GCSE (9–1) Mathematics J560/03: Paper 3 (Foundation tier) General Certificate of Secondary Education Mark Scheme

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GCSE (9–1) Mathematics J560/03: Paper 3 (Foundation tier) General Certificate of Secondary Education Mark Scheme Oxford Cambridge and RSA Examinations F GCSE (9–1) Mathematics J560/03:... Paper 3 (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 DRAFTJ560/03 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 DRAFTJ560/03 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. DRAFTJ560/03 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. DRAFTJ560/03 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 consi DRAFT derable unfairness consult your Team Leader.J560/03 Mark Scheme November 2021 6 Question Answer Marks Part marks and guidance 1 (a) (i) 10 1 (ii) 7 1 (b) RomCom 1 (c) 20 2 M1 for 3 [+] 2 [+] 5 [+] 7[+] 3 seen May be on graph (d) 4 : 5 3 B1 for 25 or (45 – their 20) M1 for their 20 : their 25 OR M2 for 4 5 : 9 9 seen or M1 for 20 25 : 45 45 oe seen If 0 scored, SC1 for answer 5 : 4 Their Yr 10 from (c) Their 25 is any value from 12 to 44 May be on answer line For M1 ratio must be seen and not implied from a “simplified” version 20 : 25 implies B1 M1 25 : 20 implies B1 oe 0.444[...] : (0.555 to 0.556) 2 (a) 43 1 (b) 1024 1 DRAFTJ560/03 Mark Scheme November 2021 7 Question Answer Marks Part marks and guidance 3 49.50 with correct working 6 B5 for figs 495 as final answer with at least the M2 mark OR M1 for [10p =] 0.2 × 150 oe soi 30 M1 for [20p =] 0.3 × 150 oe soi 45 and M1 for (150 – their 30 – their 45) oe soi by 75 and M2 for (their 30 × 10) and (their 45 × 20) and (their 75 × 50) oe or M1 for one from (their 30 × 10) or (their 45 × 20) or (their 75 × 50) oe If 0 or 1 scored and no/insufficient working seen SC2 for figs 495 as final answer Ignore money notation Ignore money notation May be 150  2 May work in £ Implied by 300, 900, 3750 or £3, £9, £37.5[0] If M1 only and SC2 available award SC2 DRAFTonlyJ560/03 Mark Scheme November 2021 8 Question Answer Marks Part marks and guidance 4 (a) 90 360 oe fraction 1 Expect 1 4 but ignore attempts to cancel initially correct fraction but not convert to decimal or percentage Answer 0.25 after 1 4 seen scores 0 (b) Yes oe and [in 2020] they won more matches (or double the number of matches) than [in 2019] oe or The win fraction went up to ½ oe [from ¼ oe] The win fraction got bigger 1 See appendix Must be clear reference to win not “it” Do not allow comparing with unlike (e.g. W and L) only unless clearly indicating that W replaced L as majority” oe ½ or ¼ may be degrees Allow error in 2020 win fraction Must be an implied comparison 5 702 3 M2 for 600 × 1.17 oe or M1 for 600 × [0].17 oe soi by 102 May be 600 + their 102 from valid attempt at 17% May be Non-Calculator eg [10% =] 60, [5% =] 30, [1% =] 6, [2%] = 12 and sum of their 60, 30 and 12 Must have labels or correct processes 6 (a) 60, 120, 60, 120 1 Accept in any order or only on diagram Must be 120 and not 60|60 or 60+60 (b) 30, 120, 30 2 M1 for diagram with longer diagonal drawn only May be on original drawing If diagram redrawn then diagonal must join “other two” vertices 7 3 2 M1 for 6  2 oe 8 4t + 2u final answer 2 B1 for 4t or 2u seen DRAFTJ560/03 Mark Scheme November 2021 9 Question Answer Marks Part marks and guidance 9 (a) 3 B2 for one element misplaced or repeated or missing or B1 for one correct region Condone 1 and/or 2 repeated (b) [Venn diagram] 2 and [because] odd numbers cannot be multiples of 2 oe and no contradictions 2 B1 for choice of diagram 2 Must justify using properties of elements. Accept “Odd numbers cannot be even” and “All multiples of 2 are even” 10 162 4 B1 for [Area of face =] 9 B1 for [Total number of faces =] 18 M1 for their number