M A1. 4 M1 for listing at least three multiples for any two of 25, 12, (i) 24

Transcription

1 MA Practice papers Set : Paper H (Regular) mark scheme Version.0. 3 M 500 (00 00) (=0.5) 87 A M (i) M for listing at least three multiples for any two of 5,, 8 M for listing at least three multiples for all of 5,, 8 A for 4, 50, 75 cao OR M for prime factorisation for any two of 5,, 8, eg in a factor tree M for prime factorisation for all of 5,, 8 or A cao (SC B for 4k, 50k, 75k) (ii) 600 B for 600 (or ft 600k) MA Practice Papers: Set Regular (H) mark scheme Version.0 This publication may only be reproduced in accordance with Pearson Education Limited copyright policy. 06 Pearson Education Limited.

2 MA Practice papers Set : Paper H (Regular) mark scheme Version cm 3 M (or equivalent) = 4. M or 4. A = 90, 0 = 30 0 : 5 3 M for 4 0 (or equivalent) or 90 or 4 0 (or equivalent) or = 60, 30 = 6 M (indep) for ( ) 90 (or equivalent) (or 60) AND (or equivalent) (or 6) (M (indep) for ( ) 90 (or equivalent) or : 6 OR (or equivalent) or 6 80 OR both 90 (= 30) and 30 (= 4) 3 00 M (dep on at least M) for 60 : 6 or to 0 or 6 to 60 (or equivalent) or reversed ratio 6:60 A 0: cao MA practice paper H (Set ) mark scheme: Version.0

3 MA Practice papers Set : Paper H (Regular) mark scheme Version.0 5. π(6) π(5) = 3(.09 ) 78.5(39 ) = M for π(6) (or equivalent) or π(5) (or equivalent) or 3 or 78.5 M for π(6) π(5) (or equivalent) A for a = cost (p) of an apple p = cost (p) of a pear 3a + 4p = 84 5a + p = 76 7a = = tan x = =.8666 tan , 8 4 B 3a + 4p = 84 and 5a + p = 76 (or equivalent) M correct process to eliminate a or p M(dep on M) substitute found value of a or p to find other variable A cao 6 3 M for tan x = (= ) M for tan (4 7.5) A for answer in the range 6.7 to 6 MA practice paper H (Set ) mark scheme: Version.0 3

4 MA Practice papers Set : Paper H (Regular) mark scheme Version M for 3x + + 3x + + x + 3x (or equivalent) (= 0x) or 4x 5 + 4x 5 + x 3 + x 3 (or equivalent) (= x 6) M for equating perimeters, e.g. 0x = x 6 or x = 6 A for (x =) 8 M (dep M) for 3 8 (=) or 4 8 (=30) (or equivalent), provided x > 0 M for ( 8 + ) (or equivalent), provided x > 0 A for 360 MA practice paper H (Set ) mark scheme: Version.0 4

5 MA Practice papers Set : Paper H (Regular) mark scheme Version.0 9. x = 30 + correct reasons 4 M for angle BFG = 65 may be seen on diagram M (dep) for correct method to calculate x, eg (x=) (=30) or (x=) 80 (80 65) (=30) C for x = 30 and full appropriate reasons related to method shown (C (dep on M) for any one appropriate reason related to method shown) eg alternate angles; base angles in an isosceles triangle are equal; angles in a triangle add up to 80 o ; angles on a straight line add up to 80 o ; exterior angle of triangle = sum of two interior opposite angles; co-interior angles add up to 80 o (allied angles) NB Any reasons stated must be used 0. 5 x (360 ) (= 50) M Angle AOB. (AB =) cos ( 50 ) M Accept the use of the cosine rule with any angle but sides (0 and 7) must be in correct places. (AB =) cos ( 50 ) (AB =) A (awrt) 70 A (awrt) 6.4 MA practice paper H (Set ) mark scheme: Version.0 5

6 MA Practice papers Set : Paper H (Regular) mark scheme Version.0. correct graph M for 5 or 6 or 7 points plotted correctly at the ends of the intervals A cao for correct graph with points joined by curve or straight line segments No with supporting figures M for (=0) or (= 80) or sight of 80 used on cf axis or (=4) A ft for correct decision with 0 and 9 or 0 and 4 or age from reading graph at 80 OR M for method to find percentage of workers who are over 65, e.g. (= 4.5%) or method to find percentage of workers who are over 60 (from table), e.g. (= 7%) or (= 5%) A ft for correct decision with 4.5 % or 7% or 5% MA practice paper H (Set ) mark scheme: Version.0 6

