GCSE (9–1) Mathematics J560/04: Paper 4 (Higher tier) General Certificate of Secondary Education Mark Scheme for November 2020

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GCSE (9–1) Mathematics J560/04: Paper 4 (Higher tier) General Certificate of Secondary Education Mark Scheme for November 2020 Oxford Cambridge and RSA Examinations H GCSE (9–1) Mathem... atics J560/04: Paper 4 (Higher 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 2020J560/04 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 SeenJ560/04 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. 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.J560/04 Mark Scheme November 2020 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). 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. (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.J560/04 Mark Scheme November 2020 5 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.J560/04 Mark Scheme November 2020 6 Question Answer Marks Part marks and guidance 1 (a) (i) 6.5 × 103 1 In all parts condone trailing zeros (ii) 5.84 × 10-2 1 (b) 7.56 × 103 1 2 63 4 M1 for 80 + 65 + 95 or 240 seen as total M1 for their 240 × [0].6 or 144 M1 for their 144 – 43 – 38 If 0 scored SC1 for 0.6 × 95 or 57 condone 95 63 for 4 marks and mark the method leading to their answerJ560/04 Mark Scheme November 2020 7 Question Answer Marks Part marks and guidance 3 2 [h] 15 [m] 4 M3 for a fully correct method e.g. 35 270 405 5.2 ×× OR M2 for three correct steps from 35 270 405 5.2 ×× e.g. 3 270 405 5.2 ×× OR M1 for one correct step e.g. 5.2 270 , 150 270 , 3 270 , 2.5×3, 150×3, 35 , 270 405 or 5 405 if M0 or M1 scored allow SC1 for their final time as a decimal hour or their final time in minutes correctly converted to hours and minutes e.g. 2.3333[h] = 2[h] 20[min] M3 implied by 2.25, 2 [h] 25 [min] or 135 nfww note : (405 – 270 or 270 ÷ 2 )= 135 = 2[h] 15[min] scores M0 M2 could be implied by 180, 11.25, 675 or 3 nfww M1 could be implied by 108, 1.8, 90, 7.5, 450, 0.6, 1.5 or 81 allow alternative methodsJ560/04 Mark Scheme November 2020 8 Question Answer Marks Part marks and guidance 4 60 20 oe 5 B3 for x =7 OR B1 for x + 2x + x – 1 + 5x – 2 or better M1 for simplifying their linear equation to the form ax + b = c or better e.g. 9x – 3 = 60 M1 for x = (60 + 3) ÷ 9 AND M1 for 60 their20 If 0 scored SC1 for 60 x −13 Equivalent includes 13 , .333[..] and 33.3...% e.g. 9x – 3 their linear equation must include 60 FT their linear equation and show the steps to correctly solve it. third M1 FT their value of x so their 20 is their (3x − 1) evaluated with their value of x 5 (a) Accurate ruled angle B bisector with two pairs of correct arcs 2 B1 for accurate ruled angle B bisector Tolerance ± 2° e.g. one angle 49° to 53° and the line can be any length, must touch B and condone dotted line (b) Accurate ruled perpendicular bisector of BC with two pairs of correct arcs 2 B1 for accurate ruled perpendicular bisector of BC Tolerance ± 2° e.g. angle 88° to 92° and ± 2mm e.g. 27mm to 31 mm and line can be any length, must touch BC and condone dotted line (c) Correct region shaded 1 dep dep on at least B1 and B1 and both bisectors intersectingJ560/04 Mark Scheme November 2020 9 Question Answer Marks Part marks and guidance 6 482 4 M1 for 6×8×15 or 720 M1 for 3 their720 or 8.96… M1 for [6 ×] ( 3 their720 )2 M3 implied by 80.3[3...] or 481.99... M2 implied by 8.96.. i.e [6 ×] (their 8.96…)2 7 (a) Any correct reason e.g. two points identified e.g (−2,−6) and (2,4) or a triangle drawn on the graph and [gradient = ] e.g 22 64 −− −− (could be marked on graph) = 4 10 =( 52 or 2.5) oe 1 reason has to be fully correct condone triangle with base 1 and height 2.5 providing it is clear alternative 1: e.g. −6 = m(−2) + −1 leading to m = (−6 + 1) ÷ −2 = 52 − − =( 52 or 2.5) alternative 2 : −6 = m(−2) + c 4= m(2) + c subtract −10 = m(−4) 4 10 − − =( 52 or 2.5) oe (b) y = 2.5x – 1 2 B1 for y = 2.5x + c (c ≠ − 1) condone 52 for 2.5J560/04 Mark Scheme November 2020 10 Question Answer Marks Part marks and guidance 8 46.77 to 46.84 or 47 nfww or (using 9) 47.45 to 47.5 or 48 nfww 6 B2 for 9, 9.9, 9.975, 9.98 or 10 or M1 for [faulty = ] ]133[ 80 6 × oe AND M1 for [costs = ] 133 × (32 + 7) + their 10 × 25 oe or their 5187 + their 10 × 25 M1 for [income = ] 133 × 60 M1 for [percentage profit = ] 5437 7980 5437 their their − their [× 