4037 ADDITIONAL MATHEMATICS

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CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level www.xtremepapers.

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME f the October/November 013 series 4037 ADDITIONAL MATHEMATICS 4037/3 Paper, maximum raw mark 80 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners meeting befe marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Rept f Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes f the October/November 013 series f most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme Syllabus Paper GCE O LEVEL October/November Mark Scheme Notes Marks are of the following three types: M A B Method mark, awarded f a valid method applied to the problem. Method marks are not lost f numerical errs, algebraic slips errs in units. However, it is not usually sufficient f a candidate just to indicate an intention of using some method just to quote a fmula; the fmula idea must be applied to the specific problem in hand, e.g. by substituting the relevant quantities into the fmula. Crect application of a fmula without the fmula being quoted obviously earns the M mark and in some cases an M mark can be implied from a crect answer. Accuracy mark, awarded f a crect answer intermediate step crectly obtained. Accuracy marks cannot be given unless the associated method mark is earned ( implied). Accuracy mark f a crect result statement independent of method marks. When a part of a question has two me method steps, the M marks are generally independent unless the scheme specifically says otherwise; and similarly when there are several B marks allocated. The notation DM DB ( dep*) is used to indicate that a particular M B mark is dependent on an earlier M B (asterisked) mark in the scheme. When two me steps are run together by the candidate, the earlier marks are implied and full credit is given. The symbol implies that the A B mark indicated is allowed f wk crectly following on from previously increct results. Otherwise, A B marks are given f crect wk only. A and B marks are not given f ftuitously crect answers results obtained from increct wking. Note: B A means that the candidate can earn 0. B, 1, 0 means that the candidate can earn anything from 0 to.

3 Page 3 dy = 3x 1x 36 dx 1 [5] (a) (i) Calculates any case(s) crectly Partitions all cases crectly 140 Eliminate x y * Obtain kx + 8x + k 6 (= 0) Use b 4ac*0 D Obtain 4k + 4k + 64*0 oe Solve 3 term quadratic (k =, 8) k <, k > 8 A = 3, B =, C=4 (a) (i) (b) 10 π 3 Syllabus 4037 Paper 3 Allow if terms crect Or one codinate pair F two y values e.g = 60, = 80 [3] 5 5 B, 1, 0 Equate to 0 and solve 3 term quadratic x = and x = 6 y = 56 and y = Mark Scheme GCE O LEVEL October/November 013 (a) (i) (b) S T ' ( S ' T )' oe Others will be seen but only accept completely crect set notation

4 Page 4 Mark Scheme Syllabus Paper GCE O LEVEL October/November (c) 3x 18 x 14 x x 18 x + x + 14 x + 3x = 40 x = 4 [3] f any two of x, 3x, 18 x 14 x in crect place ( implied by crect equation) 6 (a) (i) Equate f( 3) to zero Equate f() to a 3b + 1 = 0 (9a 3b = 33) a + b + 1 = 65 (4a + b =8) Solve simultaneous equations a = 5, b = 4 [5] 1 1 a b Calculate f = Or use long division 0 [] 7 Eliminate x y Rearrange to quadratic in x y crectly x 10x + 16 (= 0) y + 8y 18 (= 0) oe Solve 3 term quadratic x =, x = 8 y = 8, y = 16 Or one crect codinate pair Crect method f at least one codinate of C C (4, 0) [8] e.g. x c = 3 1 [ () + 1 (8)], OC = OA AB oe

5 Page 5 Mark Scheme Syllabus Paper GCE O LEVEL October/November (a) (i) X (14, 1) m AX = 3 1 Use m 1 m = 1 f grad CD from grad AX CD is y 4 = 3(x 10) y = 3x + 34 on grad AX AX is y 6 = 3 1 (x + 4) 3y x = Solve eqn f CD with eqn f AX D (8, 10) [7] on grad AX Method f area 100 [] 9 (a) (i) 9 a = k cos t 1 cos t 7.84 [3] No other functions of t constants on k only Must be negative (if crect) say deceleration 7π t = awrt t 3 cos t, 7π Use limits of 0 and their 1 finds c ( 0) and substitutes their 7π 1 Upper limit must be positive 7π [5]

6 Page 6 Mark Scheme Syllabus Paper GCE O LEVEL October/November (a) (i) Radius is 4 h Use 3 1 πr h On water cone 1 h π πh h = 48 ag [3] dv πh = 16 Use dv = dv with h = 50, 0.18 d V = 0π [3] πh A= 16 da πh = 8 da da Use = with substitution of h = 50, their π.51 [3] 11 (a) (i) (i + 4j)t ( 1i + j) + (5i + 3j)t [] Subtract position vects 1 + 3t i + t j (( ) ( ) ) Or use t = to find position vects of A, B 4i + 8j, 11i + 8j Substitute t = and use Pythagas Crectly reach 5 [3] Subtract position vects and use Pythagas ( ) + ( t) = 5 t oe Set expression f distance apart to 5 t 17t + 30 (= 0) Solve 3 term quadratic Not essential to solve quadratic t = 15 (and ) e.g. t 1 + t = 17 and t 1 = 13 hours [5]

4037 ADDITIONAL MATHEMATICS

4037 ADDITIONAL MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the October/November 0 series 40 ADDITIONAL MATHEMATICS 40/ Paper, maimum raw mark 80 This mark scheme is published as an aid to