Mock paper mark schemes

Transcription

1 Mock paper mark schemes GCSE Edexcel GCSE in Mathematics Linear 40, Modular 44 Linear 0, Modular January 00

2 Edexcel, a Pearson company, is the UK's largest awarding body offering academic and vocational qualifications and testing to more than,000 schools, colleges, employers and other places of learning here and in over 00 countries worldwide. Our qualifications include GCSE, AS and A Level, GNVQ, NVQ and the BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas and Foundation Degrees. We deliver 9.4 million exam scripts each year, with over. million marked onscreen in 006. As part of Pearson, Edexcel has been able to invest in cutting-edge technology that has revolutionised the examinations system, this includes the ability to provide detailed performance data to teachers. Acknowledgements This document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel recognises and values all those who contributed their time and expertise to the development of GCSE specifications. References to third party material made in this specification are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.) Authorised by Roger Beard Prepared by Ali Melville Publications code UG09 All the material in this publication is copyright Edexcel Limited 00

3 Contents GCSE Mathematics 40 and 0 (Linear) mock papers Paper (Foundation) mark scheme Paper (Foundation) mark scheme GCSE Mathematics 40 (Linear) mock papers 7 Paper (Higher) mark scheme 9 Paper 4 (Higher) mark scheme 9 GCSE Mathematics 44 (Modular) mock papers 7 Unit 4 (Foundation) mark scheme 9 Unit 4 (Higher) mark scheme 4 GCSE Mathematics 0 (Linear) mock papers Paper (Higher) mark scheme Paper 4 (Higher) mark scheme 6 GCSE Mathematics (Modular) mock papers 7 Unit Stage mock papers 7 Unit Stage mark scheme 76 Unit Stage mock papers 77 Unit Stage (Foundation) mark scheme 79 Unit Stage (Higher) mark scheme Unit mock papers Unit (Foundation) mark scheme Unit (Higher) mark scheme 9 Notes on marking principles 99

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5 GCSE Mathematics mock papers 40 and 0 (Linear) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

7 GCSE Mathematics 40 and 0 Paper (Foundation) mark scheme Number Working Answer Mark Notes (a) 67 Five thousand three hundred and seven B cao B accept thousand hundred and seven (condone 0 tens) (c) (d) B cao B accept 600 or 6 hundred or 00 or hundred (a) B cao B cao (a) Dolphin llll Elephant llll 4 Lion lll Parrot ll Tiger llll l 6 Table M for attempt to tally or one frequency correct in either column A for frequency correct or all tallies correct in correct column A for all frequencies correct (accept if /0) Tiger B cao 4(a) (c) 9, 4, 7, 4, 7-6, -, -,, , 0.099, 0., 0.97, 0.99 B cao B cao B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

8 (a) (c) 4 B for (B for 7 or 9) B cao B cao 6(i) (ii) (iii) 0 B cao B cao B cao 7(a) Pattern B cao i ii (c) 4 4n + B cao B cao B for 4n+ (B for an expression in 4n ± p (p > 0)) M for 4 or 00 used A for 90 or 400 9(a) (c) 7.6 cm radius B for 7.6 cm ± 0. cm or 76 mm ± mm (B for appropriate unit cm or mm) B ± º B for line from centre to circumference 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

9 0(a) A and D B for both correct (B for correct) B and C B for both correct (B for correct) (a) (c) (d) 0 B for cross on or very near 0 (within cm) B for cross on or near (within cm) B for cross on or near ½ (within ± cm) B for cross on or near / (within ± cm) (a). Explanation B for. or ½ m B for changing 700 m to.7 km or. km to 00 m and explaining which is the larger or smaller appropriately. (a) (c) (d) Synthetic polymers B accept B cao B cao B for / B for /00 oe 4 7 B cao B cao B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

10 (a) x 4 t B cao B cao 6 i ii 7 7(a) (c) (d) x y g k + k + k 7 k B cao M for 7 A for 9 B cao B cao M for +7 oe A for M for k + M for k 7 A cao 0 9 B for 0 9 (B for fully correct method with two errors in either + or ) (B for a correct multiplication structure condone error in ) or UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

11 9 9 M A A 9 Or M A 9 Or M for attempt to find 0% and % of 0 A A Table B for all 6 correct (B for 4 correct) (B for correct) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

12 , B for 0 B ft for M for writing / as 6/0 or using common denominator A for 9/0 seen M for 9/0 A for /0 (a) Tessellation Enlargement B for fully correct with or more additional shapes, no gaps (B for 4 shapes tessellating with at least shape inverted, with or without existing shape, ignore extras) B for fully correct (B for length enlarged by scale factor ) 4 0 (0 ) M for 0 (0 ) A for (a) B B 4-6 or 9 0 or B ft on (a) M for attempt to write the fractions over a common denominator 4 A A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

13 7(a) B cao M for using 6 th item or circling in 0s row in diagram A for (4,, 0) B 4, B M for 0 A cao M 7 A cao x M sight of 6 A 46 Angles on straight line sum to 0 Corresponding angles Angles in a triangle sum to 0 B any correct relevant statements UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

