

A1 for 40

Section A Total: 25

5


6

Section B 8 A (75°) correct, line AC (6 cm)

correct and Δ complete with all lines ruled

2 M1 for either the angle or the line correct allow ±2° for angle and ±2mm for line; condone freehand line or incomplete triangle

9 (a) as the Maths marks increase the Science marks increase

1 allow equivalent statements eg positive (correlation)

(b) correct line 1 line must be ruled and between 20 ≤ x ≤ 55 where x = 20, 8 ≤ y ≤ 22·5 where x = 55, 50 ≤ y ≤ 65

(c) 35 – 45 1 or ft their ruled line tolerance ±1

10 (a) (i) 17

1

(ii) 43

1

(b) 7B and the mean (average) is greater

1 any statement including 29·5 and 26 implies the selection of the mean and choice of 7B implies that 29·5 is greater do not award the mark if there is any statement showing confusion with mode or median

11 (a) correct ruled line from (0, 2) to (4, 10)

3 M2 for three correct points identified by any means (table, coordinates or plotted points) or the correct line but short Or M1 for two correct points identified by any means (table, coordinates or plotted points)

(b) 1·5 1 or ft their ruled line

12 (a) 1·56 2 M1 for 1·55(647……), 1·6, 39·69 or 25·5 seen

(b) 5 hours 24 minutes 1

13 (a) 51·45, 51·46 or 51·5 and cm2 3 M1 for 1/2 × 8·3 × 12·4 A1 for 51·45, 51·46 or 51·5 W1 for cm2

(b) 40·19 - 40·22 or 40 www 2 M1 for π × 12·8

14 (a) 4x+8

1

(b) 3(2x+5)

1


15 (a) 60

2 M1 for 360 ÷ 6 or 180 − 120

(b) 120 is a factor of 360 or all sides (lengths, lines) are equal

1 Allow equivalent or correct statements eg they fit together without gaps they fit together at the corners they fit together to make 360° interior angles fit together perfectly

Section B Total: 25

7




GCSE






1


messaging system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme

(although if this leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors. A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot

be awarded. W (workless) marks are independent of M (method) marks and are awarded for a correct

final answer or a correct intermediate stage. 5. Subject to 4, two situations may be indicated on the mark scheme conditioning the award

of A marks or independent marks: i. Correct answer correctly obtained (no symbol) ii. Follows correctly from a previous answer whether correct or not (“ft” on

mark scheme and on the annotations tool).


7. Always mark the greatest number of significant figures seen, even if this is then rounded

or truncated on the answer line, unless the question asks for a specific degree of accuracy.

8. i. Allow full marks if the correct answer is seen in the body and the answer given in



9. When the data of a question is consistently misread in such a way as not to alter the

nature or difficulty of the question, please follow the candidate’s work and allow follow through for A and W marks. Deduct 1 mark from any A or W marks earned and record this by using the MR annotation. M marks are not deducted for misreads.

10. For methods not provided for in the mark scheme give as far as possible equivalent

marks for equivalent work. If in doubt, consult your team leader. 11. For answers scoring no marks, you must either award NR (no response) or 0, as follows:

Award NR if:

• Nothing is written at all in the answer space • There is a comment which does not in any way relate to the question

being asked (“can’t do”, “don’t know”, etc.)


2

• There is any sort of mark that is not an attempt at the question (a dash, a question mark, etc.)


Award 0 if:






14. Anything in the mark scheme which is in square brackets [ … ] is not required for the

mark to be earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor. The following annotations are available:

and





3

Abbreviations











4

Section A

1 (a) (i) 57

2

M1 for 64 www or for 7 www or answer 71

(ii) 25 www

2

M1 for 5²

(b) 1/8 or 0.125 1

isw conversion to decimal

2 Multiplying by less than 1 should reduce the value/answer oe Dividing by less than 1 should increase the value/answer oe

1

1

all 3 underlined elements need to be mentioned in answers unless using an approximation approach accept symbols × and ÷ instead of multiply and divide accept the word ‘decimal’ or 0.93 and 0.47 for ‘less than 1’ do not accept either if accompanied by an incorrect written statement (ignoring any evaluations) see exemplars

3

112 www 3

W2 for 28 seen or M2 for 0.8 × 140 oe or M1 for 0.2 × 140 oe

4 (1, 3) 2

W1 for the abscissa; W1 for the ordinate

If 0 scored, allow M1 for 2

42 +−oe or

2

15 +

oe shown

5 (a)

Positive

1

ignore embellishments

(b)

No and refers to diameter compared to height for this tree or refers to this tree not fitting the correlation or pattern or trend [of the others]

1

eg too thin for the height too tall for the diameter oe accept ‘outlier’, anomalous result, does not fit the pattern, too tall and thin for an oak tree etc if figures given for other trees – check scattergraph for reasonableness accept eg an oak tree with diameter 1.6 m should have a height of (about) 13 m


5

6 (a)

20 80

1 +1

(b)

5 points plotted

Correct curve through 6 correct points

1ft

1

correct or ft their points. condone feathering and double lines if in range and linear section from (4, 80) to (5, 125)

(c) 29 – 32.5 1ft correct or ft their wrong or ruled curve read at 2.5 ( ± 1m height reading by eye)

7 ∠ODC = 25 or ∠ODA /ODB = 90 soi 90 – 25 oe (from angle between tangent and radius)

65 www

1

1

1

could be written on diagram – accept box marked for 90° may be implied by next step eg 180 – 90 – 25 (from angles on a straight line) implies previous mark, provided no contradiction this mark must not be awarded if finding/leading to wrong angle

8

(a)

(x ) ≤ 4

2

M1 for 4 obtained correctly without correct inequality sign or for 3x ≤ 10 + 2 Or SC1 for answer x ≤ 8/3 o.e.

(b) shows x ≤ 4 1ft correct or ft their (a) inequality only accept dot or circle (condone unshaded) and line to the left as far as -6 if no arrow condone extra dot/circle on -6

Section A Total: 25


6

Exemplar responses for question 2 Q1 responses Accept When timesing by a decimal the answer/it/number should be lower

Has all 3 elements - accept decimal for ‘less than 1’ – refers to outcome as well

Timesing a decimal by a whole number the answer is no more than the whole number

condone the use of ‘whole number as meaning the number – has all 3 elements

It should be less than 124.7 as she has x by 0.93 All 3 elements accept x and 0.93 Multiplying by 0.93 makes the answer/it/number smaller

All 3 elements - accept answer/number/it as meaning 124.7

Because 1 x 124.7 is 124.7 so the answer/it/number must be smaller

Uses approximation - allow because of correct comment

If you round 0.93 up to 1 then the answer would be 124.7 and therefore the answer/it must be lower if you use 0.93

Uses approximation – condone lack of multiplication or times when using this approach as long as clearly explained

Do not accept The answer is too high no justification or mention of times or decimal The answer should be less than 124.7 no mention of 0.93 or times Because 1 x 124,7 is 124.7 no comment on outcome + no link to 0.93 Any number x a number less than itself is smaller no mention of decimal If you round them to the nearest whole number, it would come to 125 so the answer should be less than 125

uses approximation (nearest whole number) but does not show the rounded values used

It has to be smaller than 128.1 no justification, no mention of decimal or times

Her answer has increased when it should have decreased

no justification, no mention of decimal

You are timesing it by less then 1 no reference to outcome Because 0.93 will make the answer smaller omits the word multiplication 0.93 is too small because 1 x 124.7 = 124.7 needs to reference the answer/outcome as it

has been asked for in the question 0.93 is too small a number to make 128.1 No mention of times Q2 responses Accept Dividing by 0.47 will make the answer/it/number bigger

