GCSE. Mathematics B (Linear) Mark Scheme for November General Certificate of Secondary Education Component J567/04: Mathematics Paper 4 (Higher)

Transcription

1 GCSE Mathematics B (Linear) General Certificate of Secondary Education Component J567/04: Mathematics Paper 4 (Higher) Mark Scheme f November 203 Oxfd Cambridge and RSA Examinations

2 OCR (Oxfd Cambridge and RSA) is a leading UK awarding body, providing a wide range of qualifications to meet the needs of candidates 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 f developing new specifications to meet national requirements and the needs of students and teachers. OCR is a not-f-profit ganisation; any surplus made is invested back into the establishment to help towards the development of qualifications and suppt, 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 befe marking commenced. All examiners are instructed that alternative crect 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 rept on the examination. OCR will not enter into any discussion crespondence in connection with this mark scheme. OCR 203

3 Annotations used in the detailed Mark Scheme. Annotation Meaning Crect Increct Benefit of doubt Follow through Igne subsequent wking (after crect answer obtained), provided method has been completed Method mark awarded 0 Method mark awarded Method mark awarded 2 Accuracy mark awarded Independent mark awarded Independent mark awarded 2 Misread Special case Omission sign These should be used whenever appropriate during your marking. The M, A, B, etc annotations must be used on your standardisation scripts f responses that are not awarded either 0 full marks. It is vital that you annotate these scripts to show how the marks have been awarded. It is not mandaty to use annotations f any other marking, though you may wish to use them in some circumstances.

4 Subject-Specific Marking Instructions. M marks are f using a crect method and are not lost f purely numerical errs. A marks are f an accurate answer and depend on preceding M (method) marks. Therefe M0 A cannot be awarded. B marks are independent of M (method) marks and are f a crect final answer, a partially crect answer, a crect intermediate stage. SC marks are f special cases that are wthy of some credit. 2. Unless the answer and marks columns of the mark scheme specify M and A marks etc, the mark scheme is banded, then if the crect answer is clearly given and is not from wrong wking full marks should be awarded. Do not award the marks if the answer was obtained from an increct method, ie increct wking is seen and the crect answer clearly follows from it. 3. Where follow through (FT) is indicated in the mark scheme, marks can be awarded where the candidate s wk follows crectly from a previous answer whether not it was crect. Figures expressions that are being followed through are sometimes encompassed by single quotation marks after the wd their f clarity, eg FT 80 (their ), FT 300 (their ). Answers to part questions which are being followed through are indicated by eg FT 3 their (a). F questions with FT available you must ensure that you refer back to the relevant previous answer. You may find it easier to mark these questions candidate by candidate rather than question by question. 4. Where dependent (dep) marks are indicated in the mark scheme, you must check that the candidate has met all the criteria specified f the mark to be awarded. 5. The following abbreviations are commonly found in GCSE Mathematics mark schemes. - figs 237, f example, means any answer with only these digits. You should igne leading trailing zeros and any decimal point eg , 2.37, 2.370, would be acceptable but would not. - isw means igne subsequent wking after crect answer obtained and applies as a default. - nfww means not from wrong wking. - oe means equivalent. - rot means rounded truncated. - seen means that you should award the mark if that number/expression is seen anywhere in the answer space, including the answer line, even if it is not in the method leading to the final answer. - soi means seen implied. 2

5 6. In questions with no final answer line, make no deductions f wrong wk after an acceptable answer (ie isw) unless the mark scheme says otherwise, indicated by the instruction mark final answer. 7. In questions with a final answer line following wking space, (i) (ii) (iii) if the crect answer is seen in the body of wking and the answer given on the answer line is a clear transcription err allow full marks unless the mark scheme says mark final answer. Place the annotation next to the crect answer. if the crect answer is seen in the body of wking but the answer line is blank, allow full marks. Place the annotation next to the crect answer. if the crect answer is seen in the body of wking but a completely different answer is seen on the answer line, then accuracy marks f the answer are lost. Method marks could still be awarded. Use the M0, M, M2 annotations as appropriate and place the annotation next to the wrong answer. 8. In questions with a final answer line: (i) (ii) (iii) If one answer is provided on the answer line, mark the method that leads to that answer. If me than one answer is provided on the answer line and there is a single method provided, award method marks only. If me than one answer is provided on the answer line and there is me than one method provided, award zero marks f the question unless the candidate has clearly indicated which method is to be marked. 9. In questions with no final answer line: (i) (ii) If a single response is provided, mark as usual. If me than one response is provided, award zero marks f the question unless the candidate has clearly indicated which response is to be marked. 0. When the data of a question is consistently misread in such a way as not to alter the nature difficulty of the question, please follow the candidate s wk and allow follow through f A and B marks. Deduct mark from any A B marks earned and recd this by using the MR annotation. M marks are not deducted f misreads. 3

