GCSE (9–1) Mathematics J560/05: Paper 5 (Higher tier) General Certificate of Secondary Education Mark Scheme

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GCSE (9–1) Mathematics J560/05: Paper 5 (Higher tier) General Certificate of Secondary Education Mark Scheme Oxford Cambridge and RSA Examinations H GCSE (9–1) Mathematics J560/05: Pape... r 5 (Higher 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 DRAFTJ560/05 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 DRAFTJ560/05 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. DRAFTJ560/05 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. DRAFTJ560/05 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. DRAFTJ560/05 Mark Scheme November 2021 6 Question Answer Marks Part marks and guidance 1 2 1 2 3 Mark final answer B2 for 175 70 oe or M1 for 25 7 seen 2 (a) No oe and he has not written the answer in index form oe 1 e.g. it should be 23 × 5 2 (b) –4 1 3 5000 [ml] or 0.45 [ L] soi 9 × 450 oe Correct attempt to find 80% or 20% of 5000oe 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%] After 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 e.g.4.05[L] and 4[L]and must have no incorrect statement For B1 accept e.g. 4.05[L] or 4[L] 4 (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 4 (b) Positive 1 Ignore embellishments DRAFTJ560/05 Mark Scheme November 2021 7 Question Answer Marks Part marks and guidance 4 (c) (i) Circles (30, 66) only 1 Accept any clear indication 4 (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 4 (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 e.g. the graph only goes DRAFTup to 90 for the second testJ560/05 Mark Scheme November 2021 8 Question Answer Marks Part marks and guidance 5 32 4 M2 for correct method to find area of L shaped face e.g 6 × 3 – 5 × 2 or M1 for finding one of the relevant partial lengths of 2 or 5 M1 for their area × 4 OR M1 for 3 × 4 × 1 M1 for 5 × 4 × 1 A1 for 12 or 20 OR M1 for 6 × 3 × 4 M1 for 2 × 5 × 4 A1 for 72 or 40 M1 could be on diagram Treat extra volumes as choice A1 Implies M1 Mark as oe for other correct products if split into two different cuboids that make the solid Not 6 × 3 × 4 × 1 × 1 Treat extra volumes as choice A1 implies M1 unless 72 comes from 6 × 3 × 4 × 1 × 1 6 (a) C 1 6 (b) D 1 7 (a) x < 4 3 Mark final answer M1 for 4x – 12 < x or x – 3 < x 4 M1 for correct step[s] to ax < b FT their first step For method marks, condone incorrect inequality sign or ‘equals’ sign e.g. Answer x = 4, x > 4 implies M1M1 DRAFTJ560/05 Mark Scheme November 2021 9 Question Answer Marks Part marks and guidance 7 (b) Correct representation of their (a) on number line 2 Strict FT their (a) dep on an inequality in (a) B1FT for their correct hollow or solid circle B1FT for their correct arrow direction If e.g. 3 on answer line and x < 3 in working then allow FT from x < 3 If answer 4 in (a) then allow x < 4 here Both B1’s must be with their value from part (a) If no arrow then their line must stretch to end of line 8 (a) - 3 1 8 (b) Correct graph 3 Curves must not be joined or touch either axis B2FT for 7 or 8 correct plots Or B1FT for 5 or 6 correct plots Mark in 50% zoom, use overlay, mark curve first For 3 marks, curve must pass through or touch circles on overlay Condone slight feathering, no ruled segments If curve incorrect, mark the plots use the overlay, plots must lie inside or touch circles. If large blob for plot, DRAFTcheck centre of blobJ560/05 Mark Scheme November 2021 10 Question Answer Marks Part marks and guidance 9 Shows actual increase is 21 [%] with correct working 5 M3 for [k ×] 1.1 × 1.1 oe A1 for 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 10 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) DRAFTJ560/05 Mark Scheme November 2021 11 Question Answer Marks Part marks and guidance 11 13 with correct working 7 M1 for sin30 10 BD = oe B1 for sin 30 = 0.5 soi A1 for [BD =] 5 M1 for their BD × 2.4 oe A1 for CD = 12 M1 for (their BD)2 + (their CD)2 [ = BC2] oe If 0 scored SC3 for answer 13 with no working or SC2 for CD = 12 with no working or SC1 for BD = 5 with no working “Correct working” requires evidence of at least M1 or B1 and M1M1 or alternate convincing approach Answer 12 gets A0 unless CD = 12 shown in working or on diagram SCs may be seen on the diagram 12 (a) 0.64 2 M1 for 7.64 – 7 or 7 to 7.64 12 (b) 45 2 M1 for 0.75 × 60 oe 12 (c) (i) Sam’s mouse/median is longer than the box plot’s median oe 1 With no incorrect statement Accept ‘middle’ for ‘median’ Accept 7.35 > 7.28 It is above the box plot median [7.28] 12 (c) (ii) Spread/range/IQR of Sam’s lengths is not known oe or sample is too small oe 1 With no incorrect statement Accept ‘He only measured the middle mouse’ oe Accept ‘Lengths of Sam’s other mice are not known’ oe Sam only has 5 mice which makes the data unreliable for comparison DRAFTJ560/05 Mark Scheme November 2021 12 Question Answer Marks Part marks and guidance 13 (a) 0.27 2 M1 for attempt to divide 3 by 11 For 2 marks accept 0.2727…. Implied by 0.27 to 0.28 13 (b) 22 45 final answer 3 B2 for 44 90 oe or M1 for 4.88[8…] or 48.8[8...] seen or for 4/10 + 8/90 If 0 scored, SC1 for answer 16 33 B2 for e.g. 4.4 9 For M1 accept any other decimal value[s] that would eliminate the recurrence when subtracted M1 implied by 44 and 90 (SC mark from 0.4848….) 