of faces  their 9 Alternative B1 for [area of face=] 9 B1 for [total surface area of cube=] 54 M1 for their 54  4 – 6  their 9 oe Alternative B1 for [area of face=] 9 M1 for 24  their 9 soi 216 M1 for their 216 − 6  their 9 e.g. 4+4+3+3+2+2 or 5+4+4+5 May be in stages e.g. 59+49+ etc DRAFTAccept other alternative methodsJ560/03 Mark Scheme November 2021 10 Question Answer Marks Part marks and guidance 11 (a) a + 2b cao 1 Do not accept extras (b) 2y < x cao 1 Do not accept extras (c) 2x = 5 cao 1 Do not accept extras 12 2 2 P h w − = oe 2 M1 for 2 2 P h − oe or correct first step eg P – 2h = 2w or P w h 2 2 2 2 2 = + or for next correct step towards isolating w following first error Note 2 2 h P w − = − oe is correct May be P 2 = + w h e.g. Following 2w = P + 2h w = 2 + 2 P h 13 40 with correct working 5 B1 for 2800 [cm] or [0].6[0] [m] M1 for 28 6 figs figs soi 46.6 to 46.7 or 46 40 60 oe M1 for their 46.6… truncated soi 46 M1 for figs 28 – their 46 × figs 6 If 0 scored with no/ insufficient working SC2 for answer 40 or SC1 for answer 0.4 If both seen and one incorrect award B0 Correct working requires all part marks soi At least 4 repeated additions or repeated subtraction May have indication of continuing 46 implies M2 B1 2800 – 2760 implies M3 B1 May be (their 46.6... – 46)  60 DRAFTJ560/03 Mark Scheme November 2021 11 Question Answer Marks Part marks and guidance 14 (a) 5120 1 (b) Topozero, Tana, Mweru, Ladoga, Victoria or 986, 3200, 5120, 18 100, 68 900 oe in standard form 2 B1 for Topozero as smallest or Victoria as largest or all in correct reverse order 9.86  102, 3.20  103, 5.12  103, 1.81  104, 6.89  104 condoning superfluous zeros and slip in index (c) 1.5 × 104 nfww isw 4 B3 for 15000 oe or 1.49[0..] × 104 or B2 for 14900 oe or M1 for figs 181 – figs 32 If 0 scored SC1 for their value correctly rounded to 2 significant figures e.g. 15000 may be 15  103 Subtraction may be implied e.g. by figs 15 or figs 149 Their unrounded value must be seen 15 (a) 285 2 M1 for ( ) 760 2 3 3 + + soi 95 (b) 24 2 M1 for 2 36 3  oe Allow (0.66 or 0.7)  36 for M1 only DRAFTJ560/03 Mark Scheme November 2021 12 Question Answer Marks Part marks and guidance 16 (a) Triangle at (-8, 6), (-8, 2), (0, 6) 2 B1 for reflection in x = k or in y = 0 Mark intention, condone freehand (b) Enlargement 1 4 or 0.25 (0, -6) 3 B1 for each element Marks spoilt if extra transformations Condone omission of brackets Accept centre as a vector 0 6       − 17 (a) 0.14, 0.09, (0.19), 0.2[0], 0.13, 0.25 2 B1 for three or four correct relative frequencies in the correct place Accept fractions (b) (i) [Unbiased dice] would have each [rf =] 0.16-0.17 or [Unbiased dice] would have each [f =] 50 or comment about very unequal [relative] frequencies and implied comparison 1 Accept “about 0.16” Accept “about 50” Not enough to say one number was rolled the most. Must say 6 [and 4] or some numbers are much higher or 2 or 5 or some numbers are much lower (ii) need larger sample oe 1 18 (a) 3.39 and 3.44 only 2 B1 for one only or for two correct and one extra (b) (i) 10 cm [between 3.35 and 3.45] oe or [If to nearest cm it should be between] 3.395 and 3.405 1 Mention of 10 cm (range or difference) oe (ii) 3.405 1 DRAFTJ560/03 Mark Scheme November 2021 13 Question Answer Marks Part marks and guidance 19 (a) 4 with correct working 3 M1 for 210 – n where 40 ≤ n ≤ 50 soi by 160 to 170 M1 for (their number of characters)  40 Alternative M2 for two from [4 letters] 210  5 [5 letters] 210  6 [6 letters] 210  7 or M1 for one from [4 letters] 210  5 [5 letters] 210  6 [6 letters] 210  7 Alternative (trials): M2 for two from 3 × 40 + [40 to 50] 4 × 40 + [40 to 50] 5 × 40 + [40 to 50] or M1 for one from 3 × 40 + [40 to 50] or 4 × 40 + [40 to 50] or 5 × 40 + [40 to 50] OR M1 for 210  40 A1 for final answer of 5 If 0 scored and no/insufficient working SC1 for answer 4 Correct working requires at least M1 n represents an estimate of the number of spaces and/or punctuation, digits, symbols etc] Allow 40 × 5 = 200 for M1 Answer “4 to 5” or 5 with no working score 0 DRAFTJ560/03 Mark Scheme November 2021 14 Question Answer Marks Part marks and guidance (b) 72 [seconds] 40 72 60  their oe or 52 60 72  their oe OR 1.2 oe 40  their 1.2 oe or 52  their 1.2 AND 48 or 43.