14 0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

15 GCSE Mathematics 40 and 0 Paper (Foundation) mark scheme Number Working Answer Mark Notes (a) (c) (d) 4. Arrow Arrow B cao B cao B cao for 40 marked correctly B cao for. marked correctly i ii Cylinder Cuboid B ignore spelling as long as meaning is clear B ignore spelling as long as meaning is clear (a) Bars B cao B for both bar heights correct M for attempt to add,, 6 and 9 A for 4(a) i ii 60 0 Diagram B for 60 ± B for 0 ± B for both correct B for correct (a) i ii i ii (, 4) (4, 0) Points B cao B cao B for P marked correctly B for Q marked correctly UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

16 6 i ii iii g fh p³ B accept g, g B for 4fh accept fh4 or 4hf or hf4 B for p³ 7(a) (c) Line Point Circle B for cm line drawn B for R marked 4 cm from P ± mm B for circle drawn within mm tolerance M for 4.0 or for M for A for / B cao B cao B cao B ft 0(a)i ii 0. 0% B cao B cao B for squares shaded (a) (c) London and Reading 9 B cao B cao M for of 9, 7, 97 M for adding their distances A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

17 (a) (. +.6). M for adding. and.6 twice A cao M for multiplying lengths A cao cm miles litres B B B 4(a) (c) Shape Shade Shade B for correct reflection B for correct square shaded B for correct square shaded (a) (c) Explanation B cao B cao B for is odd, all the pattern members are even oe 6(a) 0 4 B cao M for or 4 4 A for 4 cao 7(a) M for 00.4 A cao M for 4..4 A for 7.0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

18 (i) (ii) (iii) 9(a) (c) B cao B oe B cao 0(a) x + x r+s 4 B for r + s (B for r or s) M for x A for 4 Triangle Triangle M for a reflection in x or y axis A for correct triangle with coords (, ), (, 4), (, ) M for a rotation of 90º clockwise or anticlockwise A for correct triangle with coords (, ), (4, ), (, ) 6 M for A for 6 kg of apples costs. kg of lemons costs.76 (.).9 96p B for. M for.76. A cao 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

19 4 4.% of M for 4.% of 000 M A cao (a) ( x + y ) + ( x 4 y ) x y 6 M ( x + y ) + ( x 4 y ) A cao 6 6x 4 0 M 6 6x 4 A 0 ft on (a) 6 x x + 7x + A cao M for correct expansion A cao 7 0² + 4² ( 4) + ( 0) 94 4 M for 0² + 4² or M for 676 A for 6 seen A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

20 Number Working Answer. Mark Notes (a) π 0 6. M π 0 A '6.' M A '6.' or 0 m 6. cm 9(a) M A cao 0% of M 0% of 60 A 0 o 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

21 GCSE Mathematics mock papers 40 (Linear) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

22 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

23 GCSE Mathematics 40 Paper (Higher) mark scheme Number Working Answer Mark Notes (a) B or or 40 B 4-6 B ft on (a) M A A 9 Or M A 9 Or M for attempt to find 0% and % of 0 A A 9 x B for any correct (x,y) y B any other correct (x,y) B correct line UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

24 4 x M sight of 6 A 46 Angles on straight line sum to 0 Explanation B any correct relevant statements Corresponding angles Angles in a triangle sum to 0 Square Trapezium (4 + ) ( 4) M for 4 4 or 6 (4 + ) M for ( 4 ) or 4 M (dep on at least previous M) A for 64 Or Rectangle 4 4 Triangle 4 6 Or M 4 or 4 M 4 or 6 M (dep on at least previous M) A for 64 0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

25 Key 4 represents.4 cm Diagram B fully correct including key (B error or omission in table or key) (B errors or omissions in table or key) (B unordered, no errors otherwise, with key) (B unordered or more errors, with key or unordered, no errors, with key) 7 Males 60% of Females 40% of Males like tennis 0% of Females like tennis 40% of (a) q + q + 4 q + 0 q 0 4 B for 900 B for M for attempt to find 70 or 40 B cao + 9 q + 0 M for sight of or 4 out of 4 terms correct A cao 6 k 9 mk + 4 km 6 m 6 k mk 6 m M for sight of out of 4 terms correct including signs or 4 out of 4 terms correct ignoring signs A cao 9 x + x + x x. B x + ( x + ) M correct process to isolate x or x A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

26 0 i M for 4 6 A cao ii (a) M for A oe M 7 A cao ' 440' M ' 4' A ft M for attempt to write the fractions over a common denominator 4 A A cao M Σ fx use of x consistently in each interval (may include endpoints) M (dep) use of midpoints M (dep on st M) A cao Σ Σ fx f UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

27 4 (a) M for 6 0 A cao (a) (c) ' 40' 6 + 0, M ' 40' 6 A ft B on the first branch B, M A cao M M A cao respectively on each pair of the second branches + (d) M 7 A oe UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

