Edexcel gcse math s foundation paper 3 june 2023 + mark scheme

Mark Scheme (Results) Summer 2023 Pearson Edexcel GCSE In Mathematics (1MA1) Foundation (Calculator) Paper 3FEdexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at or . Alternatively, you can get in touch with us using the details on our contact us page at Pearson: helping people progress, everywhere Pearson aspires to be the world’s leading learning company. Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We’ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: Summer 2023 Question Paper Log Number P75151A Publications Code 1MA1_3F_2306_MS All the material in this publication is copyright © Pearson Education Ltd 2023General marking guidance These notes offer general guidance, but the specific notes for examiners appertaining to individual questions take precedence. 1 All candidates must receive the same treatment. Examiners must mark the last candidate in exactly the same way as they mark the first. Where some judgement is required, mark schemes will provide the principles by which marks will be awarded; exemplification/indicative content will not be exhaustive. When examiners are in doubt regarding the application of the mark scheme to a candidate’s response, the response should be sent to review. 2 All the marks on the mark scheme are designed to be awarded; mark schemes should be applied positively. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme. If there is a wrong answer (or no answer) indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. Questions where working is not required: In general, the correct answer should be given full marks. Questions that specifically require working: In general, candidates who do not show working on this type of question will get no marks – full details will be given in the mark scheme for each individual question. 3 Crossed out work This should be marked unless the candidate has replaced it with an alternative response. 4 Choice of method If there is a choice of methods shown, mark the method that leads to the answer given on the answer line. If no answer appears on the answer line, mark both methods then award the lower number of marks. 5 Incorrect method If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. Send the response to review for your Team Leader to check. 6 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working as you can check the answer, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.7 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question or its context. (eg an incorrectly cancelled fraction when the unsimplified fraction would gain full marks). It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect (eg. incorrect algebraic simplification). 8 Probability Probability answers must be given as a fraction, percentage or decimal. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer. 9 Linear equations Unless indicated otherwise in the mark scheme, full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously identified in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded (embedded answers). 10 Range of answers Unless otherwise stated, when an answer is given as a range (eg 3.5 – 4.2) then this is inclusive of the end points (eg 3.5, 4.2) and all numbers within the range 11 Number in brackets after a calculation Where there is a number in brackets after a calculation eg 2 × 6 (=12) then the mark can be awarded either for the correct method, implied by the calculation or for the correct answer to the calculation. 12 Use of inverted commas Some numbers in the mark scheme will appear inside inverted commas eg “12” × 50 ; the number in inverted commas cannot be any number – it must come from a correct method or process but the candidate may make an arithmetic error in their working. 13 Word in square brackets Where a word is used in square brackets eg [area] × 1.5 : the value used for [area] does not have to come from a correct method or process but is the value that the candidate believes is the area. If there are any constraints on the value that can be used, details will be given in the mark scheme. 