6 . Unless the question asks f an answer to a specific degree of accuracy, always mark at the greatest number of significant figures even if this is rounded truncated on the answer line. F example, an answer in the mark scheme is 5.75, which is seen in the wking. The candidate then rounds truncates this to 5.8, 5 6 on the answer line. Allow full marks f the Ranges of answers given in the mark scheme are always inclusive. 3. F methods not provided f in the mark scheme give as far as possible equivalent marks f equivalent wk. If in doubt, consult your Team Leader. 4. Anything in the mark scheme which is in square brackets [ ] is not required f the mark to be earned, but if present it must be crect. 4

7 Question Answer Marks Part marks and guidance (a) B f 6.20[5 ] seen (b) B f 5.8[7 ] an answer of 34 2 (a) 0.05, 5% 20 oe 2 M f - ( ) oe isw attempt to simplify 0.05 accept (b) 2 2 M f isw attempt to simplify 0.48, 48% oe accept 3 attempt to extend the straight line from (9.0, 4) with a straight line sequence of dots of similar gradient crect ruled line a sequence of crect points plotted e.g. every 0 minutes, within tolerance fully crect response using all their evidence and a clear decision given M A A Within blue lines on overlay must be up to either the time=0.00 the distance=70 lines and tolerance is between the red lines on the overlay f first 2 marks mark to the candidates advantage tolerance ± 2 small square allow alternative methods by applying e.g. M f a crect and appropriate reading from the graph, A f a crect figure which they can use to answer the question, usually time speed and A f a fully crect response from all their wk M f 6 km in 5 minutes 5 6, A f 72 kmph oe and A f arrives just befe hour [as 72 > 70] if 0 sced SC f yes it arrives at either 9.45 to to 5 minutes early 4 M f 4 km in 0 mins oe 0 A f 50 A f e.g. arrives just befe hour at

8 Question Answer Marks Part marks and guidance 4 (a) 5n + 2 as final answer 2 B f 5n seen (b) 92, 84, 76 2 B f 92 in crect place 00, 92, 84-92, - 84, - 76 two crect oe 3 B f 2x 8 2x 3 = 4 M f their 2x = 24 + their 8 better M f ax = b leading to x = b/a (a ) to a maximum of 2 marks 6 (a) (i) 33 [000] 2 B f 9 [000] 24 [000] seen Note 0.5 sces 0 (ii) 0 < length 0 accept 0 to 0, 0<m>0, 0 0, 0 < 0 (b) B f at least 4 mid-points seen (from 5, 5, 25, 35, 45, 55) implied by products M f Σmf where m is a value within each group allow one err Mdep f their 965 Σf (25) isw rounding 39 must not come from wrong wking ie [0] = 965 (c) (i) December and it has a higher mean accept any crect statement condone numbers f mean and implied statement (ii) November and it has a higher range accept any crect statement condone numbers f range and implied statement 6

9 Question Answer Marks Part marks and guidance 7 Plan 2 B f crect plan with one err such as allow centre point not at centre wrong scale one dimension increct no diagonals Front Elevation 2 B f crect elevation with one err such as wrong scale, one dimension increct, one point increct, missing base to triangle all crect with extras allow centre point not at centre If reversed then SC2 f both crect SC f one crect and the other with one err in both condone freehand attempt at straight line, otherwise deduct mark in (b) if lines are excessively wavy 8 (a) (i) 3 allow the other ientation and any other table chart that shows the infmation in the four classes such as igne any totals columns such as junis and 5 males allow a bar chart, tally chart a pictogram classes mean the headings seni/juni and male/female any other crect diagram B2 f any table with no class missing with no extra cells, classes can be implied by tallies letters B f a table which has a class missing extra cells and B f crectly completed table (ii) 24 [0].45[8 ] [0].46 46% oe crect FT their table isw when they attempt to simplify 7

10 Question Answer Marks Part marks and guidance (b) 24 3 M2 f ( 3 ) 00 oe 25 e.g. ( 3 ) M f oe 3.24 oe 25 and their 6 M f SC2 f answer of 24 SC f answer not 3 9 ruled perpendicular bisect of AB with at least one pair of crect arcs and then an intended route due West, which is always between cm and 2 cm from the coast, it must be a joined up line = = 24 4 B f crect ruled line between A and B going through and beyond the midpoint of AB, condone extension of bisect towards coastline B f at least one intersection of one pair of crect arcs B f an intended route due west B f a route always within cm and 2 cm of coast 2 accept = = 9 ( 9.3 f 580) = = = 20 M f 560, 570, 580, 600, seen on between the two V lines route parallel to coastline (due West) by eye, could be anywhere on diagram must remain between the two parallel lines f its length which has to be at least 5 mm by eye. 8

11 Question Answer Marks Part marks and guidance E accept equations in the place of A F A E in either der in either der letters 2 (a) M2 f oe M f (0) (b) M2 f oe M f.06 06% oe seen 3 (a) x 2 + 4x 2 2 M f three crect terms from x 2 [+] 7x 3x 2 (b) 6x(y 2x) 2 M f a crect partial factisation eg 6(xy 2x 2 ), x(6y 2x) 3x(2y 4x) 2x(3y 6x) 3(2xy 4x 2 ) 2(3xy 6x 2 ) (c) [x =] A + 4y 2 M f first step crect A + 4y = x 2 f square root seen (d) xy = 20 oe 3 M f xy = k oe B f [k =] 20 accept in a grid condone missing final bracket k accept 30 f M 4 4 (a) 54 alternate segment [theem] (b) 02 angles [in a] triangle [add to 80 ] triangle [adds to] 80 angle[s on a] straight line opposite and/ angles [in a] cyclic quadrilateral [add up to 80 ] may be on diagram may be on diagram 9