All 3 elements

35 divided by 0.5 = 70 so the answer/it/number is too low

All three elements + approximation approach

Dividing by a decimal makes the answer/it/number bigger

All three elements

A whole number divided by a decimal increases the whole number/it/answer

All three elements - condone the use of ‘whole number as meaning the number

When dividing by a decimal the answer/it/number is higher

All three elements

If you round 0.47 to 1 then the answer would be 35.4, if you use 0.5 the answer/it would be 70.8 so using 0.47 will make the answer/it higher

Uses approximation – very clear correct explanation condone lack of ‘divide’ in this approach


7

Do not accept The answer should be bigger than 35.4 no reference to 0.47 or division If you double the answer it is almost 35.4 and she is dividing by 0.47 not 2

muddled - not clear – approximation approach

Because she is dividing by a decimal no reference to answer When you divide by less than 1 you multiply it not clear, no ref to answer This is wrong as 1 goes in to this more than 16.8 times

not clear – no ref to decimal or outcome

Only dividing by 2 would give an answer around 16.8 and the number is nowhere near 2

not clearly referring to division by a decimal

The answer should be bigger than 16.8 no ref to decimal or division When the number you are dividing by is smaller, it cannot equal 16.8

no ref to decimal or outcome

You are dividing it by less then 1 no ref to outcome Because you are dividing by a decimal – it can’t be right

no ref to outcome

35 divided by 1 is 35 and her answer is way too small

no refer to decimal

Any number between 0 and 1 makes an answer bigger than the original number

no mention of dividing

Because the answer is too low no reference to decimal or dividing


8

Section B 9

3.5 oe 28

1 1

after 0 scored, M1 for 31.5 ÷ 9 or 3.5 seen eg answers reversed

10

(a)

4.25 oe www

3

M1 for 20x – 35 or 4x – 7 = 50/5 M1 for 20x = 85 or 4x = 17 ft their first step to kx = b M1 for x = 4.25 oe ft their kx = b with k ≠ 1

(b)

x² + 5x + 2x + 10 or x² + 7x + 10 isw

2

M1 for 3 correct terms seen but not 2x from x times x or 2 correct terms from the 3 term final answer x² + 7x + 10

(c) (x =)

3

5+yoe

2 M1 for y + 5 = 3x or answer (x =)

3

5

±±± y

or y + 5 ÷ 3 or y/3 + 5

11

(a)

64.7 isw

4

M1 for mid-intervals: at least three of 45, 55, 65, 75, 85 soi M1 for 6470 seen

or their fx where each x is in the correct interval including the end boundaries

M1dep (on 2nd M1) for their fx /100 (allow division by their attempt at 10 + 26 + 30 + 25 + 9)

(b)

100

34 oe

2

M1 for 34 seen as numerator in fraction answer

or 100

925 +

or 100

)302610(100 ++−

After 0, SC2 for 59.7 or 69.7 final answer

12

(a)

0.235 to 0.236 or 0.24 www

3

M1 for π × 0.25² (0.196…) seen M1 for their(π × 0.25²) × 1.2 ft their cross sectional area; dep on use of π for area

(b)

Does not fit and 1.3 shown 4 M3 for 1.3 shown www, with no/wrong conclusion

Or M2 for 22

5.02.1 + Or M1 for 1.2² ± 0.5² or 1.69 seen


9

13

11.252 or 11.25 or 11.3 (mark at most accurate)

3

M2 for 42.195/3.75 oe or answer 0.187 to 0.188 or 0.19 (if 0.18 – check working mark at most accurate) Or M1 for 42.195 / their time in hours or mins implied by answer 12.2… or figs 187 to 188 seen

Section B Total: 25




GCSE






1

















Award NR if:





2


Award 0 if: • There is any attempt that earns no credit. This could, for example, include

the candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.







and





3

Abbreviations










Viewing tips for this paper In general, set your screen to ‘fit width.’ You may find it helpful to set to ‘fit height’ for the following questions: 2a, 10a, 10bi, 10biii (+ zoom in once for 10bi and 10biii to focus on relevant part of graph and see more clearly! – similarly for 11)


4

Section A 1 (a) 1

36

2 M1 for evidence of equivalent fractions

attempted: two fractions with a correct common denominator with at least one of the numerators correct

(b) 26

3 www

3 condone

86

12 oe mixed number, since lack

of simplifying is penalised in (a)

M1 for ×5 16

4 3 oe seen or implied

M1 for attempt to multiply numerators and denominators, ft their top heavy fractions

2 (a) Δ with vertices at (5, −2) (10, −2) and (5, 8)

3 M2 for two vertices correct or for enlargement with sf 2·5 but wrong centre Or M1 for enlargement centre (0, 3) with wrong sf

(b) centre (0, 3) sf 0·4 or 2/5

1 1

3 (a) 4·2 × 10-3 1 do not accept poor notation

(b) 9(·0) × 104 2 condone poor standard form notation; M1 for 84 000 + 6000 or 90 000 or for 8·4 × 104 + 0·6 × 104 or for 84 × 103 + 6 × 103

or for 9(·0) × 10n with n ≠ 4


5

4

(a)

(i) [3x + 1 =] 8x − 6 or 1·5x + 0·5 = 4x − 3 7 = 5x or 3·5 = 2·5x oe or ft

[x = ] 7/5 isw or 2

15

or 1·4 or ft

M1

M1

M1

M1 for each of three correct constructive steps (expanding brackets or dividing both sides by 2; collecting terms and simplifying to form ax = b or b = ax; division by x coefft), ft from previous error; no ft for final M1 if their x coefft is already ±1 after collecting terms if ft fractional answer simplifies to an integer it must be given as such to earn final M1 for M3 must reach 7/5 or −7/−5 oe isw allow W3 for 1·4 oe as final answer following trials

(ii) x > 7/2 oe

2 M1 for 7/2 oe found with wrong inequality or equation or for 2x > 7 or for −7 > −2x

(b) (x − 1)(x − 4) oe

2 isw expansion to check, or finding roots; may be seen in grid M1 for other versions of (x ± 1)(x ± 4) or for other factorisation giving two terms of expansion correct

5 (a) C or y = 2x − 2

1

(b) A and D or y = 3x − 1 and y = 3x + 4

1

6 (a) 0·7 on both unlabelled branches and ‘go to cinema’ oe on blank 0·3 branch and ‘do not go to cinema’ oe on last branch

1 accept 7/10 or 70% oe

(b) 0·07 or 7/100 or 7% or ft their tree 2 M1 for 0·1 × their 0·7

Section A Total: 25


6

Section B

75 560 ÷ 0.65 oe

M2

allow M2 for [ ]75560100

65× or for 1% = 1162

to 1163 Or M1 for 65% of ? = 75560 or better

7 (a)

116 000 to 116 300

A1 or W3 for answer in range www

(b) 8500 × 1.043 oe 9560 to 9562 or 9600

M2

A1

or for at least two years of correct values seen (may be rot to 3sf or more) or for equivalent method of repeated calculation of 4% of previous year with addition, condoning errors in calculation if M0, allow SC2 for answer of 9193.6 rounded or truncated to 3 sf or more or 9940 to 9944·… or for answer of 1060 to 1062 allow W3 for answer of 9560 to 9562 or 9600 www if 0, allow SC1 for 8840 seen or for 9520 or 23324 as answer

8 380 www 2 M1 for 612+718+301+177+201+265+386 or for 2660

9 6x − 4y = 8 and 6x − 9y = 0 or 9x −6y = 12 and 4x − 6y = 0 5y = 8 or 5x = 12 x = 2·4 and y = 1·6