14 Misread If a candidate misreads a number from the question. eg uses 252 instead of 255; method or process marks may be awarded provided the question has not been simplified. Examiners should send any instance of a suspected misread to review.Guidance on the use of abbreviations within this mark scheme M method mark awarded for a correct method or partial method P process mark awarded for a correct process as part of a problem solving question A accuracy mark (awarded after a correct method or process; if no method or process is seen then full marks for the question are implied but see individual mark schemes for more details) C communication mark awarded for a fully correct statement(s) with no contradiction or ambiguity B unconditional accuracy mark (no method needed) oe or equivalent cao correct answer only ft follow through (when appropriate as per mark scheme) sc special case dep dependent (on a previous mark) indep independent awrt answer which rounds to isw ignore subsequent workingPaper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 1 3107 B1 cao 2 30 B1 cao 3 4m B1 4 4 B1 cao 5 –5, –2, 3, 7, 9 B1 cao Accept in reverse order 6 (a) 14 B1 cao (b) 18 B1 cao 7 (a) evens C1 oe (b) certain C1 oe (c) 0.6 B1 oe Accept 60% or an equivalent fraction eg 6 10 8 (a) Square C1 for statement of shape Accept unambiguous misspellings. (b) Cuboid C1 for statement of solid Accept unambiguous misspellings. Accept square based prismPaper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 9 (a) 6 M1 for ordering the numbers or showing a complete method of (5+7) ÷ 2 A1 cao (b) 8 B1 cao (c) Bar chart B1 for correct person labels or a linear scale Accept key in place of labels Accept unambiguous abbreviations eg Frequency or Number, X,M,K,T M1 for correct bars showing information for at least 2 people Condone bars of varying widths Condone no gaps or inconsistent gaps A1 for a fully correct bar chart with linear scale of numbers on the vertical axis and a set of person labels on the horizontal axis 10 Yes (supported) P1 for starting a process of working with time eg for undertaking some time conversion eg 85 mins is 1 hr 25 mins, 1 hr 45 min is 105 mins or for recognition that 1 h = 60 min (eg 85 = 60 + 25) Time conversion may be implied by a correct addition over the hour eg 8.30 + 1h 45m = 10.15, 10.30 + 85 = 11.55 Can be shown at any stage. P1 for a correct addition of at least two times eg 15 + 85 =100 or a correct duration eg 8 30 + 1 h 45 m = 10 15 or a correct subtraction eg 12 (noon) – 15 = 11 45 A correct duration can be shown using their times for any of the stages. Subtraction of any of the time durations P1 for a complete process to justify the decision eg 8 30 + 1 hr 45 min + 85 + 15 (= 11 55) or 105 + 15 + 85 (=205 min) and 12 (noon) − 8 30 (= 210 min) Accept their figures for 1 hr 45 min, 85 etc as long as it is clear they are related. C1 Yes and accurate figures eg 11 55 or 205 and 210Paper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 11 13 P1 for beginning to process problem eg 72 – 7 (= 65) or writing 5x + 7 = 72 oe P1 for a complete process eg “65” ÷ 5 oe or writes 5x = 65 oe A1 cao 12 (a) Merit B1 cao (b) 24 M1 for beginning to work with proportion eg 105 ÷ 7 (= 15) or 7 ÷ 105 (= 0.07 or 0.06....) or 360 × 7 (= 2520) or 360 105 (= 3.4…) or works out a quantity for one sector eg 7 30 105  (= 2), 7 75 105 (= 5), 7 150 105  (= 10), M1 for a complete method eg 360 7 105  oe or “3.4…” × 7 or 360 ÷ “15” or 360 × “0.06..” or “2520” ÷ 105 or 7 + “2” + “5” + “10” A1 caoPaper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 13 (a)(i) 30 B1 cao (ii) 10 B1 cao (b) Drawn M1 for a line from (1330 , 35) to (1500 , 35) or a line to the x axis from a point on y = 35 to 1600 on the x axis A1 fully correct graph (c) 35 B1 for 35 or ft their graph ft must be 35 ÷ time duration for their line 14 1.3 M1 for working with boxes or bags eg 600 ÷ 120 (= 5) or 1000 ÷ 270 (= 3.7(037..)) 6 ÷ 120 (=0.05) or 10 ÷ 270 (= 0.037(037..)) Cost ÷ quantity For the M marks allow working in £ instead of p. M1 for working with bags and boxes where they are working to the same quantities of boxes and bags eg 600 ÷ 120 (= 5) and 1000 ÷ 270 (= 3.7(037..)) 