GCSE (9–1) Mathematics J560/05: Paper 5 (Higher tier) General Certificate of Secondary Education Mark Scheme for November 2020

Document Content and Description Below

GCSE (9–1) Mathematics J560/05: Paper 5 (Higher tier) General Certificate of Secondary Education Mark Scheme for November 2020 Oxford Cambridge and RSA Examinations H GCSE (9–1) Mathemat... ics J560/05: Paper 5 (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 2020J560/05 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 SeenJ560/05 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.J560/05 Mark Scheme November 2020 4 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. 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.J560/05 Mark Scheme November 2020 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. 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.J560/05 Mark Scheme November 2020 6 Question Answer Marks Part marks and guidance 1 3 × 52 oe 2 B1 for only 3 and 5 or M1 for any correct factor pair of 75 Condone inclusion of 1 for B1 Not 1 and 75 2 (a) 2.5 oe 2 M1 for 4x = 13 – 3 or for x + 3 4 = 13 4 Accept 10 4 or 52 isw Embedded answer scores M1 max 2 (b) 12x + 7 final answer 3 M1 for 10x + 15 M1 for 2x – 8 3 (a) 5 2 B1 for 225 [ min] or for 0.75 and 3.75 oe seen 3 (b) 9 9 16 + [x k] or 16 9 16 + [x k] oe or better Correct method to convert their fraction to a percentage or a fraction with 100 as denominator or a decimal or correct method for 60% of 25 64[%] or 15 or a pair of other correctly calculated comparative values with a correct conclusion and no error seen M1 M1 A1 or [60% =] 0.6 oe or 0.6 × k oe eg 64 > 60 64%, so Reece is correct Where k is a chosen value implied by 64, 0.64, 64 100 , 15 and all imply previous M1 k is same value as used previously. Same k must be used in both parts to get this second mark accept 0.64 and 0.6[0], 64 100 and 60 100 or equivalent fractions with same denominator or with correctly evaluated values from using kJ560/05 Mark Scheme November 2020 7 Question Answer Marks Part marks and guidance 4 (a) Correctly completes table 7 6 7 1 4 (b) (i) 13 25 oe 2 B1FT for their correct numerator B1 for fraction with denominator 25 In (b)(i) and (ii), not ratio or words, eg 13 25 , likely but not 13 25 , unlikely isw cancelling/conversion to other forms FT numerator 12 + any evens in their (a) 4 (b) (ii) 14 25 oe 2 FT their correct numerator / 25 B1FT for their correct numerator but denominator incorrect FT numerator 13 + any multiples of 3 or 4 in their (a)J560/05 Mark Scheme November 2020 8 Question Answer Marks Part marks and guidance 5 5.6[0] with correct working 6 M2 for 1 2 10 3 5     + ×   oe or M1 for 1 10 3 × or 2 10 5 × A1 for 110 15 oe or M1 for 1 2 3 5 + oe A1 for 11 15 oe AND M1dep for their improper fraction/decimal/mixed number rounded up to next integer M1 for their integer multiplied by 70 or 0.7 If 0 scored, SC1 for answer 5.6[0] or 5.6 “Correct working” requires full evidence of M1A1 AND M1 or convincing pictoral/alternate convincing approach For method accept equivalent decimals or percentages (to 2 sf) M2 could be split into 1 10 3 × + 2 10 5 × The method may be shown pictorally For A1 eg 7⅓ , accept 4 + 3⅓ oe , 733[..]