GCSE (9–1) Mathematics J560/02: Paper 2 (Foundation tier) General Certificate of Secondary Education Mark Scheme for November 2020

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GCSE (9–1) Mathematics J560/02: Paper 2 (Foundation tier) General Certificate of Secondary Education Mark Scheme for November 2020 Oxford Cambridge and RSA Examinations F GCSE (9–1) Ma... thematics J560/02: Paper 2 (Foundation tier) General Certificate of Secondary Education Mark Scheme for November 2020Oxford Cambridge and RSA Examinations OCR (Oxford 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, Cambridge Nationals, Cambridge Technicals, 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 2020J560/02 Mark Scheme November 2020 2 1. Annotations available in RM Assessor. These must be used whenever appropriate during your marking. Annotation Meaning Correct Incorrect Benefit of doubt Follow through Ignore subsequent working (after correct answer obtained), provided method has been completed Method mark awarded 0 Method mark awarded 1 Method mark awarded 2 Accuracy mark awarded 1 Independent mark awarded 1 Independent mark awarded 2 Misread Special case Omission sign Blank page SeenJ560/02 Mark Scheme November 2020 3 For a response awarded zero (or full) marks a single appropriate annotation (cross, tick, M0 or ^) is sufficient, but not required. For responses that are not awarded either 0 or full marks, you must make it clear how you have arrived at the mark you have awarded and all responses must have enough annotation for a reviewer to decide if the mark awarded is correct without having to mark it independently. It is vital that you annotate standardisation scripts fully to show how the marks have been awarded. Subject-Specific Marking Instructions 2. M marks are for using a correct method and are not lost for purely numerical errors. A marks are for an accurate answer and depend on preceding M (method) marks. Therefore M0 A1 cannot be awarded. B marks are independent of M (method) marks and are for a correct final answer, a partially correct answer, or a correct intermediate stage. SC marks are for special cases that are worthy of some credit. 3. The following abbreviations are commonly found in GCSE Mathematics mark schemes. - figs 237, for example, 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. - isw means ignore subsequent working after correct answer obtained and applies as a default. - nfww means not from wrong working. - oe means or equivalent. - rot means rounded or truncated. - soi means seen or implied. - dep means that the marks are dependent on the marks indicated. You must check that the candidate has met all the criteria specified for the mark to be awarded. - with correct working means that full marks must not be awarded without some working. The required minimum amount of working will be defined in the guidance column and SC marks given for unsupported answers. 4. 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. 5. Unless the command word requires that working is shown and the working required is stated in the mark scheme, then if the correct answer is clearly given and is not from wrong working full marks should be awarded. Do not award the marks if the answer was obtained from an incorrect method, i.e. incorrect working is seen and the correct answer clearly follows from it.J560/02 Mark Scheme November 2020 4 6. Where follow through (FT) is indicated in the mark scheme, marks can be awarded where the candidate’s work follows correctly from a previous answer whether or not it was correct. For 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. Figures or expressions that are being followed through are sometimes encompassed by single quotation marks after the word their for clarity, e.g. FT 180 × (their ‘37’ + 16), or FT 300 – √(their ‘52 + 72’). Answers to part questions which are being followed through are indicated by e.g. FT 3 × their (a). 7. In questions with no final answer line, make no deductions for wrong work after an acceptable answer (i.e. isw) unless the mark scheme says otherwise, indicated by the instruction ‘mark final answer’. 