GCSE (9–1) Mathematics J560/01: Paper 1 (Foundation tier) General Certificate of Secondary Education Mark Scheme

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GCSE (9–1) Mathematics J560/01: Paper 1 (Foundation tier) General Certificate of Secondary Education Mark Scheme Oxford Cambridge and RSA Examinations F GCSE (9–1) Mathematics J560/01: ... Paper 1 (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 DRAFTJ560/01 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 DRAFTJ560/01 Mark Scheme November 2021 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 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. DRAFTJ560/01 Mark Scheme November 2021 4 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. 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. DRAFTJ560/01 Mark Scheme November 2021 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. 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. DRAFTJ560/01 Mark Scheme November 2021 6 Question Answer Marks Part marks and guidance 1 (a) 9.3 1 Allow 9.1 to 9.5 (b) (i) 57 1 Allow 55 to 59 (b) (ii) acute 1 2 (a) Any odd number 1 If more than one, all must be correct (b) Any square number 1 If more than one, all must be correct Do not accept k2 (c) 31 or 37 1 If more than one, both must be correct (d) Any multiple of 8 1 If more than one, all must be correct 3 (a) 2 correct lines 2 B1 each correct line Treat extra lines as choice Mark intention Accept dashed lines (b) 2 cao 1 4 (a) 8 2 B1 for only 1 and 9 identified (b) 5 2 M1 for (6 + 9 + 2 + 3 + 9 + 1) ÷ 6 Condone missing brackets for M1 5 (a) 560 cao 1 (b) 439 000 cao 1 DRAFTJ560/01 Mark Scheme November 2021 7 Question Answer Marks Part marks and guidance 6 0.502, 0.51, 0.529, 0.54 2 B1 for 3 in the correct order Condone trailing zeros 7 (a) 44 1 (b) 3.5 final answer 2 M1 for 6y = 28 – 7 or better Accept 3½, 7 2 or 21 6 for 2 marks 8 (a) ( 3, -4) 1 (b) H plotted at (-2, 4) 1 Must be labelled if more than 1 point plotted 9 17 2 B1 for 289 or 172 or M1 for √295 – 6 Accept -17 10 (a) 6c2d2 cao, final answer 2 B1 for 6c2 or d2 in final answer or correct answer seen and spoilt. B1 for e.g. 6c2×d2 (b) 7x(5 + x) final answer 2 B1 for 7(5x + x2) or x(35 + 7x) as final answer or correct answer seen and spoilt Accept 7x(5 + 1x) Condone final bracket missing 11 32.1 to 32.14 nfww 4 M1 for 3 × 6 may be implied by 18 AND M2 for 32� 2 soi by 14.1 to 14.15 or M1 for 32π soi by 28.2 to 28.3 18 must not come from wrong working Not part of longer multiplication e.g. 3 × 6 × 3 12 (a) Straight line oe Passes through origin oe 1 1 (b) 26 1 DRAFTJ560/01 Mark Scheme November 2021 8 Question Answer Marks Part marks and guidance (c) $195 < $221 or £150 < £170 With correct working 4 Allow exchange rates of 1.25 to 1.35 leading to $212.5[0] to $229.5[0] or £144 to £156 M2 for 195 ÷ 1.3 or 170 × 1.3 A1 for [£]150 or [$]221 or M1 for a correct exchange rate e.g 26 ÷ 20 OR M2 for building up to $ equivalent of £170 or £ equivalent of $195 e.g. 17 × 13 or 8.5 × 26 or 15 × 10 A1 for [£]150 or [$]221 or M1 for building up to £170 or $195 e.g. 17 × 10 or 8.5 × 20 or 15× 13 or 170 ÷ 10 = 17 OR M2 for 195 ÷ 13 and 170 ÷ 10 A1 for 15 and 17 or M1 for 195 ÷ 13 = 15 or 170 ÷ 10 = 17 If 0 scored SC1 for $195 < ($212.5[0] to $229.5[0] ) or (£144 to £156 )< £170 with no or insufficient working, but not wrong working Comparison in symbols or words required Allow FT their value from (b) Allow correctly rounded values used for M marks e.g for £7.69 or £8 for $10 used DRAFTJ560/01 Mark Scheme November 2021 9 Question Answer Marks