% A1 implies M2 The method may be shown pictorally Implies M1 Dep on their improper fraction ≠ integer Must show a more accurate value first, could be in two parts eg 4 + 3⅓ then 8 This may be earned by those with wrong working then doing eg 8 x 0.7. Must see a calculation implying an integer × 70 or 0.7, could be in several partsJ560/05 Mark Scheme November 2020 9 Question Answer Marks Part marks and guidance 6 6 with correct working 5 B2 for 40 [LCM] identified or M1 for multiples of 8 and 20 up to at least 40 AND B2 for indicates 40, 80, 120, 160, 200, 240 or B1 for [time =] 269 oe or 270 oe M1 for their time ÷ 40 oe If 0 scored, SC1 for answer 6 “Correct working” requires evidence of at least B2 AND B1 or alternate convincing approach eg attempts to count in 40 May be seen as clock times eg 0808, 0816, 0824,… 8.20, 8.40, 9.00,… condone 1 error in either list FT other values Accept also if starting from 0801 Implies previous B2 Accept as times [0800], 8.40, 9.20, 10.00, 10.40, 11.20, 12.00 Condone [0801], 8.41, 9.21, 10.01, 10.41, 11.21, 12.01 eg Accept 4 hours 30 mins For M1 accept 4 correct multiples of 40 listed condone 1 error FT other values Accept as times as aboveJ560/05 Mark Scheme November 2020 10 Question Answer Marks Part marks and guidance 7 C (24, 9) D (10, 2) 5 B4 for three correct ordinates or B3 for two correct ordinates or B2 for one correct ordinate from 24, 10, 2 or for longer length of triangle = 7 soi or B1 for 9 as y-coordinate for C or for shorter length of triangle = 3 soi OR M1 for long = 17 – 4 – 2 × their short oe A1FT for C ((4 + 2 × their short + 2 × their long) , 9) A1FT for D (4 + 2 × their short , 9 – their long) For part marks, check ordinates first (may be on diagram if answer line blank). If B2 or fewer check alt method and mark to candidates’ advantage B4, B3, B2, B1 May be on diagram For M1 and A1FT, their short and their long needs to be clear in working or on diagram 8 For Monday, does not rain should be 1 – 0.55 oe For Tuesday, 0.25 is incorrectly placed on the does not rain branch oe A pair of branches is missing for Tuesday after does not rain on Monday oe 3 B1 for each After each correct statement isw eg 0.55 + 0.35 does not equal 1 Monday not rain should be 0.45 eg For Tuesday the probabilities are placed the wrong way around 0.25 should be on the rain branch eg There should be two more branches for Tuesday See AGJ560/05 Mark Scheme November 2020 11 Question Answer Marks Part marks and guidance 9 Angle ABD = Angle CDB (alternate) BD is common oe AB = CD given oe SAS so triangles are congruent and Angle DAB = angle BCD M3 A1 M2 for 2 correct statements with reason[s] or 3 correct but no/incorrect reason[s] M1 for 1 correct statement with reason or 2 correct but no/incorrect reasons If 0 scored, SC1 for any attempt to prove congruency Not alternative angles Accept BD = BD, BD is shared Accept same length oe for ‘given’ eg attempt to list pairs of equal sides or equal angles (2 or more even if incorrect) 10 90 with correct working 5 M4 for 36 ÷ (0.8 × 0.5) oe or M3 for 0.4[t ] [= 36] oe or M2 for 0.8 × 0.5 [t ] [ = 36] oe OR M1 for 36 ÷ 0.8 oe or 36 ÷ 0.5 oe A1 for 45 or 72 M1 for their 45 ÷ 0.5 oe or their 72 ÷ 0.8 oe If 0 scored, SC1 for answer 90 with no working “Correct working” requires evidence of at least M3 or M1A1M1 or alternate convincing method where [Thurs =] t A1 implies previous M1 11 (a) 1 4 or 0.25 2 B1 for 4 in answer or answer 1 n (n is an integer > 1) or answer – 4 For B1 accept decimal equiv provided 1 n seen firstJ560/05 Mark Scheme November 2020 12 Question Answer Marks Part marks and guidance 11 (b) 3 2 final answer 2 B1 for 18 or [ 6 ] 3 2 = × Accept eg 3 × 2 as final answer for 2 marks 12 (a) She has reduced the price by 10% oe 18050 B1 B3 M2 for 20 000 × 0.952 oe or B1 for 1000 or 19000 seen e.g. She has decreased