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

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GCSE (9–1) Mathematics J560/02: Paper 2 (Foundation tier) General Certificate of Secondary Education Mark Scheme Oxford Cambridge and RSA Examinations F GCSE (9–1) Mathematics J560/02... : Paper 2 (Foundation tier) General Certificate of Secondary Education Mark Scheme for DRAFT November 2021Oxford 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 2021 DRAFTJ560/02 Mark Scheme November 2021 2 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 Seen For a response awarded zero (or full) marks a single appropriate annotation (cross, tick, M0 or ^) is sufficient, but not required. DRAFTJ560/02 Mark Scheme November 2021 3 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 1. 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. 2. 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. 3. 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. 4. 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. 5. 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. DRAFTJ560/02 Mark Scheme November 2021 4 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). 6. 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’. 7. 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. 8. 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. 9. In questions with no final answer line: (i) If a single response is provided, mark as usual. (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. DRAFTJ560/02 Mark Scheme November 2021 5 10. 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. 11. 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. 12. Ranges of answers given in the mark scheme are always inclusive. 13. 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. 14. If in any case the mark scheme operates with considerable unfairness consult your Team Leader. DRAFTJ560/02 Mark Scheme November 2021 6 Question Answer Marks Part marks and guidance 1 (a) 5 1 1 (b) Cone 1 1 (c) Right-angled [triangle] 1 Accept scalene [triangle] or right angled scalene 2 (a) 3 1 2 (b) -8 1 3 (a) 3.02 1 3 (b) 9[.00..] 2 M1 for answer figs 9... 4 (a) > 1 4 (b) < 1 5 (a) 12 1 5 (b) (5 × 7 + 1) ÷ 9 = 4 1 6 (a) 4 5 2 B1 for 8 10 or for correct answer seen 6 (b) [0]. 8[00..] 1 7 (a) 1 4 3 1 7 (b) (i) 7 9 oe 2 M1 for 3 9 or 3� 9� [+] 4� 9� where k is a positive integer For 2 marks oe equivalent fractions For M1 may be seen as part of a single fraction eg 3+4 9 DRAFTJ560/02 Mark Scheme November 2021 7 Question Answer Marks Part marks and guidance 7 (b) (ii) 9 1 Do not accept 9 1 8 (a) 35 1 8 (b) 6 2 M1 for ÷ 7 and – 3 soi or for 63 ÷ 7 = 9 soi 9 72 with correct working 5 M3 for 500 – 4 × 60 – 44 oe or M2 for 500 – 4 × 60 oe or for 4 × 60 + 44 oe or M1 for 4 × 60 or for 500 – 44 or 5[.00] –[0].44 M1 for their 216 ÷ 3 If 0 scored SC2 for answer 72 or SC1 for 216 with no working “Correct working” requires evidence of at least M2 [216] [260] [284] [240] [456] or [4.56] 10 (a) 3 : 8 2 M1 for correct partial simplification of 75 : 200 Eg 15 : 40 but not eg 37.5 : 100 1 : 2 2 3 scores M1 10 (b) 150 2 M1 for 18 ÷ 12 × 100 oe DRAFTJ560/02 Mark Scheme November 2021 8 Question Answer Marks Part marks and guidance 10 (c) Answer of 54 with 60 stated from using 10 eggs also shown in working or Answer of 54 with 9 eggs and 225g of butter also shown in working 4 M3 for 225 ÷ 50 × 12 oe or B2 for 60 or 9 [eggs] and 225 or M1 for 225 ÷ 50 or 10 ÷ 2 soi For M3 allow a table with just one error 11 (a) A B R S A R B S R A B S R B A S B R A S B A R S 2 B1 for at least 3 additional correct arrangements For 2 marks no repeats or extras apart from A B R S 11 (b) 2 6 oe isw 2 FT their table M1 for correct numerator or denominator FT their table For 2 marks or M1 denominator < 11 Not ratio or words isw cancelling/conversion to other forms 12 40 nfww 4 B2 for length of rectangle = 10 or M1 for 4 ÷ 2 × 5 M1 for 5 × 4 + 2 × their length oe 13 (a) [No,] answer is not in index form oe 1 Accept it should be 22 × 5 but do not isw if with an incorrect statement 13 (b) -3 1 13 (c) 72 3 B1 for [√81 =] 9 B1 for [2³ oe =] 8 For 3 marks condone ±72 or -72 For B1 condone ±9 or -9 DRAFTJ560/02 Mark Scheme November 2021 9 Question Answer Marks Part marks and guidance 14 5000 [ml] or 0.45 [ L] soi 9 × 450 oe Correct attempt to find 80% or 20% of 5000 oe 4050 and 4000 or 950 and 1000 and [They are] correct oe B1 M1 M1 A2 or 9 450 [ 100] 5000   oe or 5000 9 450 [ 100] 5000 −   oe or 81% [and 80%] or 19% [and 20%] If A0 scored B1 for 4050 or 4000 or 950 or 1000 Correct