8. In questions with a final answer line and incorrect answer given: (i) If the correct answer is seen in the body of working and the answer given on the answer line is a clear transcription error allow full marks unless the mark scheme says ‘mark final answer’. Place the annotation  next to the correct answer. (ii) If the correct answer is seen in the body of working but the answer line is blank, allow full marks. Place the annotation  next to the correct answer. (iii) If the correct answer is seen in the body of working but a completely different answer is seen on the answer line, then accuracy marks for the answer are lost. Method marks could still be awarded if there is no other method leading to the incorrect answer. Use the M0, M1, M2 annotations as appropriate and place the annotation  next to the wrong answer. 9. In questions with a final answer line: (i) If one answer is provided on the answer line, mark the method that leads to that answer. A correct step, value or statement that is not part of the method that leads to the given answer should be awarded M0 and/or B0. (ii) If more than one answer is provided on the answer line and there is a single method provided, award method marks only. (iii) If more than one answer is provided on the answer line and there is more than one method provided, award marks for the poorer response unless the candidate has clearly indicated which method is to be marked. 10. In questions with no final answer line: (i) If a single response is provided, mark as usual.J560/02 Mark Scheme November 2020 5 (ii) If more than one response is provided, award marks for the poorer response unless the candidate has clearly indicated which response is to be marked. 11. 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 B marks. Deduct 1 mark from any A or B marks earned and record this by using the MR annotation. M marks are not deducted for misreads. If a candidate corrects the misread in a later part, do not continue to follow through, but award A and B marks for the correct answer only. 12. Unless the question asks for an answer to a specific degree of accuracy, always mark at the greatest number of significant figures even if this is rounded or truncated on the answer line. For example, an answer in the mark scheme is 15.75, which is seen in the working. The candidate then rounds or truncates this to 15.8, 15 or 16 on the answer line. Allow full marks for the 15.75. 13. Ranges of answers given in the mark scheme are always inclusive. 14. 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. 15. If in any case the mark scheme operates with considerable unfairness consult your Team Leader.J560/02 Mark Scheme November 2020 6 Question Answer Marks Part marks and guidance 1 (a) (i) 5 1 1 (a) (ii) 10 1 1 (b) Two of 11, 13, 17, 19 2 B1 for one correct and one other or more than two of 11, 13, 17, 19 2 (a) (i) 3.5 1 Accept 3.50 or 3½ 2 (a) (ii) 1520 1 2 (b) 8.7 2 B1 for 3 [cm] or 57 [mm] Or M1 for answer of 87 [mm] 3 (a) (i) 6 1 3 (a) (ii) 8 1 3 (b) (i) [0].4 final answer oe 1 3 (b) (ii) 3.4 final answer oe 1 4 (a) 4 25 2 Mark final answer M1 for 16 100 or equivalent fraction 4 (b) 0.35 2 M1 for correct first step to convert to decimal e.g. 35 100 seen or attempt to divide 7 by 20 5 (a) (i) Equilateral 1 5 (a) (ii) Rhombus 1J560/02 Mark Scheme November 2020 7 Question Answer Marks Part marks and guidance 5 (b) (i) Draws both lines of symmetry correctly 1 Mark intention 5 (b) (ii) She is incorrect oe and gives rhombus or parallelogram as the other quadrilateral 2 M1 for correct description of RS of any other quadrilateral e.g square has order 4 For M1 ISW other comments that do not refer to symmetry See AG 5 (c) Arrows facing the same way added to AB and DC 1 Condone more than one arrow facing the same way on AB and DC 6 7 50 [am] oe 4 B2 for 2 [hours] or M1 for 100 ÷ 50 M1 for 10 10 [am] – their 2 h – 20mins B2 may be implied by 120 mins 7 (a) No and statement referencing 10 and 12 oe 1 Referencing 10 and 12 could be implied by eg United only scored 2 