14 400 2 M1 for 23 oe 15 5 5 final answer 3 M2 for 2 5 and 3 5 DRAFT or M1 for √4 × 5 or better or √9 × 5 or betterJ560/05 Mark Scheme November 2021 13 Question Answer Marks Part marks and guidance 16 15 27 oe with correct working 5 With x representing the number of smartphone and tablet: B3 for [smartphone and tablet =] 15 may be on a Venn diagram oe or M2 for [x = ] 40 + 27 + 8 – 60 oe or M1 for 40 – x + x + 27 – x + 8 = 60 oe or for Venn diagram with 40 – x, x and 27 – x correctly placed and M1 for fraction 27 n or 15 n that leads to the answer If 0 scored SC2 for 15 27 oe with no working isw cancelling/conversion to other forms For full marks “correct working” requires B3 ie [smartphone and tablet =] 15 with evidence of M1 or M2 or alternate convincing approach M1 FT their 15 provided < 27 For Venn diagrams, condone omission of universal set rectangle and 8 for M1, M2, B3 and full marks For M1 must be a proper fraction 17 2( 5) 2 x x − + or 2 10 2 x x − + final answer 5 M2 for 2(x – 5)(x + 5) or (2x – 10)(x + 5) or M1 for 2(x2 – 25) M2 for (x + 2)(x + 5) or M1 for x(x + 2) + 5(x + 2) or x(x + 5) + 2(x + 5) or for (x + a)(x + b) where a + b = 7 or ab = 10 For method marks condone omission of final bracket DRAFTJ560/05 Mark Scheme November 2021 14 Question Answer Marks Part marks and guidance 18 44 with correct working 5 B3 for angle BCD = 110 with correct working or M1 for angle BAD = 70 or for angle BDE = 180 – 70 or 110 M1 for angle BCD = 180 – their angle BAD AND M2 for their angle BCD ÷ 5 × 2 oe or M1 for their angle BCD ÷ 5 oe If 0 scored SC2 for answer 44 or SC1 for angle BCD = 110 For full marks “correct working” requires evidence of at least M1 AND M1 ie at least a correct angle and some ratio work Ignore geometric reasons if given For B3 “correct working” requires at least M1 or alternate convincing approach Angles may be indicated on diagram for part marks May be seen on diagram 19 x2 + y2 = 123 final answer 4 B2 for 123 or B1 for 98 or M1 for 52 + (7√2)2 oe B1 for x2 + y2 = k as final answer Accept ‘= k’ or numeric value where k > 0 DRAFTJ560/05 Mark Scheme November 2021 15 Question Answer Marks Part marks and guidance 20 z = 17 – 2x2 final answer 4 B3 for answer 17 – 2x2 OR M3 for 7 = 4 2 5 2   x −     + z oe or 2x2 + z = 17 oe or x2 – 2 7 5 4   − z   =   or better or M2 for y = 22 10x− 4 oe or 7 - = 4 z y oe or 4y = 2x2 – 10 or (2x2 – 4y) + (4y + z) = 10 + 7 oe or M1 for 2x2 – 4y = 10 or -2y = 5 – x2 or 4y = 7 – z or better Correct unsimplified formula in x and z M2 sets up for substitution with y explicit or for method for elimination by equating coefficients of y and correct method to eliminate y M1 equates coefficients of y or first DRAFTstep in rearrangement to eliminateJ560/05 Mark Scheme November 2021 16 Question Answer Marks Part marks and guidance 21 20 + 8  final answer with correct working 6 B3 for [angle at centre ]= 144 with correct working or 4 10 [of circle] oe or M2 for 2 [360 ]40 10    oe or M1 for 102 360    oe AND M2 for answer 20 + k  where k = �ℎ���� 18 or M1 for 2 10 360 their    oe or answer 20 + k  If 0 scored SC2 for answer 20 + 8  For full marks “correct working” requires evidence of at least M1 AND M1 ie use of formulas for sector area and arc length or alternate convincing approach For B3 “correct working” requires at least M1 for use of formula for sector area M2 method for finding fraction of circle M1 Implied by 8 π For M1 k ≠ 0 May be on diagram DRAFTJ560/05 Mark Scheme November 2021 17 Question Answer Marks Part marks and guidance 22 2n3 + 2n2 + 8n – 6 or 2(n3 + n2 + 4n – 3) 2(n3 + n2 + 4n – 3) M5 A1 M3 for 2n3 + n2 – 6n2 + 4n2 + 2n – 12n – 3n – 6 oe or better or condone one error in coefficients in simplified expression 2n3 + 2n2 + 8n – 6 or M2 for one correct expanded pair or M1 for 3 correct terms out of 4 in expanded pair (term in n counts as 2 terms) M1 for 3n2 + 21n Accept e.g. each term is divisible by 2 or (2n3 + 2n2 + 8n – 6) ÷ 2 = n3 + n2 + 4n – 3 Alt method Alt method for 6 marks Fully correct reasoning with even and odds for n and for each term when n is even and when n is odd (2n +1) (n – 3) (n + 2) and 3n(n + 7) e.g. if n is even , (2n + 1) is odd etc or M3 for fully correct reasoning with even and odds but only considering n is even or n is odd not both 2n3 – n2 –13n – 6 when simplified ie 2n2 + n – 6n – 3 or better or 2n2 + 4n + n + 2 or better or n2 + 2n – 3n – 6 or better Must include e.g. if n is even, 2n + 1 is odd, n – 3 is odd, n + 2, is even then odd × odd × even = even and 3n is even and n + 7 is odd, even × odd = even , then even + even = even and repeat when n = odd DRAFTOCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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