28 6 (a) B cao B for B cao or (a) i ii 7 o Angle sum of a triangle is 0 Angle in a semicircle is a right angle 7 o Reasons B for R 90 o B for 7 o B for both i 0 7 o B ft on 7 ii Opposite angles of a cyclic quadrilateral sum to 0 o Reason B Opposite angles of a cyclic quadrilateral sum to 0 o i ii ( x + 4)( x +, 4 ) B ( x + 4)( x + ) (B ( x + a )( x + b ), where ab 4 ) B both ft on (i) 9 (a) B cao (0,) B cao (c) x + 0 (., 0) M for x + 0 oe A cao 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

29 0 (a) π 0 + π 0 0 π M for π 0 or π 0 M for π 0 + π 0 A cao (a) SF length 64 New radius 0 y + ax b ax b y x b a y x, x, x + x ( x ) + x ( x + ) + ( x )( x + 4 x 4 x + 4 x + x + 4 x x x 4 x ) x ± 0 b a y B for 64 or B for 0 M isolate b M x ± ax correctly B B cao x 4 4 B for, + 4 x a x x seen M for at least one term of y x ( x ) + x ( x + ) + ( x )( x + M for all terms A cao ) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

30 (a) i B cao ii iii 9 B cao B cao 4 4 M A 4 oe A 4 or 4(a) i ii (0, 0) (90, ) B cao B cao See below B y x 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

31 (a) ( y )( y + ) B cao (B ( ay + b )( cy d ), with a, b, c, d all positive and ac 6 and bd 6) (i) ( ( y y )( )( y y + + ) ) y y B ( y )( y + ) B cao (ii) ( { [ x + ] }{[ x + ] + } ) or 6 x + 4 x + 4 x x + 9 x + ( x + )( x + ) M substitute x + for y in (a) A cao or M expand and collect terms A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

32 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

33 GCSE Mathematics 40 Paper 4 (Higher) mark scheme Number Working Answer Mark Notes (a) 0% 00 M 00 0 ( + ) A cao M 0 ( + ) A cao (a) ( ) 0.9 M for ( ) A 0.9 oe M A 0.7 oe kg of apples costs. kg of lemons costs p B for. M for.76. A cao 4(a) M A cao 0% of M 0% of 60 A 0 o UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

34 (a) x x. M x 4 y + y x A. oe M 4 y + y A oe 6 (a) M for 6 4 A cao 7 (a) y + 4 q 4 q p π 0 p y q p y 4 6. M for a correct method to isolate ± 4 q or 4 correctly A q p y oe 4 M π 0 A 6. or '6.' M A '6.' or 0 m 6. cm 0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

35 (a) B reflection Reflection in the line x B line x 9 (a) ( x + y ) + ( x 4 y ) Triangle with vertices at (4, ) (, )(, ) x y 6 B correct enlargement in correct place (B correct enlargement in wrong place) M ( x + y ) + ( x 4 y ) A cao 6 6x 4 0 M 6 6x 4 A 0 ft on (a) 0 ( ) 000 OR 4.% of % of () M ( ) 000 A 49.4 or 49. OR M for 4.% of 000 M 4.% of 4.4 A 49.4 or M M M A UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

36 (a) 0 a 4 M a 4 b. A 0 M b A M M oe 0% 0% A cao 4 (a) (c) LQ. kg, UQ.4 kg 4 x + 4 y x 4 y 6x 6 6. kg.9kg IQR ignores outliers B tol ± 0. B for either LQ or UQ B..0 B ignores outliers oe x, y 0. M for a correct process which leads to the elimination of either x or y, allow arithmetical error M sub for one variable in one of the equations A cao (both) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

37 6 i a B cao ii b B cao (B + b ) iii pq B pq oe (B + pq ) M A (a) Length Volume B cao B cao 9 tan x x. 0 tan (0.) B cao 7. M tan x. 0 M x ) A tan (0. UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

38 0 (a) M kr M 0R M M kr 70 k M 70 k 70 k 0 A k 0 M M M A cao ' 0' '740' 0 4 M M 0 '740 ' 0 A 0.9 A (a) sin sin x x sin 0 0 sin M M sin sin x x sin 0 0 A oe sin sin.. M use of absin C M 0 sin'. ' must be the included angle A.. 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

39 (a) x ( x + ) B cao (c) x ( x + ) 40 x x μ ± x + x 40.4, -. 0 M x ( x + ) 40 A M x ± ± M x A.4, (d).4 B ft cos 4 4cos M cos 4 M correct use of Bidmas A (a) x + + xy y B cao n M for n + k, oe, where k is a constant A k (c) ( n ) 9 n n + 4 ( 4 ) n n + ( n 4 n + ) B for sight of ( n ) M correct expansion of ( n A for a full argument which proves Sophie s statement ) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

40 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

41 GCSE Mathematics mock papers 44 (Modular) Unit 4 Number, Algebra and Shape, Space and Measures UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

42 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

43 GCSE Mathematics 44 Unit 4 (Foundation) mark scheme Section A Number Working Answer Mark Notes (a) 7 (c) M for 7 A cao M for M for 0.90 A cao M for evidence of adding hour 40 minutes to 0 A cao (a) (c) C E B and E B cao B cao B for B B for E (a) (c) % % B cao B cao B cao 4 (a) (c) (a) (c) 7. cm 6 o AB and DC marked Isosceles A B and D B cao B cao B cao B cao B cao B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