M1

M1

W2

for multiplication to make coefficients of one variable the same; condone one error for subtraction, dependent on one pair of coefficients the same; condone one error A1 for one correct NB if no algebraic method seen, both correct answers gain W2, but W0 for just one correct


7

18·5 × tan 34

M2

or for sin34

18 5sin56

⋅ × oe or for complete

method using Pythagoras + appropriate trig function

Or M1 for [ ]tan 3418 5

h=⋅

or for correct sine rule statement without h as subject

10 (a)

their h + 1·7 14·09 to 14·2

M1

A1

ft their attempt (involving trig) at height of triangle [may be implied by their answer] W4 for 14·09 to 14·2 www Or W3 for 12.39 to 12.5 www

(b) (i) plots with correct heights 12, 35, 62, 78, 86, 90 and plots at 5, 10, 15, 20, 25 and 30 join with smooth curve or straight line segments

1

1

condone one error or omission allow ±1 mm may be implied by curve through correct points within 2 mm of their plots; ft ascending plots only; ignore curve for h < 5

(ii) 11.5 to 12.5

1

(iii) [reading at 18 =] 71 – 73 seen (their reading – 35) ÷ 90 [× 100] or (their reading – their reading at 10) ÷ 90 [× 100] 40 – 42·2… cao

M1

M1

A1

or ft from graph; may be implied by 36 to 38 or ft used in division calculation after subtraction seen, division may be implied by correct answer; allow 2nd M1 for (36 to 38)/90 [× 100] or ft W3 for 40 – 42·2… www if M0, allow SC1 for 47 to 48%

11 [sf =] 1·5 or 2/3 oe shown with correct calculations for both pairs of sides ∠ACB = ∠DCE [and [vertically] opposite oe]

2

1

or for scale factor used implicitly to show

this eg 8 1

4 2 6 35 4

⋅⋅ × = ⋅⋅

or for 5 4 8 1

1 28 to 1 294 2 6 3

⋅ ⋅= = ⋅ ⋅⋅ ⋅

or for 4 2 6 3

0 77 to 0 785 4 8 1

⋅ ⋅= = ⋅ ⋅⋅ ⋅

or for 5·4 × 6·3 = 4·2 × 8·1 = 34·02 Or M1 for [sf =] 1·5 or 2/3 stated or seen allow if marked the same on diagram; condone ‘the angles at C are the same’

Section B Total: 25




GCSE






1

Marking instructions 1. Mark strictly to the mark scheme. If in doubt, consult your team leader using the messaging

system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme (although if

this leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors. A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot be














Award NR if:





2


Award 0 if:






14. Anything in the mark scheme which is in square brackets [ … ] is not required for the mark to

be earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor. The following annotations are available:

and





3

Abbreviations











4

Section A 1 (a) tree diagram completed;

Saturday 0.4, 0.6 oe Sunday 0.3, 0.7, 0.3, 0.7 oe

1

(b) 0.46 oe ignore subsequent cancelling from fraction answer

3 M2 for 0.4 × 0.7 + 0.6 × 0.3 FT their tree Or M1 for 0.28 or 0.18 or correct pairs identified ft their tree if 0, SC2 for 0.58 (from 0.46 + 0.12)

2 (a) 1 www 2 M1 for 50 or

2

2

5

15 × oe

Or W1 for 10 =k

(b) 25 www 2 M1 for 54 or 625 seen in working or answer

Or W1 for answer 52 3 (a) C = 5r² oe 2 M1 for C = kr² or (k=)5

(b) 245

1

4 oe 0.05 or

20

1 or

10

1

2

1 ×

5% www

M2

A1

Or M1 for6

7

7

6

7

6

109.2

108.5 or

108.5

109.2 or

106

103

×

×

×

×

×

×

oe 103

106 or

6

7

×

×

or 580

29 or

600

30 or

29

580 or

30

600


5

5 (a) 6x² − x − 2 2 M1 for 6x² − 4x + 3x − 2 (3 out of 4 terms

correct; may be in grid) or 2 out of 3 terms correct

(b) (i) 6x² − x − 2 = 33 cao 1

(ii) (2x − 5)(3x +7) 5/2, -7/3 isw

M2

A1

M1 for (2x ± 5)(3x ± 7) or for factors, using integers excluding 0, giving two terms correct when expanded; ft their factors, dep on M1 if 0, W1 for 5/2, −7/3

(iii) length 6, width 5.5 1 condone reversed answers or ft their x substituted in 2x + 1 and 3x −2 leading to positive length and width

6 (a) gradient 8/2 = 4 intercept (0, 3)

1

1

accept gradient 4 with 8 (or 11 − 3) and 2 (or 2 − 0) seen accept ‘diff in y’/’diff in x’ = 4 accept ‘crosses y axis at 3’ accept ‘intercept is 3’ condone ‘c = 3’

(b) (y =) −0.25x + 3

2 M1 for (gradient) −0.25 oe seen

Section A Total: 25


6

Section B 7 m = 3p + 35 oe

8 3 M1 for 2m + 3p = 5(2m – 7) or better

M1 for 8m = 3p + 35 ft 1st step to Am = Bp + k M1 for m = Bp + k A ft 2nd step (providing neither A or B = 0)

8 41.78 to 41.79 accept 41.8 if M1 earned

2 M1 for 4.25, 3.45, 2.85

9 (a) 4.8... www 3 M2 for 6.4 sin 49 (or cos (90 – 49)) Or M1 for sin 49 = BD/6.4

(b) 59.5 to 59.9

3 M1 for tan BCD = their BD/2.8 M1 for inverse trig function used correctly or correct statement ft their trig function accept answer of 60 if M2 earned; if M1 scored and answer of 60 then second M1 can be implied

10 x = 146° angle at centre double angle at circumference (or vice versa) y = 34 tangent meets radius at 90º sum of angles of quadrilateral (is 360) or, using ΔBCE, accept (using symmetry) either radii equal or tangents equal or, using ΔBCD and ΔEBD, accept using isosceles triangle or radii equal

1 1

1 M1

A1

or ft 360 − 180 − their x (providing x ≠107)


7

11 (a) correct histogram 3 W2 for correct heights; 2.6, 3, 2.5, 3.26,

2.85, 1.8, 0.32 Or W1 for 3 correct heights (or 3 correct frequency densities) in table) AND W1 for all widths correct

(b) (i) 15 + 28 + 31 + 66 + 48 + 26 + 5 (= 219)

2 condone omission of × 1000 M1 for 3 × 5 + 2.8 × 10 + 3.1 × 10 + 4.4 × 15 + 2.4 × 20 + 1.3 × 20 + 0.2 × 25; condone 2 errors Or W1 for 4 frequencies from 15, 28, 31, 66, 48, 26, 5

(ii) correct statement, eg ‘more older people in Bexley’

1 do not allow simple comparison of one interval allow correct comparison of two or more adjacent intervals combined, eg ‘more under 25s in Haringey’ or ‘more over 60s in Bexley’ allow ‘on average people are older in Bexley’ allow ‘Bexley is a flatter distribution’

12 2048 www 3 M2 for 1.6³ seen Or M1 for 1.6 or 32/20 A1 for 2050

Section B Total: 25




GCSE






1

















Award NR if:






