Mark Scheme (Results) November 2007

Transcription

1 Mark Scheme (Results) November 007 IGCSE IGCSE Mathematics (4400_4H) Edexcel Limited. Registered in England and Wales No Registered Office: One90 High Holborn, London WC1V 7BH

2 4400 IGCSE Mathematics November 007 Paper 4H Q Working Answer Mark Notes M1 for 1.6 or.5 seen or for A1 16 Accept 5 Total marks. (a) 5(x 4) 1 B1 cao (b) y(y + 6) B B1 for factors, which, when expanded and simplified, give two terms, one of which is correct except (y + 6)(y 6) and similar SC B1 for y(y + 6y) Total marks M1 60 for or 41.8 or better or or or 91.5 or 0.55 seen or 1.8 seen 50 A1 Accept or 50 Total marks 1

3 4. Reflection in x = 4 B1 for reflection, reflect B1 for x = 4 stated or eg in dotted line Total marks or 1 seen M1 84 A1 cao Total marks 6. (a)(i) 57 B1 cao (ii) alternate angles B1 (b) corresponding angles B1 for one pair Do not accept and sum of angles on a straight line is 180 Z angles or allied or co-interior angles or and (vertically) opposite angles F angles or alternate angles and sum of angles on a straight line is B1 cao

4 7. (a) for oe or oe seen 150 M1 55 for A1 cao (b) M1 products m f where m is within each = interval and consistent (inc end points) M1 (dep) for use of halfway values (c) 594 A1 Accept 500 or 590 if M1 + M1 scored eg no upper limit for extra large, no lower limit 1 B1 for small, don t know midpoints for XL, S Total 7 marks 8. (a) B B1 for either open circle at or solid circle at (b) B B1 for all correct + 1 wrong or for four correct and none wrong 9. arc centre B cutting AB and AC at (say) P and Q B1 arcs centre P and Q of equal radii which intersect at B1 R (say) and BR joined (dep) bisector within tolerance Total marks

5 10. (a) 7 ( 1) 1 7 B B1 for 4 correct (b) graph B B1 for 5 points plotted correctly + ½ sq ft from (a) if at least B1 scored B1 for correct curve or, if there are 1 or errors in (a) and no plotting errors, award for a curve passing through the 7 points from their table M1 for or 7.5 seen 750 A1 cao M1 (dep) for 100 Total marks or or M1 for squaring and adding M1 (dep) for square root 17.5 A1 cao Total marks 4

6 or M for or M1 for, 114% = or 18.5 seen A1 cao 14. (a) 6n 1 B1 cao (b) x y B B1 for x or y (c) t 1 1 B1 cao (d) 6 p B 8 B1 for 8 1 oe or for p 6 Total 6 marks 5

7 15. (a) (b) (c) M1 10. A1 cao M1 8. A1 cao 15 or 1.5 oe 10 M1 15 for or 1.5 oe or for or or 0. 4 & oe 15 9 or for correct expression which, if accurately evaluated, gives the correct answer or for the area of one of the triangles evaluated correctly Area ABC rounds to 6. (6.700 ) NOT 6.7 Area CDE rounds to 7.7 ( ) NOT 7.88 Note: the angles of the triangle are 4.5, 54.5 and oe A1 for.5 or ¼ or 9 / 4 or for answer rounding to.5 Even if M1 awarded, do not award A1 for a correct answer, if there are any errors in the working. Total 6 marks 6

8 16. (a)(i) 15 B1 cao (ii) 7 or 8 B1 (b) 6 or 6½ M1 may be stated or indicated on graph inc A1 17. (a) 7 = and 90 = 5 or or 1,,,4,6,8,9,1,18, 4, 6,7 and 1,,,5,6,9,10,15,18,0,45,90 (b) 5 or 7, 144, 16, 88, 60 and 90, 180, 70, 60 M1 Need not be products of powers; accept products or lists ie,,,, and,,,5 Prime factors may be shown as factor trees 18 A1 cao M1 60 A1 cao 7

9 18. (a) y = 6 x M1 for y = 6 x or for stating coordinates of points on line x 6 x M1 for correct rearrangement of equation y = or y = with y as subject or for attempt to find gradient of line joining two stated points ½ for ½ oe A1 dep only on first M1 SC if M0, award B1 for correct ft from incorrect rearrangement (b) y = ½x + 5 oe 1 B1 correct answer or ft from (a) Equivalent equations include x + y = (i) 8 4 B1 cao (ii) 1 B1 cao (iii) 0 B1 cao (iv) 16 B1 cao 8

10 0. (a) (b) dy = x 10x + 8 dx M1 (dep on at least B1) for substituting x = 0 A1 cao (could be) turning point, max or min, 1 B1 (is) stationary point tangent is parallel to the x=axis Total 5 marks 1. (a) bar height 1 little squares B1 Allow + ½ sq bar height 6 little squares B1 Allow + ½ sq (b) 8 1 B1 cao Total marks. (a)(i) 8 B1 cao (ii) Angles in the same segment oe B1 Award if same segment, same arc or same chord stated or implied (b) 5 B B1 for ADC = 90 or COD = 76 stated or indicated on diagram 9

11 . (a) (x 5) + or 6x 15 + M1 (b) + eg or attempt to make x the subject of y = x + or x = y + 6x 1 A1 x oe M1 A M for sum of both products (M1 if one correct product seen) 1 A1 0 Total marks 10

12 5. (a) x + x(4 x) = 11 or 4 x + x( x) = 11 M1 or ( 4 x )( x) = 1 Award M1 A1 or 1 (4 x)( x) = 11 for 4x + x x = 11 x + 4x x = 11 A1 or 4x + x x = 11 or 1 4x x + x = 1 or x + x x = 11 (b) 7 ± ( 7) 4 11 M1 for correct substitution Condone omission of brackets 7 ± 5 M1 for correct simplification 4.6,.8 A1 for sf or better (4.6180,.8196 ) (c)(i).8 B1 for.8 or better (ii) eg x < B1 Total 7 marks 11

13 6. (a) 1 π r r + πr r or 1 π r + πr M1 4 π r A1 dep on M1 (b) π rl + πr + πr oe M1 l > r or l = r oe M1 > 4πr A1 Total 5 marks 1