44 6 (a) B cao M for or A cao 7 (a) B cao B cao (a) B cao M for 4 4 or 6 A cao M for 0 seen A cao 0 (a) 6 ( 4) + 0 M for 6 A cao M for substitution A cao (a) M for A cao M for fraction with denominator of or numerator of 6 A cao 40 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

45 Correct net B for correct net (B for rectangles or two right angled triangles within a net) (a) : 4 Correct rotation B cao B cao B for correct rotation (B for triangle of correct orientation but wrong position) Diagram B for bearing of 40 o ± o from Blackport B for bearing of 00 o ± o from Clancy Bay B for within guidelines M for 0 00 oe 0 A cao M for A cao (a) (c) 9 (a) 6 (0 60) or Graph B cao M for 6 (0 60) or 6 A cao M for straight line with negative gradient A for line starting at (0,6) and finishing at (6,0) B (B for one square missing or extra) B (B for one square missing or extra) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 4

46 Section B Number Working Answer Mark Notes (a) lines of symmetry B for both lines of symmetry correct (B for line correct) i ii (a) i ii i ii (c) Shape reflected 6.9,., 9. Cylinder Sphere 7 B for fully correct reflection (B for any line correctly reflected) B for 6.9 B for. B ft for 9. B cao B cao M for 0 0 oe A cao B cao B cao B for or B for or B cao 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

47 6 (a) p or 0.94 M for 0 40 (70) M for 70 6 A for A for 97.0 M for A for digits 94 A for correct units with answer 7 Drawing B for angle B drawn within tolerance B for angle A drawn within tolerance B for completely correct triangle within tolerance M for A cao i ii (a) 700 ( 40) (46) (0 0) M for ( 40) 00 oe M for A cao 7 M for (0 4) A cao 0 4 B for angles in a triangle add to 0 o and isosceles triangle M for A cao M for (0 0) 40 A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 4

48 (a) (c) 0 4. B cao B cao B cao Enlargement B for correctly enlarged shape (B for any two lines correct length) 4 (a) (c) 4y 9 w ( ) B cao M for 4y 9 A oe M for w + 0 or w + A cao 6.0 M for 4.0 (+) (.0) M for.0 or.0 or.0 A cao 6 π 7. cm M for π A cao B for cm 7 (a) i ii AC x 7 y 4 Explanation B cao B cao B for no equals sign or it is an expression oe.7 M for M for A cao 44 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

49 GCSE Mathematics 44 Unit 4 (Higher) mark scheme Section A Number Working Answer Mark Notes (a) B 7 9 M for 7 or seen A cao (c) M for a valid attempt to divide by or 0. seen A cao 7 M for common denominator of 7 M dep for one numerator correct or seen A cao (a) x x x M for x x oe A cao y (6 y) y y y + y + y M for y (6 y) or y M for y + y + oe 7 A for 6 M for 4 6 or 4 seen A cao oe UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 4

50 (a) 6 B 6 (0 60) 4 M for 6 time A cao (c) Line to 0 B for straight line from (0, 6) to (6, 0) (B for straight line from (0,6) to time axis) 6 Correct P B for line 40 from Blackport ± B for line 00 from Clancy Bay ± B for correct position 7 y 7 x 7 x M for y 7 x oe (a) x A for 7 x oe B (B for x or x > ) 9 (a) 0 y > 7 y > 0,, 0,, 9 7 B (B for omission or extra) B B y > M for y > 7 or y > 0 A cao 46 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

51 (a) B (B for one square missing or extra) B (B for one square missing or extra) rotation 0 centre (0, 0) (x +)(x ) or M for rotation or correct reflections on diagram ignore labels M (dep) for 0 or correct centre A cao B for (x +)(x ) (B for (x ±)(x ± )) B ft 4 (D), C, E, A, F, B B for all correct (B for or 4 correct B for or correct ) 4 reason B for 4 B for angle at centre angle at circumference oe UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 47

52 6 explanation B for if n odd, then n odd, and odd + odd even if n even, then n even, and even + even even oe (B for less clear explanation or substituting at least different values to show it is true 7 (a) 6 B M for A cao + M for 6 + M for oe A cao (accept p, q ) 9 Let BP x AP 4x AB x BC x AC (x) (x) AC 4x sin B 4 x x 4 Proof 4 M for AB x or BC x M for correct use of Pythagoras A for AC 4 x B for sin B 4 x x 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

53 Section B Number Working Answer Mark Notes Reflection B (B for lines in correct position) M for 4. or. seen A for 9. or. B for 6.0 π() 7. cm M for π() oe A for answer that rounds to 7. B (indep) for cm 4 C a + f B for C a + f oe (B for a + f B for C an expression in a and b or a oe or f oe seen) 0 0 M for converting both to the same units 6 A cao 6 Rotation B for correct rotation (B for correct orientation or 90 clockwise rotation) 7(a) i ii x y 4 B B reason B for no equal sign or it is an expression UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 49