Part marks and guidance (d) 26 or FT their (c) 1 dep Dep on A1 or SC1 awarded in part (c) Accept 25.99 13 0.12 0.48 4 B3 for 0.12 OR M2 for 1 – (0.1 + 0.1 + 0.2) soi by 0.6 in working or two values in the table which sum to 0.6 or M1 for 0.1 + 0.1 + 0.2 soi by 0.4 in working M1 for their 0.6 ÷ 5 Accept percentages or fractions 14 (a) (i) 36 1 Condone further terms if correct (a) (ii) added 7 1 Needs quantity and direction eg Add 7, plus 7, +7 Not n[th] +7 (b) 32−2 4 is not an integer 2 M1 for 32−2 4 or 30 and 34 Accept any full alternative methods or arguments e.g. 32 is a multiple of 4 and 4n+2 is not a multiple of 4. 15 E C B F 4 B1 for each Accept correct equations DRAFTJ560/01 Mark Scheme November 2021 10 Question Answer Marks Part marks and guidance 16 11 30 cao 4 B3 for answer of 440 1200 or better nfww or M1 for 1200 ÷ 4 soi by 300 M2 for 1200 – (�ℎ��� 300+ 460) 1200 or M1 for 1200 – (their 300 + 460) soi by 440 or �ℎ��� 300 + 460 1200 soi by 760 1200 17 24 2 M1 for 32×15 20 oe or 32 20 = � 15 oe or 15 20 = � 32 oe or scale factor of 1.6, 0.625, 0.75, 1.3̇ or DRAFT 1.33[3]J560/01 Mark Scheme November 2021 11 Question Answer Marks Part marks and guidance 18 16 4 oe nfww 4 M2 for 16 correct outcomes shown or for [4 × 4 =] 16 [outcomes] or M1 for table, list etc, with at least 10 correct outcomes to a maximum of 16 (ignoring repeats) AND M2FT for correctly indicating all the primes in their outcomes (at least 6) and gives the correct response for their outcomes or M1FT for writing their correct response from their outcomes or for indicating all the primes in their outcomes with maximum one error to a maximum of 3 marks if 0 scored then SC3 for a correct response from adding 16 outcomes i.e. 9 16 or SC2 for a correct response from adding (at least 6 outcomes), primes must be indicated or SC1 for correct response from adding (at least 6 outcomes), primes are not indicated Note : an alternative method is M3 for [P(1 with 2,3 OR 2,3 with 1)=] 1 4 × 2 4 + 2 4 × 1 4 or M2 for the above method with one error or M1 for a correct tree diagram drawn M marks are for products The outcomes may be a list or table showing 16 outcomes which may have numbers or ticks and crosses to show primes etc, if just numbers with nothing above 8 assume addition By e.g. shading, underlining or ringing M1 implied by a correct numerator and a correct denominator for their list Note that 2 4 × 2 4 is an incorrect method DRAFTJ560/01 Mark Scheme November 2021 12 Question Answer Marks Part marks and guidance 19 (a) 18 07 [pm] or 6 07 pm 4 B3 for 18 07 am or 6 07 [am] OR B2 for listing the next three correct times of both fountains, i.e. 15 43, 16 07, 16 31 and 16 01, 16 43, 17 25 OR B1 for listing the next three correct times of one fountain, i.e. 15 43, 16 07, 16 31 or 16 01, 16 43, 17 25. Alternative method B3 for 2[h] 48[m] OR B2 for [LCM=] 168 OR B1 for listing the next three multiples of 24 and 42, i.e. 48, 72, 96 and 84, 126, 168 OR M1 for [24 =] 2 × 2 × 2 × 3 or [42 =] 2 × 3 × 7 allow in a factor tree or table or [LCM=] 168k (k ≠ 1) and M1 for correctly converting their time(mins) to hours and mins Condone use of 12 hour clock e.g. [0]3 43 and 3 43 am for B1 and B2 their time must be over 60 DRAFTJ560/01 Mark Scheme November 2021 13 Question Answer Marks Part marks and guidance (b) [size] 15 [number] 11 4 B3 for 15 and 11 OR B2 for [HCF or group size =] 15 or M2 for [60] = 2× 2 × 3 × 5 and [105] = 3 × 5 × 7 or for listing complete factors of both numbers allow in a factor tree or table OR M1 for one of 2 × 2 × 3 × 5 or 3 × 5 × 7 