Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. Through a network of UK and overseas offices, Edexcel’s centres receive the support they need to help them deliver their education and training programmes to learners. For further information, please call our GCE line on 0844 576 0025, our GCSE team on 0844 576 0027, or visit our website at www.edexcel.com. If you have any subject specific questions about the content of this Mark Scheme that require the help of a subject specialist, you may find our Ask The Expert email service helpful. Ask The Expert can be accessed online at the following link: http://www.edexcel.com/Aboutus/contact-us/January 2011 Publications Code US026235 All the material in this publication is copyright © Edexcel Ltd 2011 www.mymathscloud.com
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: method marks are awarded for ‘knowing a method and attempting to apply it’, unless otherwise indicated. •A marks: Accuracy marks can only be awarded if the relevant method (M) marks have been earned. •B marks are unconditional accuracy marks (independent of M marks) •Marks should not be subdivided. 3.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 www.mymathscloud.com
GCE Core Mathematics C2 (6664) January 20111January 2011 Core Mathematics C2 6664 Mark Scheme Question Number Scheme Marks 1. (a) 43 2f( )2xxx xaxb=++ ++Attempting f(1) or f( 1).−M1 f(1)1127or47 3ababab=++ + + =+ + =⇒ + = (as required) AGA1 * cso (2) (b) Attempting f( 2)− or f(2).M1 {}f( 2) 16 8 8 28224abab−= −+− +=− ⇒− +=−A1 Solving both equations simultaneously to get as far as ...a= or ...b=dM1Any one of 9or6ab==−A1 Both 9and6ab==−A1 cso (5) [7] Notes(a) M1 for attempting either f(1) or f( 1).−A1 for applying f(1), setting the result equal to 7, and manipulating this correctly to give the result given on the paper as 3.ab+= Note that the answer is given in part (a).(b) M1: attempting either f( 2)− or f(2).A1: correct underlined equation in a and b; eg 168828ab−+− +=− or equivalent, eg 224.ab−+=−dM1: an attempt to eliminate one variable from 2 linear simultaneous equations in aand .bNote that this mark is dependent upon the award of the first method mark. A1: any one of 9or6ab==−. A1: both 9and6ab==− and a correct solution only. Alternative Method of Long Division:(a) M1 for long division by (1)x−to give a remainder in a and b which is independent of x. A1 for {}Remainder47ba=++= leading to the correct result of 3ab+= (answer given.) (b) M1 for long division by (2)x+to give a remainder in a and b which is independent of x. A1 for {}{}Remainder2(8)8224baab=− −=−⇒−+=−. Then dM1A1A1 are applied in the same way as before. www.mymathscloud.com
GCE Core Mathematics C2 (6664) January 20112Question Number Scheme Marks 2. (a) ()22 211872 8 7 cosC=+−××M1 22 28711cos287C+−=×× (or equivalent) A1 {}ˆˆ1.64228...awrt 1.64CC=⇒=A1 cso (3)(b) Use of Area 1sin(their)2ABCabC∆=, where ,ab are any of 7, 8 or 11. M1 ()178sin2C=× using the value of their C from part (a). A1 ft {}27.92848... or 27.93297...awrt 27.9== (from angle of either c1.64 or 94.1 )°A1 cso (3)[6]Notes(a) M1 is also scored for ()22 28711 2711cosC=+ −×× or ()22 278112 8 11cosC=+ −×× or 2227118cos2711C+−=×× or 2228117cos2811C+−=××1st A1: Rearranged correctly to make cos...C=and numerically correct (possibly unsimplified). Award A1 for any of 22 28711cos287C+−=×× or 8cos112C−= or 1cos14C=− or cosawrt0.071.C=−SC: Also allow 1st A1 for 112 cos8C=− or equivalent. Also note that the 1st A1 can be implied for ˆawrt 1.64C= or ˆawrt 94.1 .C°=Special Case: 1cos14C= or 22 21187cos287C−−=××scores a SC: M1A0A0.2nd A1: for awrt 1.64 caoNote that ()()cc0.6876... or 39.401... ,0.8116... or 46.503...AB°°==(b) M1: alternative methods must be fully correct to score the M1.For any (or both) of the M1 or the 1st A1; their C can either be in degrees or radians.Candidates who use 1cos14C= to give 1.499...C=, can achieve the correct answer of awrt 27.9 in part (b). These candidates will score M1A1A0cso, in part (b).Finding 1.499...C= in part (a) and achieving awrt 27.9 with no working scores M1A1A0. Otherwise with no working in part (b), awrt 27.9 scores M1A1A1. Special Case: If the candidate gives awrt 27.9 from any of the below then award M1A1A1. ()c17 11 sin(0.8116 or 46.503 )awrt 27.92°×=, ()c18 11 sin(0.6876... or 39.401... )awrt 27.9.2°×=Alternative: Hero’s Formula:1 3(1 3 1 1) (1 38) (1 37 )aw r t 2 7 . 9A=−−−=, where M1 is attempt to apply (11)( 8)( 7)Ass s s=−−−and the first A1 is for the correct application of the formula.www.mymathscloud.com
GCE Core Mathematics C2 (6664) January 20113Question Number Scheme Marks 3. (a) 4750 and6arar==− (could be implied from later working in either (a) or (b)). B1 36750r−=M1 15r=−Correct answer from no working, except for special case below gains all three marks.A1 (3)(b) (0.2) 750a−=M1 75037500.2a⎧⎫==−⎨⎬−⎩⎭A1 ft (2)(c) Applies 1ar− correctly using both their a and their 1.r< Eg. 375010.2−−−M1 So, 3125S∞=−A1 (2)[7]Notes(a) B1: for both 4750 and6arar==− (may be implied from later working in either (a) or (b)).M1: for eliminating aby either dividing 46by750arar=−= or dividing 4750 by6arar==−, to achieve an equation in 331orrr Note that 46750rr−=− is M0. Note also that any of 36750r−= or {}37501256r==−− or 316750r−= or {}317501256r==−− are fine for the award of M1.SC: 750 and6ararαβ==− leading to 6750rδ−= or {}7501256rδ==−−or 16750rδ−= or {}17501256rδ==−− where δβα=−and 2δ≥are fine for the award of M1.SC: 25750 and6arar==− leading to 15r=− scores B0M1A1.(b) M1 for inserting their r into either of their original correct equations of either 750ar=or {}750ar= or 46ar=− or {}46ar−= in botha and r. No slips allowed here for M1.A1 for either 3750a=− or a equal to the correct follow through result expressed either as an exact integer, or a fraction in the form cd where both c and d are integers, or correct to awrt 1 dp.(c) M1 for applying 1ar− correctly (only a slip in substituting r is allowed) using both their aand their 1.r< Eg. 375010.2−−−. A1 for 3125−In parts (a) or (b) or (c), the correct answer with no working scores full marks.www.mymathscloud.com