2

Award 0 if:








and





3

Abbreviations











4

Section A 1 (a) 73/99 cao

2 M1 for 100(r) = 73·73 or better

(b) 1/6 2 M1 for evaluating square root or interpreting reciprocal

(c) 9 – 4 5 2 M1 for 3 or more terms correct soi of

5 5 – 2 5 – 2 5 + 4

2 (a) 1.4 oe 1

(b) Y11; more of the students (a greater proportion) are closer to the correct time of 50 seconds

1 any comment referring to more Y11 in the intervals around 50 or less in the extreme intervals at both ends, but not just about spread see exemplars

3 (a) b – a

1

(b) 41 (b – a ) oe

1 ft their (a) if in terms of a and b

(c)

4

3a +

4

1b or

4

1(3a + b)

or a + 4

1(b – a) or b +

4

3(a – b)

accept correct equivalents

2 mark final answer M1 for correct route identified eg

⎯→⎯⎯→⎯+ OCOA , a +

4

1AB, a + their (b), etc but

not just for arrows on the diagram ft their (b) for M1 only

4 (a) (x – 4)2 – 6 3 M2 for (x – 4)2 – 16 (+ 10) or x2 – 4x – 4x + 16 – 16 (+ 10) Or M1 for (x – 4)2 or (.....)2 – 6 Or SC2 for (x + 4)2 – 6

(b) −6 1ft ft their −6 from (a)


5

5 3x + 4 + x – x2 = 7 oe

or 7 – 3x = 4 + x – x2 oe x2 – 4x + 3 (= 0) or –x2 + 4x – 3 (= 0) seen as part of solution leading to final answer (x – 3)(x – 1) oe x = 3, y = –2 x = 1, y = 4

W1

M1

M1

W1 W1

for eliminating x or y for correctly collecting their terms on one side, (allow x2 – 4x = –3 if going on to complete the square) ft factorising their quadratic equation or correct substitution to reach their

2

314)4(4)(

2 ××−−±=x or better

if W0, allow W1 for two correct x values correct answers from trial and improvement scores W2 only

6

90

36 oe www

ignore subsequent cancelling

4 M1 for one colour correct (seen)

10

6 ×

9

5 or

10

3 ×

9

2 or

10

1 ×

9

0

or better M1 for both red and yellow correct

10

6 ×

9

5 and

10

3 ×

9

2 or better

M1 for adding probabilities for RR, YY and BB (clearly identified)

10

6 ×

9

5 +

10

3 ×

9

2 (+

10

1×

9

0)

Section A Total: 25


6

Exemplar responses: 2(b) Responses scoring 1 mark: Y11 because …

• no-one took longer than 70s and fewer took less than 40s unlike Y7. (Reference to less Y11 in extreme intervals. Reference to Y7 not necessary in this example.)

• they had a smaller frequency density than year 7 at 20 – 40 and 60 – 90 seconds. (Condone reference of frequency density for number of students. Refers to extreme intervals.)

• there were less students who estimated too high or too low. (Condone too high and too low as reference to extreme intervals.)

• more students estimated 50 seconds or near. (Accept this as a reference to the intervals around 50.)

• there are more in the interval 40 – 60 (or 40 – 55) than Y7. (Refers to the intervals around 50.)

• more took over 70s and less than 40s unlike Y11. (Refers to less Y11 in the extreme intervals. Without '..unlike Year7' this would not have been allowed as the words identify that Year 7 have less in the extreme intervals.)

• frequency density between 40 to 55 is higher student per second. (Refers to more Year 11 students around 50 seconds.)

• there are 141 year 11 students between 40 and 60 but year 7 have only 127. (Accept correct numerical evidence from both years.) Responses scoring 0 marks: Y11 because …

• they have a higher frequency density of 50 seconds than the Year 7s. (Incorrect to talk about frequency density of a single value.)

• Y7 had a bigger range. (True but has no bearing on which year group were closer to 50.)

• there is a much lower fluctuation of values, they are less spread out which makes it easier to see the trend.

(No reference to closeness to 50.) • frequency density between 40 to 60 is high student per second.

(Not a comparison. Would need to say fd is higher.) • the frequency density is higher for the year 11 students.

(Does not make it clear which intervals are referred to.) • year 7s estimates have a range of 70s which means they are more spread whereas year

11s estimates have a smaller range of 50s so they are overall closer to the answer due to a smaller spread of estimates.

(Smaller spread does not imply that the data is closer to 50 for year 11.) • there were more people in the modal group that estimated 50 seconds and there’s a

smaller range than year 7. (Only refers to one interval, rather than a group of intervals around 50. Spread irrelevant.)

• year 7 have more people who took longer than 60 seconds. (Only refers to one of the extremes.)

• they had a higher frequency density at 50 to 55 seconds. (Only refers to one interval rather than a group of intervals around 50.)

• most of the students had estimated closer to the 50 second mark. (Not a comparison but a statement about Y11 which is also true for Y7.)


7

Section B 7 (a) (i) 18·8 - 18·9

1

(ii) points plotted correct curve

1 1

ft their table; condone one error

(b) 8·0 – 8·6 1 or ft their graph (±2 mm)

8 (a) (average) weight decreasing (untll 2002) and then increasing again

1

(b) 1821 – 1921 answer must ft their moving average

2 M1 for 5

1530947525677 x++++ = ‘1110’

or 5 × ‘1110’ – 3679 condone 1100 – 1120 for the moving average

9 (a) 9·16(…) or 9·2 ignore subsequent rounding after correct answer seen

3 M2 for

35sin

115sin8·5

Or M1 for 35sin

8·5

115sin

BD =

(b) 48·7 – 48·94 2 M1 for 0·5 × 13·5 × 'BD' × sin52

3(2x – 1) + 4(x + 2) = 2(2x – 1)(x + 2)

or better 4x2 – 4x – 9 (= 0) or –4x2 + 4x + 9 (=0)

(x =) 8

160 4 ±

M2

A1

M2

for M1 and M2, condone one error or omission if the brackets are expanded without brackets being shown M1 for multiplication by one denominator or left in the form fraction = 2 or denominators removed with 2 of the three terms correct as an equation or expression dep on M2 award when first seen even if then spoilt for M1 and M2 ft their quadratic equation

M1 for (x =) 4 2

9 – 4 4 – 4 4 2

×××±

substitution into formula (condone two errors)

10

2·08 and –1·08

A2

A1 for either value correct or both given to wrong accuracy eg 2·081, –1·081 or 2·1, –1·1 If A0 then SC1 for their answers seen and rounded to 2dp


8

11 13043·8 or 13044 or 13040 or 13000

www 4

M1 for 3

1 × 27·52 × 66 or 16637·5

M1 for 3

1 × 16·52 × “66 – 26·4” or 3593·7

M1 for subtraction of their volumes (soi)

12 123·6 - 123·7 303·6 - 303·7

1 1

SC1 for two answers differing by 180° between 0 and 360

Section B Total: 25



GCSE


Terminal Paper (Foundation tier)






1

Marking instructions for examiners (June 2010) GCSE Mathematics C (Graduated Assessment) – J517 Units B271 to B282

Please ensure you familiarise yourself with the mark scheme before you complete your practice scripts. You will be required to complete ten practice scripts and ten standardisation scripts for each section (A and B) of the unit. Make sure you turn on the comments box when working on the practice scripts. You should do the practice scripts before attempting the standardisation scripts. If you are unsure why the marks for the practice scripts have been awarded in the way they have, please consult your team leader. Marking instructions 1. Mark strictly to the mark scheme. If in doubt, consult your team leader using the










the answer space is a clear transcription error, unless the mark scheme says ‘mark final answer’ or ‘cao’. ii. Allow full marks if the answer is missing but the correct answer is seen in the body. iii. Accuracy marks for an answer are lost if the correct answer is seen in the working but a completely different answer is seen in the answer space. Method marks would normally be given.