more oe United’s bar would be a height of 20 oe Do not accept ‘scale should go up in 2s’ See AG 7 (b) Start the vertical scale from 0 oe 1 Accept other values <8, or suggestion of inserting zig-zag on ‘goals’ axis line See AG 7 (c) All teams played the same number of games oe 1 United may have played less games 8 (a) 34 1J560/02 Mark Scheme November 2020 8 Question Answer Marks Part marks and guidance 8 (b) 64 [×] 1 4 16 is a square number oe 2 1dep B1 for each correct value Dep on 2 previous marks earned Allow B1 for 26 ÷ 4 or 4 seen as a denominator or 0.25 for 1 4 Accept 16 = 4 × 4 or 16 = 42 9 (a) 4 : 5 1 9 (b) 1 : 3 3 B1 for 0.6 [kg] or 1800 [g] seen M1 for correct partial simplification of the given ratio or their first ratio 10 (a) 5b4 1 Condone 5 x b4 10 (b) x12 1 11 (a) 30 2 M1 for 6 500 100 × oe Answer 530 implies M1 11 (b) 650 2 M1 for 500 + 5 × their (a) 12 70 3 M2 for 56 ÷ 0.8 oe or B1 for 0.8[0] oe seen or for 56 associated with 80% isw For B1 0.8 oe seen allow fraction but not just for 80%J560/02 Mark Scheme November 2020 9 Question Answer Marks Part marks and guidance 13 0.28 and 0.14 5 B4 for 0.14 identified as white or for 0.28 and 0.14 reversed or M1 for 1 – (0.34 + 0.24) A1 for 0.42 M1 for their 0.42 ÷ (1 + 2) A1 for 0.14 Allow equivalent fractions or percentages Condone lack of % sign for M marks A1 Implies previous M1 or may be implied by their y + their w = 0.42 14 (a) (i) x = 3 sketched correctly with 3 indicated on x-axis as x – intercept 2 M1 for a vertical line or a dotted vertical line passing through 3 Condone good freehand 14 (a) (ii) y = x2 + 1 sketched correctly with 1 indicated as y-intercept 2 M1 for correct shape or y-intercept at 1 but not y = 1 Condone good freehand 14 (b) It should not touch the axes oe It should also have a curve in the 3rd quadrant oe 1 1 Accept responses on the graph 15 (a) 2a + 3b final answer 2 B1 for 2a or 3b in answer If 0 scored, SC1 for correct answer seen then spoilt Eg 2a + 3b = 5ab 15 (b)(i) 4x + 12 final answer 1 15 (b)(ii) x2 + 3x – 10 2 Mark final answer B1 for 3 of x2, 5x, –2x, – 10 [+]3x counts as two terms For B1 could be in a gridJ560/02 Mark Scheme November 2020 10 Question Answer Marks Part marks and guidance 16 4x – 10 = 11 – 2x 4x + 2x = 11 + 10 x = 3.5 [Dimension of square =] 4 One perimeter/area calculation correctly evaluated Perimeter and area both shown to be 16 M1 M1 A1 B1 B1 A1 or better Correct or FT 4 × their x – 10 or 11 – 2 × their x FT 4 × their length of square or (their length)2 Alt method M1 for (4x – 10)(11 – 2x) = 2(4x – 10) + 2(11 – 2x) or better M1 for 2x² - 15x + 28 = 0 Dep on use of algebra Identifying 4 as the side of the square may be implied by later calculations B1FT Dep on previous B. Allow embedded solution Dep on all previous marks earned and that only x = 3.5 leads to perimeter = area 17 (a) Correctly completes table 7 6 7 1 17 (b) (i) 13 25 oe 2 B1FT for their correct numerator B1 for fraction with denominator 25 In (b)(i) and (ii), not ratio or words, isw eg 13 25 , likely but not 13 25 , unlikely isw cancelling/conversion to other forms FT numerator 12 + any evens in their (a) 17 (b) (ii) 14 25 oe 2 FT their correct numerator / 25 B1FT for their correct numerator but denominator incorrect FT numerator 13 + any multiples of 3 or 4 in their (a)J560/02 Mark Scheme November 2020 11 Question Answer Marks Part marks and guidance 18 5.6[0] with correct working 6 M2 for 1 2 10 3 5     + ×   oe or M1 for 1 10 3 × or 2 10 5 × A1 for 110 15 oe or M1 for 1 2 3 5 + oe A1 for 11 15 oe AND M1 dep for their improper fraction/decimal/mixed number rounded up to next integer M1 for their integer multiplied by 70 or 0.7 If 0 scored, SC1 for answer 5.60 or 5.6 “Correct working” requires full evidence of M1A1 AND M1 or convincing pictorial/alternate convincing approach For method accept equivalent decimals or percentages (to 2 sf) M2 could be split into 1 10 3 × + 2 10 5 × The method may be shown pictorially For A1 eg 7⅓, accept 4 + 3⅓ oe, 733[..]