12 Question Answer Marks Part marks and guidance 5 (a) condone [.9 ] (b) 2336[.448 ] B f 53.5 M f their their 53.5 isw after crect answer seen their 53.5 can be in range 52 to 55 6 (a) (i) full crect argument e.g [=] use of appropriate symbol ( ) a statement that these two numbers are not the same 3 M f an appropriate method e.g , , oe cosine rule f angle B A f crect result to compare e.g. 5.6, 2.6, B = 94.7 A f a statement that the result does not equal the actual figure accept any crect method including a drawing tolerance ±2 mm, M f a triangle with one side crect A f all three sides crect A f measuring their angle accurately (±2º) stating clearly it is not 90 e.g. another equivalent method would be = f M A allow these results rounded (ii) 36.2 to M2 f (cos a) = ( ) M f.5 2 = cos (their a) Make sure that 36 does not come from a wrong method (b) 0.89 to 0.9[0] 2 M f 2 [ ] 8 [ ] 6 [ ] sin 27 oe 7 fully crect histogram 3 M f crect bar widths e.g , 50 60, 60 80, M f two crect heights three crect figures seen from 0.8,.5, 0.3, 0. must be fully crect method tolerance on graph is ± 2 small square condone freehand bars 0

13 Question Answer Marks Part marks and guidance 8 (a) (x =) 4 (y =) - with an algebraic solution 4 M f multiplying first equation crectly e.g. 5x 6y = 66, allow one err M f multiplying second equation crectly e.g. 4x + 6y = 0, allow one err M f adding subtracting the equations appropriately, allow one err mark best attempt if 0 sced SC f crect answers with little no suppting algebraic wk substitution: M f rearranging one equation to make x y the subject, allow one err M f substituting crectly into the other equation M f rearranging to get the value of x y, allow one err (b) (i) (x 3) 2 5 as final answer 3 B f (x 3) 2 B2FT f 5 a crect FT from their (x 3) 2 condone and FT (x p) 2 only If this is blank (NR) then you can award SC2 if (x 3) 2 5 [= 0] is seen in (b)(ii) (ii) 0.8, B, B crect FT their (i) accept 3 + 5, 3 5 f 2 marks if 0 sced SC f and rot to at least 2 dp

14 Question Answer Marks Part marks and guidance with crect calculations of two further years f both species 4 B3 f crectly calculating both species f two additional years e.g. 204 and 206 B2 f crectly calculating both species f one additional year e.g. 204 one species crect f two additional years B f crectly calculating one species f 204 another year igne extras like Spring in their answer the figures need only be rot to at least 2 sf e.g could be but do not FT their increct rounding condone the wrong labels f the years 2

15 Question Answer Marks Answer 20* The crect answers f the surface area of the Earth (4π = ) [and the water area ( )]. They show that land area is = 29.2% = roughly 30% so 30:70 = 3:7. They may use an equivalent method to achieve the same result. Clear annotation and explanation of reasoning. Crect spelling, punctuation and grammar. 5 The crect answers are obtained, but the wking is difficult to follow parts are missing, there is just one err in all the wking and their answer is consistent with their wking. They may obtain the crect answers, but fail to connect with the infmation given in the question. Clear annotation and explanation of reasoning. Crect spelling, punctuation and grammar. The crect answers f the surface area of the Earth (4π = ) and no further progress is made they find the sea area surface area from the land area. Reasoning is evident and there is crect spelling, punctuation and grammar. 4 3 The crect answers f the surface area of the Earth (4π = ) and the water area ( ) found, they make an attempt to find the proption of land but they do not reach 30%. Reasoning is coherent and clear but they are unable to show the ratio is crect. 2 An attempt is made to find the surface area of the Earth and 4πr 2 is seen used, but the crect answer is not found, f finding one third of the area of land. No progress is made although an attempt is seen. 0 3

16 APPENDIX Exemplar responses f Q6ci. Response Mark December was 39.7 and it was 34.2 in November December as 39.7 > 34.2 December because it has a higher mean December it has the greatest mean December as the mean is greater by 6.5 (BOD greater is enough) December because the mean is big 0 December if you sum the mean and range it is larger 0 December as it has a lower range 0 December as it has a higher mean and a higher range 0 December as it has a higher mean and a lower range (both comments are true but range is not relevant f average) 0 Exemplar responses f Q6cii. Response Mark November has a higher range 67.4 > 43.8 so November November the range is wider November the range is bigger and the mean is bigger 0 November the range is bigger and the mean is smaller 0 November the range is big (no comparison) 0 November the range is me spread out 0 4

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