100] oe or )1 5437 7980 ( − their their [× 100] oe equivalents include 7.5% M1 implied by 5412, 5434.5, 5436.375, 5436.5 or 5437 M1 implied by 7980 numerator could be e.g. 2543 accept any correct method 9 (a) Point accurately plotted and line drawn 1 for the ‘4’ mark intent and 32 must lie between 30 and 35 and not on the lines, condone solid/dotty line (b) Correct comment e.g. it peaks in Q1 or the lowest is in Q3 1 Condone winter/spring for Q1 and summer/autumn for Q3 and in (b)(c)(d) mark best comment unless contradictory (c) Correct comment e.g. there is a slight rise in sales year on year 1 (d) The trend in her sales will continue [at a similar rate] oe 1 Accept any correct relevant comment referring to general trend or quarter 1 trend isw extra statementsJ560/04 Mark Scheme November 2020 11 10 142.2[0] with correct working 6 M1 for 362 or 1296 M1 for k ×π × 182 oe where k = ½, 1, 1½ or 3 AND M1 for their area × 30 M1 for their mass ÷ 1000 and ÷ 10 or counting up in 10 000s to their mass AND M1 for their 9 × 15.8 If 0, 1 or 2 scored instead award SC3 for answer of 142.2[0] with insufficient working If 0 or 1 scored instead award SC2 for 2822 to 2823.02 If 0 scored award SC1 for 1526 to 1527.02, 1017 to 1018.008, 508 to 509.004, 3051 to 3054.024, 162π, 324π, 486π rot to at least nearest integer Correct working requires M1 AND M1 AND M1 M2 implied by 2822 to 2823.02 or M1 implied by 1526 to 1527.02, 1017 to 1018.008, 508 to 509.004, 3051 to 3054.024, 162π, 324π, 486π rot to at least nearest integer their area cannot be 36 and M1 implied by 84660 to 84 690.6 or 84.66 to 84.7 their mass is attempt at (rectangle and circle(s)) × 30, M1 implied by 8.46 to 8.47 their 9 dep. on fourth M1 scored with a rounding up to next integerJ560/04 Mark Scheme November 2020 12 Question Answer Marks Part marks and guidance 11 (a) 4.715 4.725 2 B1 for each or both correct and reversed (b) 7 25 5 B4 for 7.41[0...] or 7.411 OR B1 for 425 used B1 for 57.35 or 57.349[9...] used If B0 then B1 for 425 and 57.35 seen AND M2 for 425 ÷ 57.35 or M1 for use of distance ÷ speed e.g 430 ÷ 57.3 If 4 or 5 not scored SC1 for correctly changing their part hour to minutes Condone use of 57.349[9...] for M2 and for M1 420 ≤ distance ≤ 440 and 56 ≤ speed ≤ 58 12 (a) Triangle at (−1,3) (−1,5) (−4,3) 2 B1 for either a correct translation 6 left or a correct translation 2 up See overlay and for accuracy mark intent (± 2 mm by eye), condone good freehand (b) Rotation [centre] (0, 0) 90° clockwise or −90° or 270° anti-clockwise 1 1 1 if 0 or 1 scored B1 for correct reflection in y = x on graph B1 for correct reflection in x-axis on graph mark to the candidate’s advantage, for centre accept origin and O 13 (a) Fully correct box plot 3 B1 for median at 31 B1 for highest at 38 and lowest at 15 B1 for UQ at 35 and LQ at 24 Use overlay and tolerance ±½ small square, condone freehand lines (b) 16 2 M1 for 21 or 37J560/04 Mark Scheme November 2020 13 Question Answer Marks Part marks and guidance (c) Accept “No” and any correct reasoning e.g. consistency is measured by [interquartile] range and Bev’s range is higher so less consistent 2 B1 for mention of [interquartile] range or spread or unclear acceptable statement See appendixJ560/04 Mark Scheme November 2020 14 Question Answer Marks Part marks and guidance 14 15.6[1..] with correct working 6 M2 for [sin B = ] 18 15× sin 72 oe or M1 for 18 sin 72 15 sin = B oe AND M1 for 180 – 72 – their 52.4 implied by 55.6 or 55.57… and M2 for [AB=] sin 72 18 × sin their ...57.55 oe or M1 for sin 72 18 sin ...57.55 [...] = their oe If 0 scored award SC2 for 15.6… with insufficient working Correct working requires evidence of at least M1 AND M1 M2 implied by 0.7925… or 52.4… Alternative cosine rule (AB = x) M3 for quadratic equation with coefficients evaluated M2 for x2 + (-2×15×cos72)x + (152 – 182) [=0] oe or M1 for 182 = x2 + 152 - 2×x×15cos72 AND M2 for correct use of quadratic formula or M1 for use of quadratic formula with at most two errorsJ560/04 Mark Scheme November 2020 15 Question Answer Marks Part marks and guidance 15 (a) Correct reason e.g. the factors give +2x or factors are (3x − 5)(x + 1) or the signs are the wrong way round (3x − 5)(x + 1) and −1 and 53 oe B1 B2 B1 for the correct factorisation or two correct solutions FT from their incorrect factorisation See appendix (b) Correct reason e.g. the −b term