7 MA Practice papers Set : Paper H (Regular) mark scheme Version.0. e.g. 70% = M 00% 30%, or 70% or 0.3 or 0.7 % = 790 (= 56) 70 M for or % = A cao M or or or M A (or equivalent) 40 MA practice paper H (Set ) mark scheme: Version.0 7

8 MA Practice papers Set : Paper H (Regular) mark scheme Version.0 Proof 3 Mfor correct method to find area of trapezium 4. (a) ½(3x + + 5x + 3)(x + 3) = ½ (8x + 4)(x + 3) So, (4x + )(x + 3) 46 = 0 M (dep) for expanding all brackets to get a correct expression for the area 8x + 6x = 0 C for complete correct proof 8x + 6x 40 = 0 x + x 5 = 0 (b) x = = ± ± 4()( 5) 4.45, ± M for substitution ± Mfor 4 4()( 5) condone one sign error in OR (x + ) 5 = (x + ) 6 x + = ± 6 Afor.44 to.45 (and 3.44 to 3.45) OR M for (x + ) 5 (or equivalent) M for x + = (±) 6 A for.44 to.45 (and 3.44 to 3.45) MA practice paper H (Set ) mark scheme: Version.0 8

9 MA Practice papers Set : Paper H (Regular) mark scheme Version.0 5. (a) y = f(x 5) B cao (b) (4, 3) B cao (B for one coord. correct (in correct position) or (3,4).) 6. x = x = x = x = 5 x = 5 = Proof 3 M for ( x =) (...) or 000x = 5.555( ) or 00x =.555(...) or 0x = 0.555( ) M for two recurring decimals the difference of which is a rational number C (dep on M scored) for completing the proof by subtracting and cancelling to give a correct fraction OR 00x = x = x =.5 x =.5 99 = 5 = MA practice paper H (Set ) mark scheme: Version.0 9

10 MA Practice papers Set : Paper H (Regular) mark scheme Version.0 7. k k or P P = x.34 3 M for P = x x k 6 = 5 50 P = 8 (k = 50) k M for 6 = or (k =) 50 seen or 6 5 = P 8 5 A M for tangent drawn at t = M (dep) for diff diff y x ft from tangent A for answer in range Yes, average speed could have been as high as B for 4535 or or 0.5 M for 4535 ((or equivalent)) 0.5 M for 3600 and 000 A for C (dep on first M) for correct conclusion from their calculations MA practice paper H (Set ) mark scheme: Version.0 0

11 MA Practice papers Set : Paper H (Regular) mark scheme Version M for correct deduction from differences, e.g. nd difference of 4 implies n n + 5n M for use of first differences. 5 M method to find g (x) A A g (x) = 3x 4 + M 3x = (x + 5)(4 + x) x M correct expansion of brackets 0 A MA practice paper H (Set ) mark scheme: Version.0

12 Practice Papers Set H: National performance data from Results Plus Source of questions Mean score of students achieving grade: Qu No Spec Paper Session YYMM Qu Topic Max score Mean % all ALL A* A B C D E NEW Compound measures 3 5AM H 506 Q3 Factors, multiples, primes MM F 06 Q7 Pythagoras in D MM H Q06 Ratio H 06 Q05 Area of a circle AM H 406 Q Simultaneous equations MM H 306 Q5 Trigonometry AM H 506 Q4 Solve linear equations MA0 H 4 Q08 Angles MA0 H 40 Q7 Sine and cosine rule MA0 H 4 Q6 Cumulative frequency diagrams MM H Q Reverse percentages AM H 3 Q Selection with or without replacement MM H 406 Q6 Solve quadratic equations H 006 Q7 Transformation of functions MM H 306 Q0 Recurring decimals MM H Q3 Direct and indirect proportion AM H Q3 Gradients as rate of change MA0 H 4 Q3 Compound measures NEW Quadratic sequences 3 NEW Functions 5 80 MA practice paper H (Set ) mark scheme: Version.0