% A1 implies M2 The method may be shown pictorially Implies M1 Dep on their improper fraction ≠ integer Must show a more accurate value first, could be in two parts eg 4 + 3⅓ then 8 This may be earned by those with wrong working then doing eg 8 x 0.7. Must see a calculation implying an integer × 70 or 0.7, could be in several partsJ560/02 Mark Scheme November 2020 12 Question Answer Marks Part marks and guidance 19 6 with correct working 5 B2 for 40 (LCM) identified or M1 for multiples of 8 and 20 up to at least 40 AND B2 for indicates 40, 80, 120, 160, 200, 240 or B1 for [time =] 269 oe or 270 oe M1 for their time ÷ 40 oe If 0 scored, SC1 for answer 6 “Correct working” requires evidence of at least B2 AND B1 or alternate convincing approach Eg attempts to count in 40 May be seen as clock times eg 0808, 0816, 0824,… 8.20, 8.40, 9.00,… Condone 1 error in either list FT other values Accept also if starting from 0801 Implies previous B2 Accept as times [0800], 8.40, 9.20, 10.00, 10.40, 11.20, 12.00 Condone [0801], 8.41, 9.21, 10.01, 10.41, 11.21, 12.01 eg Accept 4 hours 30 mins For M1 accept 4 correct multiples of 40 listed Condone 1 error FT other values Accept as times as aboveJ560/02 Mark Scheme November 2020 13 Question Answer Marks Part marks and guidance 20 C (24, 9) D (10, 2) 5 B4 for three correct ordinates or B3 for two correct ordinates or B2 for one correct ordinate from 24, 10, 2 or for longer length of triangle = 7 soi or B1 for 9 as y-coordinate for C or for shorter length of triangle = 3 soi OR M1 for long = 17 – 4 – 2 × their short oe A1FT for C (4 + 2 × their short + 2 × their long, 9)) A1FT for D (4 + 2 × their short, 9 – their long) For part marks, check ordinates first (may be on diagram if answer line blank) .If B2 or fewer check alt method and mark to candidates’ advantage B4, B3, B2, B1 May be on diagram For M1 and A1FT, their short and their long needs to be clear in working or on diagram 21 [x =] –1 [y = ] 4 4 M1 for attempt to equate coefficients M1 for correct method to eliminate 1 variable A1 for 1 correct solution If A0, SC1 for a pair of values that satisfy one of the original equations ISW correct answers seen in working then reversed Condone 1 arithmetic error – a sign error is not an arithmetic error Condone 1 further arithmetic error Alt method M1 for rearrangement of one equation to make either x or y the subject M1 for correct substitution of their rearrangement into the other equationJ560/02 Mark Scheme November 2020 14 Question Answer Marks Part marks and guidance 22 For Monday, does not rain should be 1 – 0.55 oe For Tuesday, 0.25 is incorrectly placed on the does not rain branch oe A pair of branches is missing for Tuesday after does not rain on Monday oe 3 B1 for each After each correct statement isw eg 0.55 + 0.35 does not equal 1 Monday not rain should be 0.45 eg For Tuesday the probabilities are placed the wrong way around 0.25 should be on the rain branch eg There should be two more branches for Tuesday See AG 23 24 π 4 M2 for [r2 =] 360 8 120 × × π or better or M1 for 120 2 360 × πr [= 8] oe or better A1 for [r2 =] 24 π For method condone use of 3.1, 3.14, etc used for π M1 implied by πr 2 = 24 Implied by 7.6…J560/02 Mark Scheme November 2020 15 Exemplar responses Exemplar responses for Q5bii Response Mark A rhombus has symmetry of order 2. (No decision). 1 No, other polygons have rotation symmetry of 2 eg rhombus, kite. 1 Diagram of square drawn and 4 written by the side (BOD 1 as they haven’t contradicted that the 4 isn’t order of rotation) 1 No because if you take a square or a rhombus you can also have rotation symmetry of 2 (not a completely correct statement for both marks but M1 scored for ‘rhombus….symmetry of 2’) 1 No because other quadrilaterals have rotational symmetry 2 0 No because a square has rotational symmetry 2 0 Amaya is not correct because a rectangle is not the only quadrilateral that has rotational symmetry 2. A square also has it. 0 She isn’t correct because there are a few shapes with it 0 Yes because a square is a quadrilateral but has 4 lines of symmetry 0 Squares do not have a rotational symmetry of order 2. 