2



Award NR if:

Nothing is written at all in the answer space There is a comment which does not in any way relate to the question being

asked (“can’t do”, “don’t know”, etc.) There is any sort of mark that is not an attempt at the question (a dash, a



Award 0 if: There is any attempt that earns no credit. This could, for example, include

the candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.







and


16. The comments box will be used by the Principal Examiner to explain his or her marking of the practice scripts for your information. Please refer to these comments when checking your practice scripts. Please do not type in the comments box yourself. Any questions


3

or comments you have for your team leader should be communicated using the scoris messaging system, e-mail, or by telephone.


Abbreviations


Where you see oe in the mark scheme it means or equivalent.

Where you see cao in the mark scheme it means correct answer only.

Where you see soi in the mark scheme it means seen or implied.

Where you see www in the mark scheme it means without wrong working.

Where you see rot in the mark scheme it means rounded or truncated.

Where you see seen in the mark scheme it means that you should award the mark if that number/expression is seen anywhere in the answer space, including on the answer line, even if it is not in the method leading to the final answer.



Viewing tips for this paper In general, set your screen to ‘fit width.’ You may find it helpful to set to ‘fit height’ for the following questions: 4aii, 5d, 6b, 10a, 10b, 11a, 11b, 17(then zoom in twice), 18


4

Section A 1

(a)

(i) twenty five thousand [and] sixty two

1

(ii) 25 100 1

(b) 58

1

2 (a) (i) 21

1

(ii) 15 …. 30 1

(iii) 12 or 30 1

(iv) 11 1

(b)

9 = 3 × 3 or * * * * * * * * *

1 see exemplars

3

(a)

4·50 1

(b)

12 or 12·00 1

(c) (0)·3(0)

1

(d) 3/25 as final answer 2 M1 for 12/100 or better seen

4 (a) (i) cricket

1

(ii) appropriate numbers on frequency axis correct height bars [9, 12, 7, 3, 10] bars consistent width [and consistent gaps]

1

1

1

numbers by grid lines not in gaps ft their scale if linear; tolerance less than half a unit – mark the intent; condone unruled if in tolerance

(b) (i) magazine

1

(ii) 15

2 M1 for 60 ÷ 4 o.e. or for 6° [per person]


5

5 (a) 140

2 M1 for 35 × 4 o.e.

(b) 5·1

2 M1 for 2 × 1·4 + 2·3 o.e.

(c) 7

2 M1 for 35 ÷ 5

(d) 4·5 to 4·7 identified as length, isw 2 eg allow 2 for 4·5 to 4·7 seen in correct position on diagram M1 for 9 to 9·4 seen OR SC1 for 5 m

6

(a)

−1 3 1

(b)

three points plotted ruled straight line joining (0, −5) to (4, 3) or further, tolerance 2 mm

1

1

ft their points, tolerance 2 mm no ft; mark correct line only; ignore line outside x from 0 to 4

(c) No because 2 × 12 − 5 is not 9 or 24 5 is not 9

1 oe eg ‘no, when y = 9, x = 7’ e.g. accept ‘no because when x is 12, y is 19’ oe see exemplars

7 (a) a = 34 [angles on straight] line add to 180 or ‘[angles round a] point add to 360 and/or opposite angles are equal’

1 1

allow omission of ‘add to 180’ if 34 obtained or condone ‘[angles in a] circle add to 360’; allow omission of ‘add to 360’ if 34 obtained

(b) b = 65 ‘[base angles of] isosceles [triangle] [are equal]’ and/or ‘[angles in a] triangle add to 180’

2

1

M1 for (180 − 50) ÷ 2 soi


6

8 (a) 200

2 M1 for 8 or 25 seen

(b)

13

35 oe (eg

26

70)

2

M1 for evidence of equivalent fractions attempted: two fractions with a correct common denominator with at least one of the numerators correct

eg 28

35 or

15

35 oe

allow SC1 for an answer which is completely correct except for a consistent

error in the denominator eg 30

28 -

30

15=

30

13

9

[2x + 1 =] 6x − 8 or x + ½ = 3x − 4 9 = 4x or 4 ½ = 2x o.e or ft 2·25 o.e. cao

M1

M1

A1

for dealing correctly with brackets for collecting terms correctly, ft allow A1 for 9/4 isw incorrect conversion allow B3 for 2·25 o.e.

10

(a)

reflection B correct (1, −2) (1, −4) (2, −2)

1 condone unlabelled (but not labelled C)

(b)

rotation C correct (−2, 1) (−2, 2) (−4, 1)

2 condone unlabelled (but not labelled B) M1 for clockwise 90° about (0,0) or anticlockwise 90° wrong centre

11

(a)

18/48 then simplified or 8 × 6 = 48 and 3 × 6 = 18 o.e. or 3/8 of 48 = 18

1

condone 18/48 only condone 18/48 seen with subsequent errors

(b)

150 www or accept answers in range 140 – 162 if supported by sensible working

2 M1 for 50 seen or for 18/48 × 400 o.e. or for 8 to 9 [boxes] seen or used, but not just for 8 from denominator of 3/8

Section A Total: 50


7

Section B 12 (a)

1 mark the intent

(b) 13 17

1

(c) 29 ‘add three more lots of 4’ or ‘add 4 each time’ oe

1

1

or ‘5 to start with then 6 more lots of 4’ or nth term is 4n + 1 oe see exemplars

13 (a) 1080 2 M1 for 1000g = 1 kg soi, eg by 1500, or for digits 108

(b) 12:25 2 M1 for 12: …. or ….. :25

(c) 22 2 M1 for 8800 ÷ 400 o.e. or for 88 ÷ 400 or for digits 22 with wrong dp

14 (a) 80(·00)

1

(b) 42·50

1

(c) 6 2 M1 for 180 – 30 [= 150] soi

15 (a) sum of numbers (= 114) their sum ÷ 10 soi 11·4

M1

M1

A1

allow implied by 88 to 124 seen or figs 114 dep on first M1; a total must be seen if not correct or W3 for 11·4 www; allow M2 for answer of 106·8 with no working accept 11 for 3 marks only if 114 or 11·4 seen NB 0 for answer of 11 with no working

(b) (i) 26

1

(ii) 48

1

(iii) 24·5

2 M1 for 24 and/or 25 identified or for 4·5

(c) (i) ACB, BAC, BCA, CAB, CBA 2 M1 for one omission or one repeat, but do not count writing ABC for themselves as a repeat 0 if extras such as AAA, BBB, CCC also included SC1 for misread of A, B, C as headings and the fully correct rearrangements of 11, 12, 13 shown

(ii) 0·6

1 accept fraction or % equivalents


8

16 (a) lines 0 order 3

1 1

accept ‘none’ or ‘zero’

(b) drawing with just one line of symmetry drawing with rotational symmetry order 1

1

1

ignore their line(s) of symmetry drawn they must have added to drawing (not just a ‘line of symmetry’) to gain any marks

17 *

mark or line indicating correct bearing measured from P or Q correct lines drawn from P and Q B marked in correct position or ft their lines

M1

M1

A1

±2° ±2° dep on at least M1 gained condone absence of label B if position clearly indicated eg with cross if M0, allow SC1 for B marked at intersection of lines coming from P and Q but wrong bearings (eg using protractor E/W)

18 (a) two rectangles 2·5 by 6 two isosceles triangles with base 4 and ht 1·5 net in correct orientation

1

1

1

tolerance 2 mm ignore construction line for height and/or right angle symbol must consist of 2 more rectangles and 2 triangles but independent of their dimensions, must be possible net if dimensions were correct