conversion at any stage Alternate approaches are possible M1 may be implied by 4000 or 1000 or 81% or 19% seen For A2 accept in other correct consistent units for comparison eg 4.05[L] and 4[L] and must have no incorrect statement For B1 accept eg 4.05[L] or 4[L] 15 x < 3 3 M1 for 2x + 10 < 16 or x + 5 < 8 M1 for next correct productive step FT their first step For method marks condone incorrect inequality sign or ‘equals’ 16 (a) C 1 16 (b) D 1 17 (a) Rectangle 8 by 6 with one internal line 2 cm from longer edge 3 B1 for a rectangular base B1 for 8 by 6 or for any rectangle with one line drawn inside parallel to longer edge Accept in any orientation eg 8 by 6 scores B1B1 8 by 6 with wrong line scores B1B1 8 by 5 scores B1B0 8 by 5 with one line scores B1B1 DRAFTJ560/02 Mark Scheme November 2021 10 Question Answer Marks Part marks and guidance 17 (b) 6 × 3 × 8 ÷ 2 [=72] M2 M1 for 6 × 3 ÷ 2 oe or for their area or cross section × 8 May be done in stages 17 (c) 6 3 M2 for 72 2 oe or M1 for l × l × 2 = 72 oe or for 72 ÷ 2 18 (a) Four correct plots (70, 86) (44, 60) (37, 48) (38, 50) 2 B1 for 2 or 3 correct plots Overlay gives guidance, tolerance ±½ small square 18 (b) Positive 1 Ignore embellishments 18 (c) (i) Circles (30, 66) only 1 Accept any clear indication 18 (c) (ii) 120 3 M2 for 66 30  100 30 −  oe or for 66 100 30  [–100] oe or M1 for 66 30 oe or for 66 – 30 oe For M2 and M1 FT their (c)(i), point must be chosen for FT (table or graph) M2 implied by 1.2 or 220 M1 implied by 2.2 or 36 18 (d) No and line of best fit should not extend beyond data provided oe 1 eg only have data up to 70 marks, No one scored that high [so the trend may not continue] He would need to extrapolate beyond the line of best fit Do not accept eg the graph only goes up to 90 for the second test DRAFTJ560/02 Mark Scheme November 2021 11 Question Answer Marks Part marks and guidance 19 Shows actual increase is 21 [%] with correct working 5 M3 for [k ×] 1.1 × 1.1 oe A1 for answer 121[%] or for 1.21 OR M1 for 1.1 oe soi A1 for a correct evaluation of the first stage with their value If 0 scored SC2 for answer 21[%] or SC1 for 121% or 1.21 with no working “Correct working” requires evidence of at least M3 or alternate convincing approach Allow method marks if contained in correct method involving any invented starting price e.g. M3 for 100 × 1.1 × 1.1 oe e.g. for M1A1 uses 80 as value then gives 88 in working 20 10 nfww 4 M1 for 5 × 4 M1 for 200 or 199 used M1dep for their 200 ÷ their area, dep on first M1 nfww for 4 marks no errors in calculating values and at least one of 5, 4, 200 or 199 used Allow for 20 or for 4.9 × 4.1 [20.09] or with one unrounded value [19.6 or 20.5] Allow for 198.5 ÷ (4.9 × 4.1) DRAFTJ560/02 Mark Scheme November 2021 12 Question Answer Marks Part marks and guidance 21 (a) 6 and – 3 2 B1 for each 21 (b) Correct curve 3 B2FT for 6 or 7 correct plots B1FT for 4 or 5 correct plots Tolerance ±1 small square for plotting and curve through correct points. Condone slight feathering – must not be ruled If large blob for plot, check centre of blob 21 (c) -2.3 to -2.2 and 2.2 to 2.3 2FT Strict FT B1 for either FT their graph Tolerance ± ½ a small square Do not allow exact answers or answers with no graph Do not FT from a straight line graph If more than 2 intersections, B1 for each correct intersection on the answer line. If more than 2 answers, mark the worst. 22 (a) Correct reason 1 e.g. all could be children oe all could be adults oe too small a sample vary the time various age groups See Appendix 22 (b) Any three from: Larger sample size Vary the time of day/day Ensure equal numbers [of older and younger people are asked] Vary the location 3 B1 for each isw incorrect reasons See Appendix DRAFTJ560/02 Mark Scheme November 2021 13 Question Answer Marks Part marks and guidance 23 40 with correct working 6 M1 for x + 85 = 2x + 30 M1dep for ±x = k or kx = ± 55 (k ≠ 0) A1 for x = 55 or M1 for at least two trials of x + 85 or evaluated for x = 55 M1 for at least two trials of 2x + 30 or evaluated for x = 55 A1 both expressions evaluated as 140 when x = 55 AND M1 for their x + 85 or 2 × their x + 30 M1 for y = 180 – (their x + 85) oe If 0 scored SC2 for answer 40 with no working or insufficient working or SC1 for x = 55 with no or insufficient working “Correct working” requires evidence of at least M1 AND M1 ie we expect to see a minimum of an equation or trials leading to x = 55 and the substitution DRAFTOCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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