Edexcel GCSE. Mathematics 2540 Paper 5540H/3H. Summer Mark Scheme (Results) Mathematics Edexcel GCSE

Transcription

1 Edexcel GCSE Mathematics 540 Paper 5540H/H Summer 008 Mark Scheme (Results) Edexcel GCSE Mathematics 540

2 5540H/H (a) M for 4 8 oe or 00 oe or or 7.5 seen 8 A for 900 (SC: B for sight of two of, 60 or 5) (b) M for use of or.5 oe, eg or 0 8 A for 80 (SC: B for sight of two of 450,.5 or 7.5)

3 5540H/H (0) M for a complete method with relative place value correct. Condone multiplication error, addition not necessary. OR = = M for a complete grid. Condone multiplication error, addition not necessary. OR M for sight of a complete partitioning method, condone multiplication error. Final addition not necessary. A for 9.6(0) (p) A (dep on M) for correct placement of decimal point after final addition or for digits 96(0) seen (SC: B for addition of 4 lots of 5.4)

4 5540H/H M for using,, 4 and 5 as stem A for ordered stem and leaf diagram A for consistent key, e.g. = (years) OR = 4 (a) 6 B for 6 or 6.0 (b) 6. B for 6. cao (c).4 B for.4 cao 5 (a) S B for S cao (b) (,, ) B for (,, ) cao M for using 0, 0, 40 and 50 as stem A for ordered stem and leaf diagram A for consistent key, e.g. 0 = (years) (NB: Condone use of comma between leafs)

5 5540H/H 6 (a) (8 6) 4 M for 8 6 or or or 4n+6=8 or 0, 4, 8 seen A for cao (b) 4n + 6 B for 4n + 6 or (cost = ) 4n + 6 (B for 4n + a or bn + 6, where a and b are numbers (b 0) or n = 4n + 6 or 4n + 6=8 or 4n + 6 or 4x + 6) 7 ( 4 ) + ( 7) + ( 4 7) + ( 5 7) = cm 4 M for ( 4 ) or 7or 5 7or 4 7 M for attempt to add 5 faces which are areas A for 96 B (indep) for cm (NB: 0 marks for calculating volume)

6 5540H/H M for any two of 00, 0 or 0.5 = M for or 00 0 or or A or 0 0 or (SC: B for answer of 500 or 50) 9 - ( ) 0.4 M for ( ) oe or 0.6 oe seen A for 0.4 oe 0 (a) 0pq B for 0pq oe (b) d 4 B for d 4 cao (c) 4 a 4 7 a 8 M for 4 a or 4 7 or a or 8 A for a 8 cao (d) 4n+ 6+ n+ 7n + 9 M for 4n + 6 or n + A for 7n + 9 (e) t B for t (accept oe) (f) m B for m (accept t + 5 m oe)

7 5540H/H Correct construction M for constructing intersecting arcs of equal radius A for a correct triangle with appropriate arcs (SC: B for a correct triangle drawn within guidelines if M0 scored) (NB: guidelines allow for mm tolerance),, 0,, B for,, 0,, cao (B for 4 correct (only) or 4 correct and one incorrect or 5 correct and one incorrect) (a) 4 B for or 0.5 or 4 4 (b) M for attempt to convert to fractions with common ( ) + = denominator, e.g. two fractions denominator 0 or A correct conversion: 6 and 5 oe, or 56 or = = A for 0 0 or OR M for (or.8.75) A for.05 (A for 0.05) (c) Reason B for correct reason, e.g. / = 0. recurring (accept 0.) or 0. = /0

8 5540H/H 4 (a) Triangle A Triangle with vertices (-,5), (-,), (,) ±90 centre (-,) ) (b) Triangle B Triangle with vertices (,-), (5,-), (5,-4) (c) Triangle C Triangle with vertices (,.5), (,4), (,4) B for triangle with vertices (, 5), (, ), (, ) (B for triangle with correct orientation or triangle rotated B for triangle with vertices (, ), (5, ), (5, 4) 5 (a) x 5xy B for x 5xy (B for x or 5xy seen) x 6 x 6 x 6 x+ 6 oe (b) ( )( + ) B for ( )( ) B for triangle with vertices (,.5), (, 4), (, 4) ( B for triangle with correct orientation or for any two of the vertices (,.5), (, 4), (, 4) (SC: B for triangle with vertices (,.5), (, k), (, k) 6 (a) Complete box plot Median Highest mark B line drawn at 0 and no other lines drawn within box B whisker drawn to 55 (b) Complete table 0 B for 0 7 (a) B for (b).9 0 B for.9 0 (c) B for.5 0 6

9 5540H/H 8 (a)(i) B for 40 cao (ii) Reason B for angle at centre is twice angle at circumference (b)(i) or 0 0 B for 0 cao (ii) Reason B for opposites angles in a cyclic quadrilateral sum to 80 degrees or angle at centre is twice angle at circumference 9 e.g. adding equations leads to x = 9 substitute x = into eqn() leads to y = 6 x = y = M for adding equations or for coefficients of x the same followed by subtracting the equations condone one arithmetical error M (dep) for substituting found value in one equation A cao OR M for ( y) 9+ + y = 0, condone one arithmetic error M (dep) for substituting found value in one equation A cao (SC: B for one correct answer only if Ms not awarded)

10 5540H/H 0 (a) 7,, B all three correct (B for any one or two correct) (b) y B fully correct graph OR x B ft for 7 points plotted correctly ± mm B for smooth curve drawn through their points provided B awarded in (a).

11 5540H/H (a) 0. and 0.4, 0.4 B for 0. oe on LH branch B for 0.4 oe on both RH branches (b) M for oe A for 0.48 oe (c) M for or oe M for 0.8 '0.4' + '0.' 0.6 oe A for 0.44 oe OR M for oe M for ( ) oe A for 0.44 oe a( b ) 5 = 7b ab 5a = 7b ab + 7b = + 5a b a+ 7 = + 5a ( ) + 5a b = a M for a(b 5) or ab 5a or ab 5 M for isolating ab and 7b on one side to get ab + 7b oe M for correctly factorising b from ab + 7b (term in ab must be present) + 5a 5a A for b = or b = a + 7 a 7

12 5540H/H (a) B for or k or k k k, where k is an integer not equal (b) to 0 (accept, + M for or three of,,, 9 (or or or 0.5 ) or ( ) ) A for 5+ cao (SC: B for a + or 5 + b if M0 scored, where a and b are integers not equal to 0) 4 (a) M for or 4 8 oe or 8 :4 or 4 :8 or :4 or 4: A for 0 cao (b) M for 600 or 600 oe 8 4 A for 75 cao

13 5540H/H 5 (a)(i) a B for a oe (ii) a c B for a c oe (b) CA uur = a c uuur MN = (a c) uuur uur MN = CA B for (CA uur =) a c or CB uur + BA uur oe B (dep) for correct proof, e.g. CA uur uuur uur = MN or CA is a uuur multiple of MN (NB: condone absence/misuse of vector notation) 6 ( ) πx ( x) = π x h 6x M for a correct volume formula in terms of x, e.g. π x (x) or π x h A for π ( x) π h x ( x) = x h (or better) A for 6x cao = or π ( ) = π or x x x h 7 (a) (4, ) B for (4, ) (b) (, 6) B for (, 6)

14 5540H/H 8 ( x ) ( x + ) ( x + ) B for ( x + ) ( x ) ( x 5) ( x 5) ( x 5) x x+ and/or B for (otherwise award B for ( )( ) ( x )( x 5), which may not appear in the context of a fraction )