Pearson Edexcel International Advanced Level In Pure Mathematics P2 (WMA12) Paper 01 Mark Scheme (Results)Summer 2022

Pearson Edexcel International Advanced LevelIn Pure Mathematics P2 (WMA12) Paper 01 Mark Scheme (Results)Summer 2022 Mark Scheme (Results) Summer 2022 Pearson Edexcel International Advanced Level In Pure Mathematics P2 (WMA12) Paper 01 Edexcel 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 2022 Question Paper Log Number P71377A Publications Code WMA12_01_2206_MS All the material in this publication is copyright © Pearson Education Ltd 2022 General Marking Guidance  All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.  Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.  Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie.  There is no ceiling on achievement. All marks on the mark scheme should be used appropriately.  All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate‟s response is not worthy of credit according to the mark scheme.  Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.  Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. PEARSON EDEXCEL IAL MATHEMATICS General Instructions for Marking 1. The total number of marks for the paper is 75. 2. The Edexcel Mathematics mark schemes use the following types of marks: „M‟ marks These are marks given for a correct method or an attempt at a correct method. In Mechanics they are usually awarded for the application of some mechanical principle to produce an equation. e.g. resolving in a particular direction, taking moments about a point, applying a suvat equation, applying the conservation of momentum principle etc. The following criteria are usually applied to the equation. To earn the M mark, the equation (i) should have the correct number of terms (ii) be dimensionally correct i.e. all the terms need to be dimensionally correct e.g. in a moments equation, every term must be a „force x distance‟ term or „mass x distance‟, if we allow them to cancel „g‟ s. For a resolution, all terms that need to be resolved (multiplied by sin or cos) must be resolved to earn the M mark. M marks are sometimes dependent (DM) on previous M marks having been earned. e.g. when two simultaneous equations have been set up by, for example, resolving in two directions and there is then an M mark for solving the equations to find a particular quantity – this M mark is often dependent on the two previous M marks having been earned. „A‟ marks These are dependent accuracy (or sometimes answer) marks and can only be awarded if the previous M mark has been earned. E.g. M0 A1 is impossible. „B‟ marks These are independent accuracy marks where there is no method (e.g. often given for a comment or for a graph) A few of the A and B marks may be f.t. – follow through – marks. 3. General Abbreviations These are some of the traditional marking abbreviations that will appear in the mark schemes.  bod – benefit of doubt  ft – follow through  the symbol will be used for correct ft  cao – correct answer only  cso - correct solution only. There must be no errors in this part of the question to obtain this mark  isw – ignore subsequent working  awrt – answers which round to  SC: special case  oe – or equivalent (and appropriate)  dep – dependent  indep – independent  dp decimal places  sf significant figures  � The answer is printed on the paper  The second mark is dependent on gaining the first mark 4. All A marks are „correct answer only‟ (cao.), unless shown, for example, as A1 ft to indicate that previous wrong working is to be followed through. After a misread however, the subsequent A marks affected are treated as A ft, but manifestly absurd answers should never be awarded A marks. 5. For misreading which does not alter the character of a question or materially simplify it, deduct two from any A or B marks gained, in that part of the question affected. 6. If a candidate makes more than one attempt at any question:  If all but one attempt is crossed out, mark the attempt which is NOT crossed out.  If either all attempts are crossed out or none are crossed out, mark all the attempts and score the highest single attempt. 7. Ignore wrong working or incorrect statements following a correct answer. 2 General Principles for Pure Mathematics Marking (But note that specific mark schemes may sometimes override these general principles) Method mark for solving 3 term quadratic: 1. Factorisation (x 2  bx  c)  (x  p)(x  q), where pq  c , leading to x = … (ax 2  bx  c)  (mx  p)(nx  q), where pq  c and mn  a , leading to x = … 2. Formula Attempt to use correct formula (with values for a, b and c). 3. Completing the square Solving x 2  bx  c  0 : (x  b ) 2  q  c, q  0, leading to x = … Method marks for differentiation and integration: 1. Differentiation Power of at least one term decreased by 1. ( x n  x n1 ) 2. Integration Power of at least one term increased by 1. ( x n  x n1 ) Use of a formula Where a method involves using a formula that has been learnt, the advice given in recent examiners‟ reports is that the formula should be quoted first. Normal marking procedure is as follows: Method mark for quoting a correct formula and attempting to use it, even if there are small mistakes in the substitution of values. Where the formula is not quoted, the method mark can be gained by implication from correct working with values, but may be lost if there is any mistake in the working. Exact answers Examiners‟ reports have emphasised that where, for example, an exact answer is asked for, or working with surds is clearly required, marks will normally be lost if the candidate resorts to using rounded decimals. Answers without working The rubric says that these may not gain full credit. Individual mark schemes will give details of what happens in particular cases. General policy is that if it could be done “in your head”, detailed working would not be required. Most candidates do show working, but there are occasional awkward cases and if the mark scheme does not cover this, please contact your team leader for advice. Question Scheme Marks 1 1024  B1 10C x  10C x 2  10C x 3  1 2 3 M1 3  3  2  3  3 10 2 9  x  45 2 8  x  120 2 7  x  8  8   8  Or two of 1920x 1620x 2  810x 3 A1 1920x 1620x 2  810x 3 A1 (4) (4 marks) Notes: B1: Correct constant term of 1024 as an integer. M1: Correct binomial coefficient multiplied by the correct powers of x for at least 2 terms in x, x 2 or x 3 . Allow e.g. 10C , 10C , 10C or 10 , 10 , 10 or evaluated coefficients and condone missing 1 2 3  1   2   3        3  3  2 3  3  3 brackets e.g. x 2 for  x  or x 3 for  x  8  8  8  8  May take out a common factor of 210 first, but again look for correct binomial coefficients multiplied by the correct powers of x for at least 2 terms in x, x 2 or x 3 .  3  10  3  10 E.g.  2  x   2 10 1 x   2 10 1 10C ...x  10C ...x 2  10C ...x 3  ...  8   16  1 2 3 A1: Allow for a fully correct unsimplified expression (ignoring the constant term) with evaluated binomial coefficients, must be expanded if a common factor of 210 istaken out first OR two of the three terms in x, x 2 and x 3 correct and simplified. 3  3  2  3  3 E.g. 10 2 9  x  45 2 8  x  120 2 7  x  8  8   8  3  3  2  3  3 Or 10 2 10  x  45 2 10  x  120 2 10  x  16 16  16  The brackets must be present unless they are implied by subsequent work. OR two of 1920x 1620x 2  810x 3 . Allow terms to be “listed”. A1: Final three terms fully correct and simplified. Allow terms to be “listed”. Once a correct expansion (or list of terms) is seen then isw. E.g. some candidates think they have to list the coefficients separately but apply isw. Ignore any extra terms if found. For reference incorrect bracketing: ... 45 2 8  3 x 2 1202 7  3 x 3 gives ... 4320x 2  5760x 3 8 8 And usually scores B1M1A0A0 if the 1024 is correct Special case: Some candidates are just finding the coefficients 1024 + 1920 + 1620 + 810 and this scores B1 only if the x’s never make an appearance