54 x x x 7 4x + 7 4x 7 4 x. Largest side (.). 0(a) 0. 4 M for x x x 7 oe M for correctly rearranging equation with x terms on one side and rest on other side (accept use of only sides) A for. oe B ft (dep on M) for M for 6..6 or. seen A cao 9,, B (B for correct) tan (.0) 6000 or Total Total graph M for plotting at least 4 points correctly and joining with a curve or plotting all correct points but not joined with a curve A cao M for correct trial between 4 and inclusive M for further correct trial between 4 and exclusive M for trial of 4.6 A cao 4.0 M for use of tan M for 9. tan 4 A for 4.0 or better B for (.0) M for (.0 ) 6000 A cao or M for or 600 seen M for and A cao 0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

55 B for answer rounds to 4.. (B for 7 or or.0 seen) b(a + c) ac b a B B for 0 or 0. seen M for oe A cao 7 (a) Area sector 0 60 π(6.) 6.6 Area triangle sin B B B cao (B for 4. x or 6. x ) accept or oe) B for.6 or better (B for. 6. or oe) 7.9 M for 0 60 π(6.) or 6. seen M for sin 0 or.9 seen M for 6. or.9. seen M for area sector area triangle A for answer that rounds to 7.9 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

56 9 4x x + 4x x 0 (4x + )(x ) 0 x 4 or y or 6 4 x 4 y 6 x y 4 B for 4x x + oe M for (4x ± )(x ± ) A for x 4 or M for substitution to get y A for y or 6 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

57 GCSE Mathematics mock papers 0 (Linear) NB Paper and Paper 4 for 0 only UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

58 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

59 GCSE Mathematics 0 Paper (Higher) mark scheme Number Working Answer Mark Notes (a) B or or 40 B 4-6 B ft on (a) M A A 9 Or M A 9 Or M for attempt to find 0% and % of 0 A A 9 x 0 4 B for any correct (x,y) y B any other correct (x,y) B correct line UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

60 4 x M sight of 6 A 46 Angles on straight line sum to 0 Corresponding angles Angles in a triangle sum to 0 Square Trapezium (4 + ) ( 4 ) Or Rectangle 4 4 Triangle B any correct relevant statements 64 4 M for 4 4 or 6 (4 + ) M for ( 4 ) or 4 M (dep on at least previous M) A for 64 Or M 4 or 4 M 4 or 6 M (dep on at least previous M) A for Key 4 represents.4 cm Diagram B fully correct including key (B error or omission in table or key) (B errors or omissions in table or key) (B unordered, no errors otherwise, with key) (B unordered or more errors, with key or unordered, no errors, with key) 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

61 7 Males 60% of Females 40% of Males like tennis 0% of Females like tennis 40% of (a) q + q + 4 q + 0 q 0 4 B for 900 B for M for attempt to find 70 or 40 B cao + 9 q + 0 M for sight of or 4 out of 4 terms correct A cao 6 k 9 mk + 4 km 6 m 6 k mk 6 m M for sight of out of 4 terms correct including signs or 4 out of 4 terms correct ignoring signs A cao 9 x + x + x x x. B x + ( x + ) M correct process to isolate x or x A cao 0 i ii M for A cao 4 0 M for A oe 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

62 (a) 7 4 M 7 A cao 4 0. M ' 4' A ft M for attempt to write the fractions over a common denominator 4 A A cao ' 440' M Σ fx use of x consistently in each interval (may include endpoints) M (dep) use of midpoints M (dep on st M) A cao Σ Σ fx f UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

63 4 (a) M for 0 ' 40' 6 A cao 0 (a), M ' 40' 6 A ft B cao on the first branch B cao branches, respectively on each pair of the second 64 M A cao (c) M M A cao + (d) M 7 A oe UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

64 6 (a) B cao B for B cao or (a) i 7 o 7 o B for R 90 o B for 7 o ii Angle sum of a triangle is 0 o Angle in a semi-circle is a right angle Reasons B for both angle sum of a triangle is 0 o Angle in a semi-circle is a right angle i 0 7 o B ft on 7 ii Opposite angles of a cyclic quadrilateral sum to 0 o Reason B opposite angles of a cyclic quadrilateral sum to 0 o i ( x + 4)( x + ) B ( x + 4)( x + ) (B ( x + a )( x + b ) Where ab 4 ) ii, 4 B both ft on (i) 9 (a) (c) x + 0 (0,) (., 0) B cao B cao M for x + 0 oe A cao 60 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

65 0 (a) π 0 + π 0 0 π M for π 0 or π 0 M for π 0 + π 0 A cao (a) SF length 64 New radius 0 y + ax b ax b y x b a y x, x, x + x ( x ) + x ( x + ) + ( x )( x + 4 x 4 x + 4 x + x + 4 x x x 4 x ) x ± 0 b a y B for 64 or B for 0 b y M x a A (condone omission of ± ) B B cao x 4 4 B for, x + 4 x x seen M for at least one term of x ( x ) + x ( x + ) + ( x )( x + M for all terms A cao ) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 6