(b) ½ × 4 × 1·5 × 6 o.e. (may be done in two steps) 18

M2

A1

M1 for ½ × 4 × 1·5 [= 3 cm2] oe or for their ½ × b × h × 6 using one wrong measurement from triangle NB correct method required allow B1 for 18 if no working but B0 if wrong working If 0 scored allow SC1 for 6 × 4 × 1·5 [=36] without further working

(b) cm3

W1


9

19 (a) 7a − 5c

2 W1 for 7a (W0 for − 7a) in their answer

W1 for −5c in their answer OR W1 for 7a − 5c seen then spoilt by further work allow W1 for 7a +−5c

(b)

5x – 20 1 mark final answer (but ignore x = 4 after 5x – 20)

(c)

x(x + 3) 1 mark final answer

(d) [x =]

2

5

y oe

2

M1 y + 2 = 5x oe (eg y/5 = x – 2/5) OR SC1 for answer of

y + 2 ÷ 5 or 25

y or

2

5

y oe

20

(a)

4 : 3 : 5

1

(b)

17 500 2 M1 for 42000 / their(4 + 3 + 5) [= 3500] or 42000 / their(16 + 12 + 20) [= 875] or for figs 175 seen in answer

21

Veggie burger with B 17·1 – 17·2 or 17[%] C 16·7 – 16·8 or 16 or 17[%] V 21·4... or 21[%] or ALT method: Veggie burger with B: 5.8 to 5.9 C: 5·9 to 6·0 V: 4·6 to 4·7

3

accept equiv decimals for full marks or for part marks labels B, C, V not required as long as working clear M2 for any two of: 17·1 – 17·2 or 17% , 16·7 – 16·8 or 16 or 17%, 21·4...or 21% seen or M1 any one of 47/274 or 29/173 or 54/252 seen or SC1 for all of B: 5·8 to 5·9, C: 5·9 to 6·0, V: 4·6 to 4·7 with wrong/no choice made

Section B Total: 50


10

Exemplar/sample comments Question 2(b)

Response Mark 32 is 9 1 Because 3 squared = 9 1 Because it is in the three times table which means 32 = 9. [last part of comment gets the mark]

1

Because you square 3 to get it 1 9 represents a square because when a square is drawn it is 9 (with square 3 × 3 drawn)

1

Because 3 goes into it 3 times 1 It can be made by multiplying the same number together 3 x 3 /32 = 9. 9 can be square rooted.

1

Because you can times 3 by itself to equal 9 1 3 × 3 = 9 and 9 × 9 =81 1 Because 3 × 3 = 9 1 3 × 3 = 9, 3 goes into 9 three times, and 9 ÷ 3 = 3 1 if a number can be timesed by itself to make 9 (3) 1 BOD It can be timesed by itself 0 Because it has 3 square number in itself 0 9 is a square number because you can multiply it by itself 0 Because 3 + 3 + 3 = 9 [would have given 1 if 3 by 3 diagram also present]

0

Because you can divide it by itself 0 It can be squared up to 9 by 3. 0 it can be split roughly 3 times 0 9 is a square number cos it can be times by itself 0 Because it’s a three times table 0 It has a number that can be timesed to make it 0 You × 9 by 9 0 Because there is only two numbers that goes into 9 0 Because a number goes into it which is 3 0 9 is a square number because only 1, 3, 9 goes into it 0 Because 9 dots can make a square [would accept with diagram] 0 Because 92 or 9 × 9 = 81 0 Because it can be doubled by itself. 0


11

Question 6(c) Response Mark Every time x goes up by 1 y is 2 more than the previous y number (copy of table included) and when you get to x 12 y is 19 and not 9. (Table above comment showing this)

1

No, 2 × 12 − 5 = 19, this needs to answer 9 and it doesn’t 1 No, x = 12 × 2 = 24 − 5 = 19 [condone string of equals without y mentioned]

1

No, 2x − 5. 2 × 12 = 24 − 5 = 19 so it won't be on the graph. 1 12 + 12 = 24 - 5 = 19 and the y-axis needs to be a 9 not 19 1 No, 12 is x and 2 × 12 = 24 then – 5 = 19 instead of 9 1 No, 12 × 2 = 24 and 24 – 5 don’t = 9 1 There is no way of equating this point on the line y = 2x − 5 however you could reach this point if you drew the line long enough but this is irrelevant in doing so as it is not on the y = 2x − 5 line. (Table above showing points (6, 7) (8, 11) (10, 15))

0 contradictory

No if you do make x 12 it becomes bigger than (12, 9) 0 No, It wouldn’t fit as 12 is 3 bigger than 9 when they all have one space apart. 0 No, if you carry on it goes (6, 7) (8, 11) (10, 15) [would have given if they had included (7, 9) or if they had commented that they had got past 9 for y]

0

No, the coordinates don’t follow the equation (y = 2x − 5) would equal 7 not 9 0 No you would have (12, 7) 0 No x = 12, 12 × 2 = 24 − 5 = 18. x = 12 y = 18 not 9 [If they give a value of y it must be correct]

0

No, the y axis is always going up in 4 so the answer instead should be (9,15) 0 No, because double 5 is 10 and double 6 is 12 but for it to be (12, 9) it would have to be on 4.5

0

No, there are no numbers that when multiplied by 2 then subtract 5 will make 19. 12 × 2 = 24 – 5 = 19 [first part of statement wrong, so 0]

0

No, it is too short 0 No, 12 × 2 – 5 = 19, 9 × 2 – 5 = 13 [choice of which is correct value of x to use]

0

No, line is too steep 0 No, all the numbers are odd so I used the same technique I did for 0, 2, 4 and got (13, 9)

0

No the y numbers go up by 4 each time 0 No, 9 × 2 = 18, 18 – 5 = 13 so it can’t be 12 as it would not fit on the line 0 No, when x is multiplied by 2, 5 – 24 does not equal to 9 [5 – 24 should be 24 – 5]

0

No, the point will be (12, 15) or (8, 9) 0 The y-axis is rising 4s so it would go 7 to 11 missing 9 completely 0 No the point is too far off for the line of best fit. 0


12

Question 12(c) Response Mark 29, 17 + 4 = 21 + 4 = 25 + 4 = 29 1, 1 29, 5 would have 21, 6 would have 25, 7 would have 29 there are 4 more lines on each pattern that is added.

1, 1

29, every line from each pattern goes up four numbers and if 4 is 3 numbers away from 7 it would make it 4 lots of 3 going up again instead of 4 lots of 1

1, 1

29, 4 × 3 = 12. 12 +17 =29 1, 1 29, every pattern has 4 more lines than the one before. 1, 1 29, it goes up in fours 4 – 7 is 3 + 4 = 12. 12 + 17 = 29 1, 1 29, you add on 4 each time 1, 1 29, you add on 4 lines from the last pattern to get the amount of lines for the next one 1, 1 29, goes up in 4's (4 × 3 = 12 17 + 12 = 29) 1, 1 29, it goes up in fours 1, 1 29, each pattern has 4 more straight lines [with diagram of pattern 7 and each line numbered] 1, 1

29, if you add pattern 3 and pattern 4 you get 30, but you need to take one off as they start and ending the same way

13 + 17 = 30 – 1 = 29

[NB correct alternative method here]

1, 1

29, add on 4 each time, pattern 6 would have 25 lines so pattern 7 must have 29 1, 1 29, the amount goes up in fours so you could do 4 × 3 = 12, 12 + 17 = 29 because there is a 3 unit difference between 4 and 7 1, 1

