Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education. Published

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1 Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper 07 MARK SCHEME Maximum Mark: 80 Published 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 before 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 Report for Teachers. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the 07 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is a registered trademark. This document consists of 0 printed pages. UCLES 07 [Turn over

2 07 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M A B Method marks, awarded for a valid method applied to the problem. Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. Mark for a correct result or statement independent of Method marks. When a part of a question has two or more method steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation dep is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt cao dep FT isw nfww oe rot SC soi answers which round to correct answer only dependent follow through after error ignore subsequent working not from wrong working or equivalent rounded or truncated Special Case seen or implied UCLES 07 Page of 0

3 07 Using tan θ + = sec θ to obtain y = (tan θ + ) or ( ) x ( x ) + + = y + = sec θ use of correct identity y = (( x + ) + ) oe dy x 0e d x = + an attempt at integration in form ae x + bx 0 e x ( ) y = + x + c condone omission of c attempt to find c using x= 0, y = 9 dep x y = e + x + 7 9< 4k( k 4) 4k 6k 9 use of the discriminant with correct values ( 9)( + ) k k dep for solution of their quadratic to obtain critical values Critical values 9, 9 k <, k > 4 a = b = 8 π = cos 8 + c π substitution of x = and y = to find c c = 4 (i) ( x ) B for ( ) k 7x 0 UCLES 07 Page of 0

4 07 (ii) a ( ) x = 4 6 ( 7a 0) ( 7 6 0) = correct application of limits for ( 7 0) k x ( ) 7a 0 4= a = 7 a = or dep for evaluation of ( ) and correct order of operations to find a, including dealing with power. 6(i) Gradient = (=.) ln y = x + c ln.9 y = x + oe Alternative method.4 = p(0.) + q 0.9 = p(0.8) + q Correct method of solution to find p and q from two correct equations ln y = x +.9 6(ii) x y = e +.9 straight line form and correct substitutions to find c dep dealing with ln x y = e e.9 dep for dealing with the index y=8.z UCLES 07 Page 4 of 0

5 07 7(i) x + x B for each correct term in final line of response 7(ii) ( ) x + x + + x x for + + x x oe at least two correctly obtained products leading to terms in x Term in x : FT for correct evaluation of their 64 + ( their 48) + their = 7 8(i) attempt to differentiate a product dy = + dx ( x 4) ( x ) ( x ) A for ( ) ( ) ( + ) x 4 x for ( ) ( + ) x 8(ii) ( x ) (( x 0) ( x ) ) = + ( x ) ( 8x ) = When x =, y= 8 h dy 8 d x = use of ( x ) = ( x ) ( x ) ( ) k or ( ) 9 (where k is any number) ( k) dep for their ( 9 ) k or 4 k h y=h 9(a)(i) 70 9(a)(ii) 40 9(a)(iii) k 4! or 40 k 4! or correct equivalents with no extra terms added or subtracted 4 4! p or correct equivalents with no extra terms added or subtracted 9 UCLES 07 Page of 0

6 07 9(b)(i) 64 9(b)(ii) With twins: C 6 or 76 Without twins: C 8 or 87 B for C6 or 76 or C 8 or 87 for ( C6 and C 8 ) or (76 and 87) with no multiples and no extra terms Total: = from a correct method 0(a) matrix multiplication, must have at least correct elements 8 AB = a b a+ 4b a b = 8 a+ 4b = 4 formation and solution of simultaneous equations leading to a = 4, b = Alternate scheme AB = Correct plan ABB = B Correct inverse A = = a b 8 4 Correct order and method of multiplication with at least two correct elements leading to a = 4, b = 0(b)(i) 7 4 oe B for 7 for 4 0(b)(ii) Z = pre-multiplication with two elements correct 9 = oe A for four correct of, 9,, 8, 8 7 UCLES 07 Page 6 of 0

7 07 (i).48 (ii) 0 θ =.8 correct use of sector area θ = 0.46 (iii) π BOC = = (.8(4) ).8(4) or unsimplified BC = 0sin BOC or 0 sin BOC BC = π BOC or sin BC = (00 00cos BOC BC =7.7( ) M for a complete correct method to find BC using their angle BOC for a correct plan using 4.8, their BC and 0 their answer to (ii) Perimeter = ( 7.7() ) = 4.7 or 4.6 awrt 4.7 or awrt 4.6 UCLES 07 Page 7 of 0

8 07 (iv) Area = sin.8(4) B for for 0 sin.8(4) = 78 awrt 78 from correct working Alternative method ( ) 0.8 sin.8 Segment area = ( ) Area required = 00π 0.8(4) sin.8(4) ( ( )) for 0 (.8(4) sin.8(4 ) ( ) = 78 awrt 78 from correct working Alternative method Area of trapezium = (( + )( )) correct area of trapezium ABCD (allow unsimplified) ( ) 0.48 sin.48 + Area of segments = ( ) ( ( )) sin 0.46 correct area of both segments (allow unsimplified) = 78 awrt 78 from correct working UCLES 07 Page 8 of 0

9 07 (i) x + x = 0 or y + y 8= 0 attempt to get in terms of one variable ( x )( x + 4) = 0 or ( )( ) y+ 7 y 4 = 0 dep for solution of a three term quadratic leading to x= 4, y = 7 and x =, y = 4 A for each pair Midpoint M ( 7), =, 4 correctly obtained midpoint Gradient of PQ = may be implied Perp gradient = their gradient of PQ Perp bisector: y+ = x + 4 dep for equation of perp bisector using their perp gradient and their midpoint. (unsimplified) 7 y = ( 0) = 8 8 all correct so far and for verification using a correct equation or = x 7 x = UCLES 07 Page 9 of 0

10 07 (ii) Area = finding R, S and RS correct method for finding area dep = 64 or.9 or 6 64 Alternative method Area = 4 8 finding R, S, RM and MS correct method for finding area dep = 64 or.9 or 6 64 Alternative method Area = = 8 oe 4 = 64 or.9 or 6 64 finding R and S to obtain their 7 8 dep for correct method of evaluation UCLES 07 Page 0 of 0

Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Published

Cambridge International Examinations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper March 07 MARK SCHEME Maximum Mark: 80 Published This mark scheme