6663 Core Mathematics C1 January 2009 Advanced Subsidiary/Advanced Level in GCE Mathematics 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. •When examiners are in doubt regarding the application of the mark scheme to a candidate’s response, the team leader must be consulted. •Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. www.mymathscloud.com
6663 Core Mathematics C1 January 2009 Advanced Subsidiary/Advanced Level in GCE Mathematics January 2009 6663 Core Mathematics C1 Mark SchemeQuestion Number Scheme Marks Q1 (a) (b) 5 (5± is B0)()21their 5or 25their 1⎟⎠⎞⎜⎝⎛ = 125 or 0.04 (251± is A0)B1 (1) M1 A1 (2) Total = 3 (b) M1 follow through their value of 5. Must have reciprocal and square. 25− is not sufficient to score this mark, unless 251 follows this. A negative introduced at any stage can score the M1 but not the A1, e.g. 25151125232=⎟⎠⎞⎜⎝⎛−=− scores M1 A0 25151125232−=⎟⎠⎞⎜⎝⎛−=− scores M1 A0. Correct answer with no working scores both marks. Alternative: 321251 or ()3121251 M1 (reciprocal and the correct number squared) ⎟⎟⎠⎞⎜⎜⎝⎛=3156251251= A1 www.mymathscloud.com
6663 Core Mathematics C1 January 2009 Advanced Subsidiary/Advanced Level in GCE Mathematics Question Number Scheme Marks Q2()6464128364223Ixxxcxxxc=−++=−++M1 A1A1A1 Total = 4 M1 for an attempt to integrate 1+→nnxx (i.e. axaxaxor or46, where a is any non-zero constant). Also, this M mark can be scored for just the + c (seen at some stage), even if no other terms are correct. 1st A1 for 62x2nd A1 for 42x−3rd A1 for 3x + c (or kx+3, etc., any appropriate letter can be used as the constant) Allow cx+13, but notcx+131. Note that the A marks can be awarded at separate stages, e.g. xxx3261246+− scores 2nd A1 cxxx++−3261246 scores 3rd A1 xxx32246+− scores 1st A1 (even though the c has now been lost). Remember that all the A marks are dependent on the M mark. If applicable, isw (ignore subsequent working) after a correct answer is seen. Ignore wrong notation if the intention is clear, e.g. Answer xcxxxd32246++−∫. www.mymathscloud.com
6663 Core Mathematics C1 January 2009 Advanced Subsidiary/Advanced Level in GCE Mathematics Question Number Scheme Marks Q3227 27272+−−, or 7 − 4 or an exact equivalent such as 2249−= 3 M1 A1 Total = 2 M1 for an expanded expression. At worst, there can be one wrong term and one wrong sign, or two wrong signs. e .g. 272727−−+ is M1 (one wrong term 2−) 472727+++ is M1 (two wrong signs 72+ and 4+) 272727+++ is M1 (one wrong term 2+, one wrong sign72+) 472727+−+ is M1 (one wrong term 7 , one wrong sign 4+) 272727−−+ is M0 (two wrong terms 7 and 2−) 414147−−+ is M0 (two wrong terms 14 and 14−) If only 2 terms are given, they must be correct, i.e. (7 − 4) or an equivalent unsimplified version to score M1. The terms can be seen separately for the M1. Correct answer with no working scores both marks. www.mymathscloud.com
6663 Core Mathematics C1 January 2009 Advanced Subsidiary/Advanced Level in GCE Mathematics Question Number Scheme Marks Q4()()3323233f( )73xxxxc=−−+ = 33227 ()xxxc−− + f(4) = 22 22 64 16 28c⇒=−−+c = 2 M1 A1A1 M1 A1cso (5) Total = 51st M1 for an attempt to integrate (332 or xx seen). The x term is insufficient for this mark and similarly the + c is insufficient. 1st A1 for 3233233 or 3xx− (An unsimplified or simplified correct form) 2nd A1 for all three x terms correct and simplified... (the simplification may be seen later). The + c is not required for this mark. Allow 17x−, but not171x−. 2nd M1 for an attempt to use x = 4 andy = 22 in a changed function (even if differentiated) to form an equation in c. 3rd A1 for c = 2 with no earlier incorrect work (a final expression for f(x) is not required). www.mymathscloud.com