29, You add 4 for each pattern so it is adding 12 in total. 1, 1 29, The nth term is 4n + 1 1, 1 29, the pattern is add 4 [accept as implying repeated addition] 1, 1 29,You add on 4 until you get to 7 5 21

6 25 7 29

1, 1

29, I use pattern 4 to answer pattern 7, easy 1, 0 29, 35 – 6 = 29, you times the pattern number by 5 then − 1 from what order it is [trying to say 5n – (n – 1) but have made error]

1, 0

29. I added on an extra 12 to the sequence. [needs to explain where the 12 comes from]

1, 0

29, I just did 7 squares and counted all the lines 1, 0 29, you add four onto the number before so 25 26 27 28 29 and that’s the rule + 3 [contradiction] 1, 0

29, the number of straight lines are going up in the 4× table 1, 0 29, add on 4 [implies 4 added once only] 1, 0 28, 4 + 17 = 21, 21 + 4 = 25, 25 + 4 = 28 [mark for reason is independent]

0, 1



GCSE


Terminal Paper (Higher Tier)






Marking instructions for examiners (June 2010)

GCSE Mathematics C (Graduated Assessment) – J517

Units B271 to B282

Please ensure you familiarise yourself with the mark scheme before you complete your practice scripts. You will be required to complete ten practice scripts and ten standardisation scripts for each section (A and B) of the unit. Make sure you turn on the comments box when working on the practice scripts. You should do the practice scripts before attempting the standardisation scripts. If you are unsure why the marks for the practice scripts have been awarded in the way they have, please consult your team leader. Marking instructions 1. Mark strictly to the mark scheme. If in doubt, consult your team leader using the messaging

system within scoris, e-mail, or by telephone. 2. Make no deduction for omission of units except as indicated on the mark scheme (although if

this leads to a later error this will of course be penalised). 3. Work crossed out but not replaced should be marked. 4. M (method) marks are not lost for purely numerical errors. A (accuracy) marks depend on preceding M (method) marks. Therefore M0 A1 cannot be

awarded. W (workless) marks are independent of M (method) marks and are awarded for a correct final

answer or a correct intermediate stage. 5. Subject to 4, two situations may be indicated on the mark scheme conditioning the award of A

marks or independent marks: i. Correct answer correctly obtained (no symbol) ii. Follows correctly from a previous answer whether correct or not (“ft” on mark







1


9. When the data of a question is consistently misread in such a way as not to alter the nature or difficulty of the question, please follow the candidate’s work and allow follow through for A and W marks. Deduct 1 mark from any A or W marks earned and record this by using the MR annotation. M marks are not deducted for misreads.

10. For methods not provided for in the mark scheme give as far as possible equivalent marks for

equivalent work. If in doubt, consult your team leader. 11. For answers scoring no marks, you must either award NR (no response) or 0, as follows:

Award NR if:

Nothing is written at all in the answer space There is a comment which does not in any way relate to the question being

asked (“can’t do”, “don’t know”, etc.) There is any sort of mark that is not an attempt at the question (a dash, a



Award 0 if: There is any attempt that earns no credit. This could, for example, include the

candidate copying all or some of the question, or any working that does not earn any marks, whether crossed out or not.



13. In cases where there is clear evidence that a calculator has been used in section A, mark the

script as normal then raise an exception (malpractice) in scoris. All suspected malpractice should be flagged using exceptions.

14. Anything in the mark scheme which is in square brackets [ … ] is not required for the mark to

be earned, but if present it must be correct. 15. Holding the F2 key on your keyboard displays the annotations toolbar next to your cursor. The following annotations are available:

and


2


3



Abbreviations


Where you see oe in the mark scheme it means or equivalent.

Where you see cao in the mark scheme it means correct answer only.

Where you see soi in the mark scheme it means seen or implied.

Where you see www in the mark scheme it means without wrong working.

Where you see rot in the mark scheme it means rounded or truncated.

Where you see seen in the mark scheme it means that you should award the mark if that number/expression is seen anywhere in the answer space, including on the answer line, even if it is not in the method leading to the final answer.




Section A 1

35

13 oe (eg 26/70)

2

M1 for evidence of equivalent fractions attempted: two fractions with a correct common denominator with at least one of the numerators correct

Eg 35

28 or

35

15 oe

allow SC1 for an answer which is completely correct except for a consistent error in the

denominator eg 30

28 −

30

15=

30

13

2 (a) 3, 8, 13 2

M1 for two correct terms in correct position or 3 terms increasing by 5 eg ─2, 3, 8

(b) 4n + 3 oe

2 M1 for 4n ± k for any k

3 -4 www 3

M1 for 3n + 7 = −5 or 5n = 2n −12 M1 for 3n = −12 ft their 1st step to reach kn = bM1 for n = − 4 ft their 2nd step (from kn = b with k ≠ 1)

4 (a) 48 www 3 M1 for 1200 used (or 0.025) M1 for division their 1200/25 oe

(b) (i) 37.5 2 M1 for 1 + 2 (×) 25 2 or correct complete method involving triangles and/or rectangle.

(ii) 375 000 or their (b)(i) × 10 000 2

M1 for their (b)(i) × 10 × 1000 seen isw A1 ft their (b)(i) × 10 000 OR M1 for their (b)(i) × 10 evaluated isw or (b)(i) × 1000 evaluated isw. or their volume in m3 × 1000 evaluated

(c) [Using exterior angles] 360 /10 (= 36) 180 – 36 (= 144) oe

1 1

Alternative method: M1 for 8 × 180 or equivalent eg adding 180 on 6 times to 360 M1 for 1440 soi divided by 10 after 1st M1 earned. Alternative method (starting from 144): M1 for 180 −144 = 36 M1 for 36 × 10 = 360 or 360/36 = 10 oe

4


5 (a) reflection B correct

(1, −2) (1, −4) (2, −2)

1 condone unlabelled (but not labelled C)

(b) rotation C correct (−2, 1) (−2, 2) (−4, 1)

2 condone unlabelled (but not labelled B) M1 for clockwise 90° about (0, 0) or anticlockwise 90° wrong centre

(c) reflection ft y = x oe ft

1

1

transformation must ft their B and C full description must ft their B and C

6 (a) ─ 2 10

1 1

(b) 6 points plotted correctly smooth curve through correct points

1 1

2mm tolerance ft their (a) 2mm tolerance from correct points; must be space between min point and (─1.5, ─2)

(c) 0.2 to 0.4 ─ 3.2 to ─ 3.4

1 1

or ft their graph ±0.1 or ft their graph ±0.1 mark solutions on answer line. if 0 scored, SC1 for evidence of attempt to read from y = 1

7 (a) 18/48 then simplified or 8 × 6 = 48 and 3 × 6 =18 oe or 3/8 of 48 = 18

1

condone 18/48 only condone 18/48 seen with subsequent errors

(b) 150 www or accept answers in range 140 – 162 if supported by sensible working

2 M1 for 50 seen or for 18 × 400 oe 48 OR M1 for 8 to 9 [boxes] seen or used, but not just for 8 from denominator of 3/8

(c) 3 oe 800

2 M1 for

8

3×

100

1 oe

5


8 (a) (x − 7)(x + 2)

7, −2

M2

A1

M1 for (x ± 7)(x ± 2) or (x + a)(x + b) where ab = −14 or a + b = −5 ft their factors If M0, then W1 for 7, −2

(b) multiplication (to eliminate x or y) eg 12x + 2y = 32 addition to eliminate y (condone 1 error) 17x = 51 x = 3, y = −2