66 (a) i ii 4(a) i ii iii (0, 0) (90, ) B cao B cao B cao M A 4 oe A 4 or B cao B cao See below B y x 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

67 (a) ( y )( y + ) B cao (B ( ay + b )( cy d ), with a, b, c, d all positive and ac 6 and bd 6 ( { [ x + ] }{[ x + ] + } ) or 6 x + 4 x + 4 x x + 9 x + ( x + )( x + ) M substitute x + for y in (a) A cao or M expand and collect terms A cao B cao B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 6

68 64 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

69 GCSE Mathematics 0 Paper 4 (Higher) mark scheme Number Working Answer Mark Notes (a) 0% 00 0 ( + ) M 00 A cao M 0 ( + ) A cao (a) ( ) 0.9 M for ( ) A 0.9 oe kg of apples costs. kg of lemons costs (a) (a) % of 60 0 x x 4 y + y 0.7 M A 0.7 oe 96p B for M for.76. A cao 7 M A cao M 0% of 60 or 0 seen A cao labelled pie chart M x x A. oe M 4 y + y A oe UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 6

70 6 (a) M for 6 4 A cao y + 4 q p p y q 4 q p y 4 7 (a) 0 π 6. M for a correct method to isolate ± 4 q or 4 correctly A q p y 4 oe M π 0 A '6.' M A '6.' or 0 m 6. cm (a) Reflection in the line x B reflection B line x 9(a) ( x + y ) + ( x 4 y ) Triangle with vertices at (4,)(,)(,) x y 6 B correct enlargement in correct place (B correct enlargement in wrong place) M ( x + y ) + ( x 4 y ) A cao 6 6x 4 0 M 6 6x 4 A 0 ft on (a) 66 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

71 Number Working Answer. Mark Notes 0 ( ) 000 OR 4.% of % of () M ( 0.04) A OR M for 4.% of 000 M 4.% of 4.4 A cm 4 M M M A (a) a 4 0 b 0. M a 4 A 0 M b A M M oe 0% 0% A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 67

72 4 (a) (c) (d) LQ. kg, UQ.4 kg 4 x + 4 y x 4 y 6x 6 6. kg.9 kg IQR ignores outliers Box plot B tol ± 0. B for either LQ or UQ B..0 B ignores outliers oe B for correct whiskers B correct quartiles B correct median marked x, y 0. M for a correct process which leads to the elimination of either x or y, allow arithmetical error M sub for one variable in one of the equations A cao (both) 6 i a B cao ii b B cao (B + b ) iii pq B pq oe (B + pq ) M A UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

73 9 (a) tan x x M. 0 tan (0.) kr 70 k 70 k 0 M 7. M 0R tan x. 0 M x tan (0. ) A M M kr M 70 k A k 0 M M M A cao ' 0' '740' 0 4 M M 0 '740 ' 0 A 0.9 A UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 69

74 (a) x 6.9 x M oe sin sin x sin 0 0 sin 0 0 M sin sin x sin 0 0 A sin 0 0 (a) sin. x. ( x + ) M use of absin C M 0 sin'. ' must be the included angle A.. B cao x ( x + ) 40 x + x 40 0 M x ( x + ) 40 A μ 4 40 ± 4 40 (c) x.4,. M x ± 4 M x ± 4 x A.4,. (d).4 B ft 70 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

75 cos 4 4cos M cos 4 M correct use of Bidmas A (a) x + + xy y B cao n M for n + k, oe, where k is a constant A k (c) ( n ) 9 n n + 4 ( n 4 n + ) ( n 4 n + ) B for sight of ( n ) M correct expansion of ( n A for a full argument which proves Sophie s statement ) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

76 7 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

77 GCSE Mathematics (Modular) Mock papers UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

78 74 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

79 GCSE Mathematics mock papers (Modular) Unit Number, Algebra and Shape, Space and Measures Stage UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

80 GCSE Mathematics (Modular) Unit Stage Foundation mark scheme Question Answer C B E D E C A C E B Question Answer D E B E A B C D C D Question 4 Answer B C E A D GCSE Mathematics (Modular) Unit Stage Higher mark scheme Question Answer D D B C D E A E D E Question Answer C D C E E A A C D B Question 4 Answer C E D D B 76 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

81 GCSE Mathematics mock papers (Modular) Unit Number, Algebra and Shape, Space and Measures Stage UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 77

82 7 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

83 GCSE Mathematics Unit Stage Foundation mark scheme Number Working Answer Mark Notes (a) (a) (c) (a) (4 ) Or (4 ) + (4 ) 4 0 ( ) i ii 0 ( ) Or.4.6(.).0.6 4m gh ef 4 B cao B for (accept and ±) B for m (accept m, m, m ) B cao B cao B cao M for (4 ) or (4 ) + (4 ) A cao.90 4 M for either. 6 or 0.90 or 6.9(0) or 7.(0) seen A for 4.0 M for A cao 4 Reason Cheaper in Spain by 0.0 Cheaper in Spain by 4p B cao B for base angles of an isosceles triangle are equal M for.0.4 or.4 M (dep) for.0 or.0.6 A for Cheaper in Spain by 0.0 or Cheaper in Spain by 4p M for 4 A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 79