should be in the numerator or 22 2 324)8()8( × ××−−±−− 22 2 324)8()8( × ××−−±−− and 0.419 and 3.58 B1 B2 B1 for 22 2 324)8()8( × ××−−±−− or 0.419 and 3.58 or 0.4188..., 0.4189 or 0.419 and 3.58[1...] allow [+] 8 for −(−8) throughout this part see appendix 16 2 50 x y = final answer 3 M2 for 2 = 5k2 or better OR M1 for 2 kx y = oe or B1 for [k =] 50 Condone proportionality symbol for equals in M1J560/04 Mark Scheme November 2020 16 Question Answer Marks Part marks and guidance 17 x3 +2x2 – x − 2 final answer 3 M2 for the correct expansion and simplification of any two of the given brackets e.g. x2 – 1, x2 + 3x + 2 or x2 + x − 2 or M1 for expansion of any two of the given brackets with three correct terms the x term counts as two correct terms 18 (a) 3 6 − or −2 and 2 1− − their [= 12 ] oe 1 1 accept any correct method Only award full marks if no wrong working condone 3 − 6 for first mark (b) 12 12 xy += 7 oe 2 B1 for 12 += cxy or y mx += 7 12 or the equation of any line which goes through (−3, 6) where m ≠ 0 19 (a) 975 3 M2 for 30) 2 2540 ( + × oe or 3015 12 ×× + 25 × 30 or M1 for one relevant area e.g. 3015 12 ×× or 25 × 30 or 40 × 30 Alternative: 40 × 30 − 3015 12 ×× for M2 (b) (i) 9 2 M1 for 24 624 − − oe For M1 condone one error in the figures (ii) tangent drawn at x = 4 12 nfww and dep on tangent drawn 1 3 M1 for using two points on their line M1 for use of difference in x difference in y Tangent should not cross the curve and should touch at 4, condone slight daylight between tangent and curve accept range of 11 to 13 for answer which should be checked from their tangentJ560/04 Mark Scheme November 2020 17 Question Answer Marks Part marks and guidance 20 [x =] -5 [y =] -3 [x =] 3 [y =] 5 with some algebraic working 6 M1 for x2 + (x +2)2 = 34 M1 for expanding their square term e.g. x2 + 4x + 4 M1 for simplifying their quadratic expression e.g. 2x2 + 4x + 4 = 34 or better M1 for correctly factorising their quadratic expression ax2 + bx + c = 0 e.g. (x + 5)(x – 3) or (2x + 10)(x – 3) or use of quadratic formula with no more than two errors B1FT for either one correct point or two correct x values B1FT for the other correct point or two correct y values If insufficient working B2 for 4 correct answers or B1 for 2 correct answers e.g. x2 + 2x − 15 = 0 a, b, c ≠ 0 Alternative : M1 for (y – 2)2 + y2 = 34 or better M1 for y2 – 4y + 4 M1 for 2y2 – 4y + 4 = 34 or better M1 for (y – 5)(y + 3) or use of quadratic formula with no more than two errors Both B1s are strict FT from their method to solve their quadratic equation e.g. they must FT correctly from their factorisationJ560/04 Mark Scheme November 2020 18 APPENDIX Exemplar responses for Q9(b) Response Mark Number sold in the Q1 is the highest 1 Number sold in the Q3 is the lowest 1 Sales decreased after Q1 and increased after Q3 1 Goes down then goes up 0 Sales decreased during Q1 and increased during Q3 0 Sales increase in Q1 each year 0 Exemplar responses for Q9(c) Response Mark Slight rise year to year 1 As years went on more umbrellas are sold 1 More sold in 2019 than in recent/previous years 1 Exemplar responses for Q9(d) Response Mark The trend year to year will continue 1 The shop remains in business 1 BOD Q1 increases by the same amount each year 1 Graph will follow the same pattern 1 More are sold in the first quarter 0 It will rain more in 2020 0J560/04 Mark Scheme November 2020 19 Exemplar responses for Q13(c) Response Mark No + Ali is more consistent because his IQR is smaller 2 No + her data is more spread out 2 No + the median represents the average or middle value and not the range 2 No + median is just the middle mark 2 No+ the median does not measure consistency it is the range 2 No+ Kareem is wrong because Beth has the larger range 2 No + Beth is more consistent as her IQR/range is lower (1 for mention of IQR or range) 1 No + IQR shows consistency 1 Exemplar responses for Q15(a) Response Mark the factors give +2x 1 factors are (3x − 5)(x + 1) 1 the signs are the wrong way round 1 Factorised incorrectly 1 BOD 53 − should be positive 1 BOD x − 1 should be x + 1 1 the symbols are the wrong way round 1 BOD Exemplar responses for Q15(b) Response Mark the −b term should be in the numerator 1 dividing line [in fraction] is not long enough 1 BODOCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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