[3…] and short/shorter word length oe B1 M1 B1 M1 A1 oe may be 1 12 60 oe their 1.2 is not 1.12 Ignore non-contradictory statements but, “He may type faster” is incorrect and, if DRAFTincluded, scores A0J560/03 Mark Scheme November 2021 15 Question Answer Marks Part marks and guidance 20 60 with correct working 5 B3 for 12 as third side with correct working or M2 for 13 5 2 2 − oe or M1 for 132 = 52 + [DC2] OR M1 for BDC = sin 1 5 13 −       oe or CBD = cos 1 5 13 −       oe M1 for 13 cos their BDC or 13 sin their CBD AND M1 for 5  their DC (or AB) If 0 or 1 scored with no/insufficient working SC2 for answer 60 or If 0 scored with no/insufficient working SC1 for 12 as third side For full marks, correct working requires Pythagoras or trig leading to 12 For B3 “correct working” requires evidence of M2 or M1 or mention of 5:12:13 triangle 22.6... or 67.3 to 67.4 oe may be in ABD Their DC (or AB) not = 13. If M1 scored and SC2 available, award SC2 only May be on diagram DRAFTJ560/03 Mark Scheme November 2021 16 Question Answer Marks Part marks and guidance 21 (a) 2 cao 1 (b) (i) y = 2x + 3 1 Allow, “The first one” oe for y = 2x + 3 (ii) Comment: Rejecting 4 [as gradient] and/or indicating 2 > 1 2 1 See appendix (c) 2 × 45 – 1 soi 89 or (90 + 1)  2 soi 45.5 oe Below M1 DRAFT A1J560/03 Mark Scheme November 2021 17 Question Answer Marks Part marks and guidance 22 (a) x  x or 4(2x + 5) seen x2 = 8x + 20 or x2 = 4(2x + 5) Correctly rearranging to x2 – 8x – 20 = 0 without error M1 M1 A1 Dependent on first M1 and not from rearrangement of original equation Allow [area of] square = x2 or [area of] rectangle = 8x + 20 x2 and /or 8x + 20 may be written with correct shape(s) (b) −2 10 nfww 3 B2 for one correct solution nfww OR M2 for (x + 2)(x – 10) = 0 or M1 for (x + a)(x + b) where ab = −20 or a + b = −8 OR M2 for two correct trials using −4  x  0 and two correct trials using 8  x  12 or M1 for two correct trials using −4  x  0 or two correct trials using 8  x  12 If 0 scored SC1 for answers 2 and –10 e.g. one trial is when x = 2, 22 – 8  2 – 20 = –32 Accept as trial x = 2 and –32 x -4 16 32 -20 28 -3 9 24 -20 13 -2 4 16 -20 0 -1 1 8 -20 -11 0 0 0 -20 -20 8 64 -64 -20 -20 9 81 -72 -20 -11 10 100 -80 -20 0 11 121 -88 -20 13 12 144 -96 -20 28 (c) Length [of square] cannot be negative 1 Dependent on negative answer in (b) Do not accept x cannot be negative (d) (i) 100 1 FT (their positive root from (b) )2 If two positive roots seen in (b) accept either or both used in (i) and in (ii) BUT, if one answer right and one wrong in any part, 0 marks (d) (ii) 25 1 FT (their positive root from (b) )  2 + 5 DRAFTJ560/03 Mark Scheme November 2021 18 Question Answer Marks Part marks and guidance 23 5 : 6 nfww 4 B3 for 5kn : 6kn k > 0 or equivalent correct unsimplified ratio seen OR M1 for two ratios with a common number of mints implied by … : 10k and 10k : … seen, k > 0 with one correct ratio or 2.5n : 5 seen A1 for 5kn : 10k : 6kn Accept for all part marks n replaced by a consistent integer e.g. 2.5n : 3n or 5n : 6n or 10 : 12 etc May be seen as two separate ratios Eg 5n : 10 and 10 : 6n or 10 : 20 and 20 : 12 etc For M1 the examples just require the common 10 or the common 20 etc DRAFTOCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge DRAFT [Show More]

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