by 1000 each year She took 10%/ found 90% [of 20000] See AG 12 (b) (i) 20000 × 0.95n oe 2 M1 for 0.95 oe or for 20000 × kn (k ≠ 0) 12 (b) (ii) Second graph indicated 1 13 (a) Correct sketch with max at (90, 1) and min at (270, –1) and crossing x-axis at 0, 180 and 360 2 M1 for correct shape starting at (0, 0) but inaccurate at roots and max/min. Needs at least one cycle, but may have more than one. Mark intention 13 (b) 120 300 1 1 FT their 120 + 180 For FT both must be in range 0 to 360 14 (a) 5 12a 2 oe final answer 2 B1 for 52 ka oe or 12ak (k ≠ 0) For B1 accept 12a 14 (b) 8a15 final answer 3 B2 for 8a5 or 6 9 8a a − or ka15 (k ≠ 0) or B1 for ka5 or 6 9 ka a − or 8 seen (k ≠ 0)J560/05 Mark Scheme November 2020 13 Question Answer Marks Part marks and guidance 15 –7.5 or –7 1 2 or 15 2 − 3 M1 for x = 5(x + 6) M1 for x −5x = 30 oe FT their first step Condone 30 4 − as final answer Embedded answer scores M2 maximum 16 (a) Refers to overlapping intervals 1 eg 10 could go into 2 intervals The same number can go in 2 places Upper value in interval should be < Both inequalities are ≤ when only one should be 16 (b) (i) 5 × 6 and 2 × 20 2 M1 for 5 × 6 or 2 × 20 Could be written on graph Allow eg 2 × 10 + 2 × 10 for 2 × 20 Not just 30 + 40, must show products 16 (b) (ii) 50.25 with correct working 5 B1 for frequencies 10, 20, 30, 40 M1 for mid-interval values 35, 42.5, 47.5, 60 soi M1 for ∑ ft where t is in the interval including boundaries FT their frequencies M1 for ∑ ft ÷∑ f dep on previous M1 FT their frequencies If 0 scored, SC2 for answer 50.25 or SC1 for 5025 with no working “Correct working” requires evidence of at least B1M1M1 Condone 1 error, could be on graph, Condone 1 error 10 × 35 + 20 × 42.5 + 30 × 47.5 + 40 × 60 350 + 850 + 1425 + 2400 [ = 5025]J560/05 Mark Scheme November 2020 14 Question Answer Marks Part marks and guidance 17 5 B2 for y = 4 – 2x broken line or B1 y = 4 – 2x solid line AND B1FT for R correct side of y = 4 – 2x B1 for R correct side of y = − 2 B1 for R correct side of y = x See marks on diagram for next 3 marks Grid assumes y = 4 – 2x is correct FT dep on sloping line drawn 18 (a) 5000 4 M2 for 2.5 × 1 80 100 sin30 2 × × × oe or M1 for 1 80 100 sin 30 2 × × × oe B1 for sin 30 = 1 2 oe soi Area of triangle = 2000 implies M1B1 18 (b) Conditions for growing may have been different in 2019 oe 1 e.g. extremes in weather oe disease in the carrots oe 2019 may not have been an “average” year oe 2019 may not have harvested the same number as other years Assumes the same amount will grow [in 2019] 19 (a) (x – 5)2 – 3 final answer 3 B1 for (x – 5)2 B2 FT for – 3 or M1 for 22 – (– 5)2 oe M1 FT 22 – (their –5)2 oe R 2 1 2 1 2 1J560/05 Mark Scheme November 2020 15 Question Answer Marks Part marks and guidance 19 (b) Correct sketch with TP at (5, –3) in 4th quadrant and y – intercept at (0, 22) 4 FT their (a) for TP M1 for U shaped curve B2FTdep their (a)for TP at (5, –3) in correct quadrant or B1FTdep for turning point at (k, –3) or (5, k) soi FT for B2 or B1 dep on answer of form (x – a)2 – b in part (a), a, b ≠ 0 B1 for y – intercept at 22 indicated Be generous for the U shape condone broken line Values for y - intercept and TP must be shown but could be marked on axes. Mark intention Accept turning point = (5, –3)FT written in working provided no contradiction on sketch If point (5, –3)FT only plotted on graph in 4th quadrant and no sketch then B2 only 20 144 with correct working 7 B2 for [AD = ] 10, [AB = ] 24, [DC = ] 12 and [BC =] 10 or M1 for 56 ÷ (5 + 