6 ÷ 120 (=0.05) and 10 ÷ 270 (= 0.037(037..)) Other values are possible where they are using alternative quantities of boxes and bags, but these must be the same quantities of each. M1 for finding the difference eg “5” – “3.7(037..)” (= 1.29.. to 1.3) or “0.05” − “0.037(037..))” (= 0.0129.. to 0.013) Must have consistent units for this mark. A1 for answer in the range 1.29 to 1.3 If an answer is given in the range in working and then rounded incorrectly award full marks.Paper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 15 175 M1 for a complete method eg 35 × (4 + 1) oe A1 cao 16 Rotation of 90(º), centre (0,0) B2 Rotation of 90 about (0,0) or Rotation of 270, clockwise about centre (0,0) Accept “origin” or “O” for (0,0) (B1 Rotation and 90 or Rotation and 270, clockwise or Rotation about (0,0)) 17 Drawing B1 for drawing point R from T at a distance of 5.5 cm. Unless ambiguous point R can be indicated by a cross, dot, or interpreted as the end of a line B1 for drawing point R from T on a bearing of 65º drawn from T. 18 4 M1 for a correct first step eg shows 4 × 2x – 4 × 3 or 8x − 12 or 20 2 3 4 x − = M1 for isolating terms in x eg 2x = 5 + 3 A1 caoPaper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 19 2.5 P1 for 450 ÷ 6 (= 75) or statement 100   y = oe or 450 3000 (= 0.15) or 450 100 3000  (= 15) P1 for “75” ÷ 3000 (= 0.025) or (y =) 450 100 3000 6   oe or "0.15" 6 (= 0.025) or "15" 6 or 3000 "75" 3000 + (= 1.025) A1 cao 20 (a) m6 B1 cao (b) x13 B1 cao (c) 4p3 + 12p2 B2 for 4p3 + 12p2 (B1 for expanding the bracket to get p3 + 3p2 or 4p3 or 12p2 )Paper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 21 (a) 11533 P1 for working with 68%, eg 800 × 0.68 (= 544 people) oe or “16960” × 0.68 oe Percentage calculation could be done at any stage P1 for a correct process, other than that of finding a %, eg “544” × 2 (= 1088) or 10.6 × 2 (= 21.2) or 800 × 2 (= 1600) or “544” × 10.6 (= 5766.4) or 800 × 10.6 (= 8480) P1 for full process to find amount of coffee required eg “1088” × 10.6 or “544” × “21.2” or “5766.4” × 2 (= 11532.8) or for an answer of 11532 A1 for answer in the range 11532.5 to 11533 If a correct answer within the range is shown in working but incorrectly rounded award full marks. (b) Statement C1 for a correct statement Acceptable examples the amount will be more; he will need more coffee it is an underestimate my answer in part (a) means there would not be enough for everyone he will need 12211(.2); needs 678(.4) more Not acceptable examples amount will decrease, amount of coffee will change If figures are given as part of the answer they must be correct, but can allow ft.Paper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 22 Shown with reasons M1 for method to find ACD using parallel lines eg BCA = 125 and ACD = 180 – 125 (= 55) or BCF = 180 – 125 (= 55) = ACD or FCD = 125 and ACD = 180 – 125 (= 55) or CFG = 180 – 125 (= 55) = ACD Angles must be clearly labelled on the diagram or otherwise identified. Correct method can be implied from angles on the diagram if no ambiguity or contradiction. M1 for method to find ADC eg 180 – 110 (= 70) or for method to find CAD eg 180 – (“70” + “55”) (= 55) or 110 ‒ “55” (= 55) A1 for ACD = 55 and CAD = 55 C1 for one correct parallel lines reason linked to their method eg Corresponding angles are equal Allied angles / Co-interior angles add up to 180 Alternate angles are equal Underlined words need to be shown; reasons need to be linked to their method, which can be implied from correctly identified angles (stated or written on the diagram). C1 for one other reason stated linked to their method eg Angles on a straight line add up to 180 Angles in a triangle add up to 180 Vertically opposite angles are equal OR Vertically opposite angles are equal The exterior angle of a triangle is equal to the sum of the interior opposite angles. Angles in a quadrilateral add up to 360. Accept “4-sided shape” 23 17.5 P1 for a first step, eg 5 × 14 (= 70) or 14 ÷ 4 (= 3.5) or 5 ÷ 4 (= 1.25) or 4 ÷ 5 (= 0.8) Could be done algebraically. 11.2 as answer scores no marks. A1 oePaper: 1MA1/3F Question Answer Mark Mark scheme Additional guidance 24 (a) 63 B1 for 63, accept 3 × 3 × 7 or 32 × 7 (b) 15 876 M1 for at least two of 22, 34, 72 or shows at least 3 multiples of 2268, eg 2268, 4536, 6804 and at least 3 multiples of 441, eg 441, 882, 1323 (A =) 22× 34 × 7 scores 0 marks A1 for 15 876 or 22 × 34 × 72 oe 25 65 P1 for a correct process to find the number of seconds, eg ÷ 11.9 (= 5 647 529.4...) or for a correct process to convert between seconds and days, eg 24 × 60 × 60 (= 86 400) oe, may be seen in stages or 11.9 × 60 × 60 × 24 (= 1 028 160) Note that this mark may be awarded at any stage in the working. P1 for a complete process, eg “5 647 529.4...” ÷ “86 400” or ÷ “1 028 160” A1 accept answers in the range 65 to 65.4 or 66 If a correct answer within the range is shown in working but incorrectly rounded award full marks. 26 (a) (1, –3) B1 cao (b) −0.7 or 2.7 B1 for an answer in the range –0.8 to –0.6 or 2.6 to 2.8