84 ( ) + or ( + ) 9(a) 7 Straight line from (, 7) to (, ) M for ( ) + or M for correct substitution of ( + ) A cao B for a fully correct table (B for or correct entries in the table) B for a straight line from (, 7) to (, ) (B ft from (a) for at least 4 correct plots or for a single line of gradient or for a single line passing through (0, ) with a negative gradient) 0 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

85 GCSE Mathematics (Modular) Unit Stage Higher mark scheme Number Working Answer Mark Notes (a) i ii 0 (90 + ) Reasons 7 6 B cao B cao B for B for angles in a triangle 0 B for corresponding angles oe x 40 + y 40x + y B for 40x + y oe (B for 40x or y) 4 60 ( ) 4 M for 60 (or 0 seen) 60 (or seen) or (or 40 seen) A cao (a) 7 B for a fully correct table (B for or correct entries in the table) Straight line from (, 7) to (, ) B for a straight line from (, 7) to (, ) (B ft from (a) for at least 4 correct plots or for a single line of gradient or for a single line passing through (0, ) with a negative gradient) B for (B for and 000 seen or or n where n 4) 7 60 ( ) 0 B for identifying a 90 o angle at S or T M for 60 ( ) oe A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

86 (a) (y )(y + ) B cao xx ( + 4) x B for x(x + 4) or (x + 4)(x ) ( x+ 4)( x ) x M for cancelling A cao 9 x 0.0 n Proof B for either 0x 0. n or 00x n. n 0x 0. n 00x n. n M for 00x 0x n. n 0. n n A for completing the proof 90x n. n 0. n n UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

87 GCSE Mathematics mock papers (Modular) Unit Number, Algebra and Shape, Space and Measures UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

88 4 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

89 GCSE Mathematics Unit Foundation mark schemes Section A Number Working Answer Mark Notes (a) 7 (c) (a) (c) (a) (c) 4 (a) (c) (a) i ii (c) C E B and D % % 7. 6 o AB and DC marked Kamloop Vancouver M for 7 A cao M for M for 0.90 A cao M for evidence of adding hour 40 minutes to 0 A cao B cao B cao B for B B for D B cao B cao B cao B cao B cao B for a correct pair B cao B cao B cao B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

90 6 (a) (c) 7 (a) (a) Isosceles A B and D B cao B cao B cao B cao M for or A cao B cao B cao B cao M for 4 4 or 6 A cao 4 M for 0 seen A cao 6 0 M for 6 A cao Net B for correct net (B for rectangles or two right angled triangles within a net) (a) : 4 Correct rotation B cao B cao B for correct rotation (B for triangle of correct orientation but wrong position) Diagram B for bearing of 40 o ± o from Blackport B for bearing of 00 o ± o from Clancy Bay B for within guidelines 6 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

91 6 y 7 x 7 x M for y 7 x y 7 x y A cao M for 0 00 oe 0 A cao M for A cao 9 (a) (c) 0 (a) 6 or 6 (0 60) 6 4 Diagram B cao M for 6 A cao M for straight line with negative gradient A for line starting at (0,6) and finishing at (6,0) B (B for one square missing or extra) B (B for one square missing or extra) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 7

92 Section B Number Working Answer Mark Notes (a) lines of symmetry B for both lines of symmetry correct (B for line correct) (a) (a) i ii i ii (c) Shape reflected 6.9,., 9. Cylinder Sphere 7 B for fully correct reflection (B for any line correctly reflected) B for 6.9 B for. B ft for 9. B cao B cao M for 0 0 oe A cao B cao B cao B for or B for or B cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

93 6 (a) p or 0.94 M for 0 40 (70) M for 70 6 A for A for 97.0 M for A for digits 94 A for correct units with answer 7 (a) (c) 4 9 (9.) ( 40) i ii 0 4 (46) cm Circle cm 6 M for 4 9 B for B for circle drawn within guidelines B ft from (a) or.6.4 M for 9. A cao 40 M for ( 40) 00 oe 7 Reason M for A cao M for (0 4) A cao M for A cao B for angles in a triangle add to 0 o and isosceles triangle UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

94 (a) (c) 0 4. B cao B cao B cao Enlargement B for correctly enlarged shape (B for any two lines correct length) 4 (a) (c) 4y 9 4w + w + 0 4w w 0 w oe. oe B cao M for 4y 9 A M for 4w + w + 0 M for 4w w 0 A 6.0 M for 4.0 (+) (.0) 6 π 7. cm M for π A cao B for cm 7 (a) i ii AC x 7 y 4 Explanation M for.0 or.0 or.0 A cao B cao B cao B for no equals sign or it is an expression oe.7 M for M for A cao 90 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