0 Rhombus drawn in the space provided with the correct lines of symmetry 0 No because some irregular quadrilaterals have 4 – depends on the shape if it is irregular shape 0 This because most other quadrilaterals don’t have the same sides as the others, leaving no symmetry (correct description of a scalene quadrilateral but they need to specify the shape by name) 0J560/02 Mark Scheme November 2020 16 Exemplar responses for Q7a Response Mark No, City scored 10 goals and United scored 12 so therefore they only scored 2 more. 1 No, they only scored two more than them 1 No, they only scored 2 more goals than City not twice as many, that would be 20. 1 No, they only scored two more not two times more. 1 No, United scored 12 goals and half of 12 is 6. 1 No, twice the number city scored is 20 and united only scored 12 1 No because he hasn’t double city to give 20 and united is less than that 1 No, United have only scored two more goals than City. This is because the number have massive gaps between them. 1 BOD NO – twice as many means times 2. (This is not enough, if they also stated “not +2” then they would get the mark) 0 Yes, City is 10 goals of scores and united 12 goals of scores 0 Exemplar responses for Q7b Response Mark She should start the graph from zero so that she can show the point clearly 1 Start number of goals from 1 (Accept other values <8) 1 Put a zero in the corner instead of an 8 1 She could start from 1 and go up in 2’s to stop at 13 1 The numbers because she started it at 8 not 0. (BOD ‘The numbers to imply vertical scale) 1 Start from 0 not 9 0 She should go up in two’s instead 0 Make the spaces of ‘number of goals scored’ smaller so it isn’t misleading to read. 0 Go up a different sequence for the number of goals scored 0J560/02 Mark Scheme November 2020 17 Exemplar responses for Q22 Mark clear intention and condone slips in language provided intention is clear. e.g. accept tree for branches Response Mark 0.35 needs to be 0.45 1 She didn’t subtract the 0.55 probability that it rain from 1 to get the probability that it doesn’t rain (0.45 seen on the diagram and 0.35 crossed out) 1 The (0.35) they did not show it, how did they get that number, because it’s wrong (error identified) 1 Don’t add to 100 on Monday (condone lack of % sign) 1 BOD They do not add up to 1 (but if 0.55 and 0.35 shown then this would score) 0 A probability tree always adds up to 1 (but if ref to 0.55 and 0.35 then this would score) 0 0.55 + 0.35 = 90, meaning she’s not taking it from 1 (statement incorrect) 0 For Tuesday it should be 0.25 for rain and 0.75 for not rain (if stated as separate reasons this is just 1 mark) 1 She says probability that it rains on Tuesday is 0.75 but it is 0.25 1 She has said that the probability it doesn’t rain on Tuesday is 0.25. (points out the error) 1 On Tuesday the chance of rain is 0.25 (just restating the stem needs further explanation) 0 For Tuesday the probability it will rain is plotted wrong (not specific enough) 0 In the second tree diagram, she has the wrong number for rain (not specific enough) 0 She wrote the probability “0.25” that it rains on Tuesday in the wrong section on the diagram (not specific enough) 0 There would be another tree diagram ( with two more branches correctly drawn on the diagram ) 1 She only drew 2 trees, she should have shown the probability of it raining and not raining on each end of the tree 1 She has put Tuesday branch following on from Monday it rains and has not done the Monday it does not rain tree 1 There is no tree for Tuesday it does not rain (BOD with position indicated) 1 She needs a second tree diagram for it does not rain (or for Tuesday) 1 There is no second branch for Tuesday, (or there is not a Tuesday for it does not rain) 1 She’s not continued the does not rain section (BOD gives some indication of position) 1 There should be another branch (Needs to indicate where) 0 She doesn’t have all the branches that are needed 0 She hasn’t completed the whole tree diagram with all the outcomes 0OCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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