allow in a factor tree or table or for common factors 3 or 5 AND B1 for [size] 3 [number] 55 or [size] 5 [number] 33 accept any correct method [60] 1,2,3,4,5,6,10,12,15,20,30,60 [105] 1,3,5,7,15,21,35,105 20 (a) (i) 0.2 and 0.8 in all the correct places 2 B1 for first branch correct or second branches correct Accept equivalent fractions and percentages (need % sign) (a) (ii) 0.64 or 16 25 oe or 64% 2 FT their tree for 1 or 2 marks (their values < 1) M1 for 0.8 × 0.8 oe Allow long method : e.g. 1 – (0.04 + 0.16 + 0.16) (a) (iii) Suggestion of dependence between the trains or unexpected events or data may not be applicable 1 Accept any correct reason, e.g. if first train is late second train may be held up e.g. unexpected delays can occur e.g. changed schedule that day (implies data not applicable) DRAFTJ560/01 Mark Scheme November 2021 14 Question Answer Marks Part marks and guidance (b) 0.73[4] or 734 1000 oe or 73.4% 3 M2 for 1 – 0.35 × 0.76 or 0.35 × 0.24 + 0.65 × 0.24 + 0.65 × 0.76 oe or M1 for two correct products or 0.35 × 0.76 e.g. common equivalent 367 500 products implied by 0.266, 0.084, 0.156, 0.494 21 1240 3 M2 for 1426 ÷ 1.15 oe or B1 for 1.15 or 115 Accept 115 100 but not 115% 22 [d =] 2.25 [c =] 1.7[0] with correct working 5 B4 for 1 correct answer with correct working OR M1 for 5d + 3c = 16.35 oe M1 for 2d + 6c = 14.7[0] oe M1 for method to find a common coefficient, allow 1 arithmetic error M1 for correct method to eliminate 1 variable, allow one arithmetic error OR If 0 or M1 scored instead award SC2 for both answers correct with no or insufficient working or SC1 for two answers which satisfy one of the original equations Accept other variables for d and c “Correct working” requires evidence of at least M1M1M1 Correct answers from trial and improvement score 5 If substitution method used M1 for correct rearrangement of equation M1 for correctly substituting into other equation A sign error is not an arithmetic error DRAFTJ560/01 Mark Scheme November 2021 15 Question Answer Marks Part marks and guidance 23 16 nfww 3 M2 for [h =] 8 ���60 or M1 for cos60 = 8 ℎ Accept alternative methods e.g M2 for [h =] 8 ��� 30 or M1 for sin 30 = 8 ℎ 24 319.44 cao 4 B3 for 9319.44 soi or for 319[.4…] as final answer OR M3 for (9000 × 1.0075) – 9000 OR M2 for 9000 × 1.0075 oe implied by 9319[.44…] or 9000 × r5 – 9000 oe OR M1 for 9000 × 1.007n oe implied by 9126[.44…] (n ≠ 5 and n ≥ 2) or 9000 × rn oe (n ≥ 2) Answers of 315 and 9315 are from simple interest and score 0 For M2 and M1 DRAFTwhere r = 1.7, 1.07 or 1.0007J560/01 Mark Scheme November 2021 16 25 3 [hours] 51 [minutes] with correct working 6 B5 for 3.85[...] or 3 [hours] 51.1[1…] [minutes] or 3 23 27 oe or 231 [minutes] with correct working OR M1 for 52 × 4 soi by 208 M2 for 15 ×60 ×60 1000 or better or M1 for 15 × 60 × 60 oe or 15 1000 oe M1 for their 208 ÷ their 15 ×60 ×60 1000 Alternative method B5 for 3.85[...] or 3 [hours] 51.1[1…] [minutes] or 3 23 27 or 231 [minutes] with correct working or M1 for 52 × 4 soi by 208 M2 for �ℎ��� 208 ×1000 15 or M1 for their 208 × 1000 or M1 for their 208 15 M1 for �ℎ��� 13866 to 13867 60×60 If 0 or M1 scored, instead award SC2 for 3 [hours] 51 [minutes] with no working or insufficient working or SC1 for 3.85[...] with no working or insufficient working “Correct working” requires evidence of at least M2 or M1M1 Accept other alternative methods. “Correct working” requires DRAFTevidence of at least M2 or M1M1OCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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