M1

M1

A1

condone 1 error or 30x – 12y = 114 and 30x + 5y = 80 subtraction to eliminate x (condone 1 error) −17y = 34 A1 is dependent on M2 scored If M0, then W1 for 3 and −2 only

9 4 statements with reasons correct AB = DC : opposite sides of a parallelogram ABD = BDC : alternate angles BAE = FCD : 3rd angle of right-angled triangle congruent: 2 angles and corresponding side

3 2 marks for 2 or 3 statements with reasons 1 mark for 1 statement with reason either opposite sides or parallelogram may be omitted condone z angles Accept ........ ASA

10 (a) (i) 1

1

(ii)

25

1 or 0.04 www

3 M1 for evaluating cube root, eg

( 3 125 ) = 5 or ( 3 15625 )= 25 M1 for evaluating square, eg 5² = 25 or (125²) = 15625 M1 for interpreting reciprocal, eg 1/25

(b) 111

47

3 M2 for r = 423/999 or better eg 141/333 Or M1 for 1000r = 423.(4...)

Section A Total: 50

6


Section B 11 mark or line indicating correct bearing

measured from P or Q correct lines drawn from P and Q B marked in correct position or ft their lines

M1

M1

A1

± 2° ± 2° dep on at least M1 gained if 0, allow SC1 for B marked at intersection of lines coming from P and Q but wrong bearings (eg using protractor E/W) condone absence of label B if position clearly indicated eg with cross

12 3.04 2 M1 for 3.04... or 3.0 or 3.05 or their ‘answer’ rounded correct to 2dp

13 (a) 5x − 20 1 mark final answer (but ignore x = 4 after 5x – 20)

(b) x(x + 3) 1 mark final answer

(c) (x =) y + 2 oe 5

2

M1 for y + 2 = 5x oe (eg y/5 = x – 2/5) Or SC1 for answer of y + 2 ÷ 5 or y + 2 or y – 2 oe 5 5

14 Veggie burger with B 17.1 – 17.2 or 17 (%) C 16.7 – 16.8 or 16 or 17(%) V 21.4 – 21.5 or 21(%) or alternative method: Veggie burger with B 5.8 to 5.9 C 5.9 to 6.0 V 4.6 to4.7

3

Accept equivalent decimals for full marks or for part marks. Labels B, C V not required as long as working clear M2 any two of 17.1 – 17.2 or 17, 16.7 – 16.8 or 16 or 17, 21.4 - 21.5 or 21 seen OR M1 any one of 47/274 or 29/173 or 54/252 seen alternative method Allow SC1 for all of B 5.8 to 5.9, C 5.9 to 6.0, V 4.6 to 4.7 with wrong/no choice made

7


15 (a) 4 : 3 : 5 1

(b) 17500 2 M1 for 42000 / their (4 + 3 + 5) (= 3500)

or 42000 / their (16 + 12 + 20) (=875) or figs 175 seen in answer

16 8.06 to 8.1 www 3 M2 for √65 or √(9²− 4²) Or M1 for a correct Pythagoras statement A1 for 8 or 8.06 to 8.1

17 (a) correct reason 1

eg ‘all 5 miles wide would give too many groups’ eg ‘not many people travel long distances’ see exemplars

(b) 9.6 or 9.65 or 9.7 isw

4 M1 for midpoints 2.5, 7.5, 15, 30 soi; condone 1 error M1 for attempt at fx [= 482.5]

M1 for their fx ÷ their or 50 fA1 for 9.6 or 9.65 or 9.7

(c) Frequency densities: 4.4, 2.6, 0·8, 0·35 all bars correct width all heights correct from histogram attempt

1

1 1

Condone 1 error. ± 1mm

18 (a) 38.(0...)www 3

M2 for 40 sin 72 or 40 cos (90 − 72) Or M1 for trig statement involving sin 72 or cos their 90 – 72

(b) 34.4 to 34.5 www 3 M2 for 1189 Or M1 for 40² + 15² − 2 × 40 × 15 cos 58

19 (a) 15(.14...) 2 M1 for figs 53 ÷ figs 35

(b) 4 104 320 or 4 100 000 4.1... × 106

2 M1 for × 0.88 or equivalent

(c) 2027 2 M1 for 2026, 2028, 21, 22 or 23 years or 2009 with 3.1... × 106 seen (or 31(78385))

20 (a) 4840 4840 plotted (± 2mm tolerance)

1 1

ft their 4840 from Σ /4

(b) (i) reading 4840 to 4900

1

(ii) (4 × their reading) – (4870 +2260 + 4370) evaluated

2 M1 for method correct with an arithmetic error eg 4870 + 2260 + 4370 + n = their (b)(i) 4

8


21 (a) (4.2, 0) (0, −4.2)

1 1

M1 for 3√2 or (±)18 www

(b) (i) x² + x² + 6x + 9 = 18

2 M1 for x² + 3x + 3x + 9 or x² + (x + 3)² = 18 or better

(ii) (−4.1, −1.1) www 3 M2 for (−6 − √108)/4 Or M1 for substitution into quadratic formula; condone 2 errors Alternative method: M2 for √6.75 ─ 1.5 M1 for (x + 1.5)² ─ ..... .

Section B Total: 50

9


10

Exemplar responses for Question 17(c) Comments need to relate either to

bigger class widths related to smaller frequency or vice versa or

group widths of 5 miles give too many classes Mark the best part of the comment and ignore subsequent work. Exemplar responses scoring 1 mark (To make it more simple and) less people travel further Second part earns the mark (Because it gives a higher frequency of results because) the higher distances may not have many people in if the range is only 5 miles

As distances travelled are so varied there will not be many employees in the smaller groups.

As you get further distances the frequency reduces. More people are likely to travel 0 < d ≤ 5 than 20 < d ≤ 40.

First part is enough

As the distances increase the frequency decreases, (so more class widths are unnecessary.)

First part is enough

Not many people live far away so don’t need so many The class width increases as frequency decreases so it keeps the chart short

Because people normally live close to work and less distance in miles would have a higher frequency (density)

Ignore density

Because then the distances increase there is only a small number of people at end of scale so smaller class widths would be pointless

All 5 miles wide would give too many groups (There may have been people who travelled between the distances if the groups were even.) Or as distances increase there may have been an insufficient amount of people.

Second sentence is enough

Many people travel short distances Not many people travelling long distances Exemplar responses scoring 0 marks To make the measurements more accurate e.g less than 5 miles is more accurate than a 10 mile class width.

Ref to accuracy is not enough

There may not be an urbanised area 30 miles away or may not be enough people that live there.

Not linked to groups

To keep the frequency more simple So the data is more direct and it shows more accurately the information. So you don’t have to have loads of different classes. Not specific To be able to see the mode faster. Means there are no classes with no employees in them. It changes the distances where people live. So there's more variety. Not enough To show the difference in frequency of how far employees travel to work. No reference to low frequency /

further distance Because the smaller groups are very popular. Too vague As accuracy is not as important it keeps chart short Reference to accuracy is not enough Easier to complete with a few groups Not relevant More accurate groups To decrease the size of the table, quicker to construct and work out As the data can be summarised easier ...it shows the data clearer This makes displaying results easier Because there are less and more people in different class widths so to make the results equal there are unequal classes

Not clear

Accuracy To make the mean more precise This is a reason for smaller class

widths not unequal class widths



Documents

GCSE Mathematics C (Graduated Assessment) Max Mark a* ......2011/06/02 · B282/01 Mathematics Terminal Paper (Higher) Raw 100 89 71 53 35 20 12 n/a n/a 0 UMS 400 360 320 280 240