12 + 6 + 5) oe AND M2 for h2 + 62 = 102 or ref to 3, 4, 5 or 6, 8, 10 triangle or B1FT for deducing perpendicular from D to AB is 6 cm from A (or B) A1 for height = 8 AND M1 for 8 ( ) 12 24 2 + or better If 0 scored SC2 for answer 144 with no working or SC1 for height = 8 with no working “Correct working” requires evidence of at least B2 AND M2 AND M1 Could be written on diagram For M2 FT their BC and ½ (AB – DC) used condone h2 + 32 = 52 (using ratio values) FT ½ (their AB – their DC) FT their AB, CD and h provided h is not their AD or 5J560/05 Mark Scheme November 2020 16 APPENDIX Exemplar responses Q8 Mark clear intention and condone slips in language provided intention is clear. e.g. accept tree for branches Response Mark 0.35 needs to be 0.45 1 She didn’t subtract the 0.55 probability that it rains from 1 to get the probability that it doesn’t rain (0.45 seen on the diagram and 0.35 crossed out) 1 The (0.35) they did not show it, how did they get that number, because it’s wrong (error identified) 1 Don’t add to 100 on Monday (Condone lack of % sign) 1 BOD They do not add up to 1 (but if 0.55 and 0.35 shown then this would score) 0 A probability tree always adds up to 1 (but if ref to 0.55 and 0.35 then this would score) 0 0.55 + 0.35 = 90, meaning she’s not taking it from 1 (statement incorrect) 0 For Tuesday it should be 0.25 for rain and 0.75 for not rain (if stated as separate reasons this is just 1 mark) 1 She says probability that it rains on Tuesday is 0.75 but it is 0.25 1 She has said that the probability it doesn’t rain on Tuesday is 0.25. (points out the error) 1 On Tuesday the chance of rain is 0.25 (just restating the stem needs further explanation) 0 For Tuesday the probability it will rain is plotted wrong (not specific enough) 0 In the second tree diagram, she has the wrong number for rain (not specific enough) 0 She wrote the probability “0.25” that it rains on Tuesday in the wrong section on the diagram (not specific enough) 0 There would be another tree diagram ( with two more branches correctly drawn on the diagram ) 1 She only drew 2 trees, she should have shown the probability of it raining and not raining on each end of the tree 1 She has put Tuesday branch following on from Monday it rains and has not done the Monday it does not rain tree 1 There is no tree for Tuesday it does not rain (BOD with position indicated) 1 She needs a second tree diagram for it does not rain (or for Tuesday) 1 There is no second branch for Tuesday, (or there is not a Tuesday for it does not rain) 1 She’s not continued the does not rain section (BOD gives some indication of position) 1 There should be another branch (Needs to indicate where) 0 She doesn’t have all the branches that are needed 0 She hasn’t completed the whole tree diagram with all the outcomes 0J560/05 Mark Scheme November 2020 17 Exemplar responses Q12(a) Response Mark She kept decreasing by 5% of 20000 1 She took off the same amount of interest as the first year 1 She should not decrease by the same amount each year [ it should be different] 1 She did simple interest rather than compound interest 1 She is decreasing by the same amount each year 1 She did not do 5% of the second year, just 5% of the first year 1 She took £1000 off each year 1 She should have done 5% for each year 1 She did not decrease the result of the first price (she did by 1000) 0 She has just decreased it by 5% each year 0OCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

Last updated: 2 years ago

Preview 1 out of 19 pages