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November 2010 Paper 3

November 2010 Paper 3. 1)a) Milk : Dark 2 : 1 24 : 12 There are 36 chocolates in total. 2) a) p x p x p x p = p 4 b) 2c x 3d = 6cd. 3)a) b) (2, 9) (4, 7) (6, 5) (8, 3) c) P(less than 6) = 3 / 20. 4)a) 2 6 10 14 18 4n – 2 b) 10 – n 2

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November 2010 Paper 3

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  1. November 2010 Paper 3

  2. 1)a) Milk : Dark 2 : 1 24 : 12 There are 36 chocolates in total

  3. 2) a) p x p x p x p = p4 b) 2c x 3d = 6cd

  4. 3)a) b) (2, 9) (4, 7) (6, 5) (8, 3) c) P(less than 6) = 3/20

  5. 4)a) 2 6 10 14 18 4n – 2 b) 10 – n2 i) 3rd term = 10 – 32 = 1 ii) 5th term = 10 – 52 = -15

  6. 5) Area of circle = π x radius2 Area = π x 102 = 314cm2

  7. 6) 3870 236 x 4.85 4000 (1 mark for any 200 x 5 one of these) 4000 1000 4 (1 mark for any answer between 3 and 4)

  8. 175 x 37 = 6475 • £64.75

  9. Line drawn through • (−2, 6) (−1, 5) (0, 4) (1, 3) (2, 2) • (3, 1) (4, 0), (5, − 1)

  10. Equilateral triangle so all angles are 60° • x = 120° • Angles on a straight line add up to 180 °

  11. 10)a) • Key 9|1 = 91 • b) Mode = 77

  12. 11) 17.5% of 6000 = 1050 (1 mark) 6000 + 1050 (1 mark) = 7050 (1 mark) 7050 – 3000 (1 mark) 4050 ÷ 10 (1 mark) = 405 (1 mark)

  13. 12) • Rotation (1 mark) • 180° (1 mark) • Centre (0,0) (1 mark)

  14. 12)b)

  15. 13) t = v + 2 5 t – 2 = v 5 (t – 2) x 5 = v 5(t – 2) = v

  16. 14) Midpoint of PQ is (7, 5)

  17. 15) B and E

  18. 16) a) 3(x + 5) + 2(5x – 6) = 3x + 15 + 10x – 12 = 13x + 3 b) 2x + 4 = x + 2 2 c) 5x + 10 = 5(x + 2) d) x2y + xy2= xy(x + y)

  19. 17) A B

  20. 18)a) 2 17/20 – 1 2/5 17 _ 2 or 20 5 17 _ 8 20 20 9 20 Answer = 19/20 or 29/20 57 _ 7 20 5 57 _ 28 20 20 29 20

  21. 18)b) 2 2/3 x 1 3/4 8 x 7 3 4 56 12 (or equivalent...e.g. 14/3 or 42/3

  22. 19)a) A 10cm 10cm x 1.5 or ÷ 2 then x 3 E B 8cm 8cm 5cm D C 15cm DC = 12cm

  23. 19)b) A Area of trapezium = ½ (a + b) x height 10cm Parallel sides E B 8cm 5cm D C Area of trapezium = ½ (8 + 12) x 5 = 50cm2 8cm 5cm 12cm

  24. 20) a) 13.2 • 13.8 – 12.6 = 1.2 • IQR ignores extreme values/outliers

  25. 21) 6x + 2y = − 3 (1) • 4x − 3y = 11 (2) • Make the ys the same • x 3 18x + 6y = -9 • x 2 8x – 6y = 22 (1 mark) • Signs Same Subtract • 26x = 13 (1 mark) • x = ½ (1 mark) • Now find y 6x + 2y = -3 • 3 + 2y = -3 • 2y = -6 • y = -3 (1 mark)

  26. 22) a) A tangent is at right angles to a radius

  27. 22) b) OB2 = OA2 + AB2 OB2 = 82 + 62 OB2 = 100 OB = 10 BC = OB – 6 = 4cm

  28. 23) (x − 3)(x + 5) • x2 – 3x + 5x – 15 • x2 + 2x – 15 • x2 + 8x − 9 = 0 • (x + 9)(x – 1) = 0 • either x + 9 = 0 or x – 1 = 0 • x = -9 x = 1

  29. 24)a)

  30. 24)b) 6 + 8 + 6 + 5 = 25

  31. 25) 180 x 50 = 9 1000

  32. 26) P is inversely proportional to V. • When V = 8, P = 5 • P = k • V • 5 = k • 8 • k = 40 • P = 40 • V

  33. 26)b) P = 40 V P = 40 2 P = 20

  34. 27)a) OP = a + b OM = ½a + ½b

  35. 27)b) TM = -a + ½a + ½b TM = -½a + ½b

  36. 28) (-1.6,2.6) (2.6,-1.6)

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