95 GCSE Mathematics Unit Higher mark schemes Section A Number Working Answer Mark Notes (a) B 7 9 M for 7 or seen A cao (c) + (a) x x 7 x 9 x M for a valid attempt to divide by or 0. seen A cao 7 M for common denominator of 4. 7 M dep for one numerator correct or seen A cao M for x x 7 oe M for correct simplification A for 4. oe y 4 y M y 4 A cao M for 4 6 or 4 seen A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

96 (a) 6 B 6 (0 60) 4 M for 6 time A cao (c) Line to 6 B for straight line from (0, 6) to (6, 0) (B for straight line from (0,6) to time axis ) 6 Correct P B for line 40 from Blackport ± B for line 00 from Clancy Bay ± B for correct position 7 y 7 x (a) 7 x M for y 7 x oe x A for 7 x oe B (B for x or x > ) 9 (a) 0(a),, 0,, 9 7 B (B for omission or extra) B B B (B for one square missing or extra) B (B for one square missing or extra) 9 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

97 rotation 0 M for rotation or correct reflections on diagram (ignore centre (0, 0) labels) M (dep) for 0 or correct centre A cao (i) (ii) (x +)(x ) or 4 reason B for (x +)(x ) (B for (x ±)(x ± ) B f. B for 4 B for angle t centre angle at circumference oe 4 explanation B for if n odd, then n odd, and odd + odd even if n even, then n even, and even + even even oe (B for less clear explanation or substituting at least different values to show it is true) (a) B oe 4 B for 4 oe (B for oe or oe) 6 i (c) i y 6x + 6 M for 6x+ c or ax + A cao B ii 9 M for A cao UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

98 M for Let BP x AP 4x AB x BC x AC (x) (x) AC 4x sin B 4 4 x x M for oe A cao (accept p, q ) Proof 4 M for AB x or BC x M for correct use of Pythagoras A for AC 4 x B for sin B 4 x x 94 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

99 Section B Number Working Answer Mark Notes Reflection B (B for lines in correct position) M for 4. or. seen A for 9. or. B for 6.0 π() 7. cm M for π() oe A for answer that rounds to 7. B (indep) for cm 4 C a + f B for C a + f oe (B for a + f B for C an expression in a and b or a oe or f oe seen) 0 0 M for converting both to the same units 6 A cao 6 Rotation B for correct rotation (B for correct orientation or 90 clockwise rotation) 7 (a) i ii x y 4 B B reason B for no equal sign or it is an expression UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 9

100 x x x 7 4x + 7 4x 7 4 x. Largest side M for x x x 7 oe M for correctly rearranging equation with x terms on one side and rest on other side (accept use of only sides) A for. oe B ft (dep on M) for M for or other valid method to reach 9 A cao 0 (a) 9,, B (B for correct) (a) graph M for plotting at least 4 points correctly and joining with a curve or plotting all correct points but not joined with a curve A cao M for correct trial between 4 and inclusive circle radius cm bisect the angle M for further correct trial between 4 and exclusive M for trial of 4.6 A cao B for circle radius cm ± 0. cm M for arc drawn centre O cutting OA and OB or line from O bisecting the angle ± 4 A for accurate bisector ± 96 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

101 (.0) B for (.0) or Total Total M for (.0 ) 6000 A cao or M for or 600 seen M for and A cao B for answer that rounds to 4.. (B for 7 or or.0 seen) b(a + c) ac b a B B for 0 or 0. seen M for oe A cao 7 (a) B B B cao (B for 4. x or 6. x ) (accept or oe) B for.6 or better (B for. 6. or oe) UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 97

102 Area sector 0 60 π(6.) 6.6 Area triangle sin x x + 4x x 0 (4x + )(x ) 0 x 4 or y or M for 0 60 π(6.) or 6. seen M for sin 0 or.9 seen M for 6. or.9. seen M for area sector area triangle A for answer that rounds to 7.9 x 4 y 6 x y 4 B for 4x x + oe M for (4x ± )(x ± ) A for x 4 or M for substitution to get y A for y or UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

103 Notes on marking principles Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks (independent of M marks) Abbreviations cao correct answer only ft follow through isw ignore subsequent working SC special case oe or equivalent (and appropriate) dep dependent indep independent No working If no working is shown then correct answers normally score full marks If no working is shown then incorrect (even though nearly correct) answers score no marks. 4 With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. If there is no answer on the answer line then check the working for an obvious answer. Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given. UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00 99

104 6 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg incorrect cancelling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect, eg algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 7 Probability Probability answers must be given as fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer. Linear equations Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded. 9 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another. 6ma900S:\LT\PD\Support\UG09 GCSE maths mark schemes.doc.-0/ 00 UG09 Mock papers mark schemes Edexcel GCSE in Mathematics 40, 44, 0 and Issue January 00 Edexcel Limited 00

105 Further copies of this publication are available from Edexcel Publications, Adamsway, Mansfield, Notts, NG 4FN Telephone Fax Publications Code UG09 January 00 For more information on Edexcel and BTEC qualifications please contact Customer Services on or or visit our website: Edexcel Limited. Registered in England and Wales No Registered Office: One90 High Holborn, London WCV 7BH. VAT Reg No