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November 2010 Paper 4

November 2010 Paper 4. 1)a) 5 x 8 ÷ 2 = 20cm 2. 2) P (Pink) = 0.12. 3)a) There are 20 beads in box A. In box B there are twice as many beads as in box A. Box B = 40 In box C there are ¾ of the number of beads as in box A. Box C = 15

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November 2010 Paper 4

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  1. November 2010 Paper 4

  2. 1)a) 5 x 8 ÷ 2 = 20cm2

  3. 2) P (Pink) = 0.12

  4. 3)a) There are 20 beads in box A. In box B there are twice as many beads as in box A. Box B = 40 In box C there are ¾ of the number of beads as in box A. Box C = 15 In box D there are 10% more beads than in box A. Box D = 22 Total = 20 + 40 + 15 + 22 = 97

  5. 4)a) 3 x 100 = 300g

  6. 4)b) 4 x 6 = 24 people

  7. 5)a)

  8. 5)b)

  9. 6)a) 7x + 2y – x + y = 6x + 3y • 2x + 3 = 10 • 2x = 7 • x = 3.5 • c)i) c5 x c6 = c11 • c)ii) e12 ÷ e4 = e8

  10. 8 x 100 = 40% • 20

  11. 8) • Modal class is 10-19 • Median is 30th person so lies in the class 20-29 19 31

  12. 8)

  13. 2.42927(0474)

  14. 10)a) −2, −1, 0, 1, 2 • b) 2x < 10 • 3 • 2x < 30 • x < 15

  15. 11) A and 3 B and 2 C and 4 D and 1

  16. 12) T = 7x + 5y

  17. 13) Speed = distance time Speed = 7120 8 = 890 km/h

  18. 14)a)

  19. 14)b)

  20. 15)a) She only asks the best students • or The sample is too small • or The sample is biased

  21. 15)b) All the choices are positive There is no box for someone who doesn’t like maths

  22. 15)c) How many hours do you spend on your maths homework in a day? 0 hours 1-2 hours 3+ hours 1 mark for question with time frame 1 mark for three non-overlapping response boxes (no marks for inequalities)

  23. 16) a) (0, 3, 2) b) (5, 3, 0)

  24. 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)

  25. 17) a) 8.25 x 107 b) 1.456 x 10-15

  26. 18) 19.5 litres = 19500 millilitres (1 mark) 19500 ÷ 210 = 92.85714 (1 mark) Therefore a maximum of 92 full cups can be poured (1 mark)

  27. 19)a)

  28. 19)b)

  29. 19)c) 2 marks for 36-38 or for correct reading from your graph ifreadinglines are drawn on

  30. 19)d) 2 marks for 9-11 or for correct reading from your graph ifreadinglines are drawn on

  31. 20)a) 56 = 2 x 2 x 2 x 7 = 23 x 7 56 28 2 4 7 2 2

  32. 20)b) 14

  33. 21) cos 37 = AB (1 mark) 8 AB = cos 37 x 8 (1 mark) AB = 6.389 (1 mark) hyp adj

  34. 22)a)

  35. 22)b)

  36. 23) 1 mark for 256° or 52 seen in working or on diagram 1 mark for x = 104° 256° 52°

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

  38. 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

  39. 24) 35.5 x 26.5 = 940.75 1 mark for 35.5 or 26.5 1 mark for 35.5 x 26.5 1 mark for 940.75

  40. 25)a) (2x + 4y)(4x – 5y) 8x2 + 16xy – 10xy – 20y2 = 8x2 + 6xy – 20y2

  41. 25)b) (x + 10)5 (x + 10)4 = x + 10

  42. 25)c) x2 – 25 x2 + 7x + 10 =(x – 5)(x + 5) (x +2)(x + 5) = x – 5 x + 2

  43. 25)d) x2 + 6x − 2 = (x + p)2 + q = (x + 3)2 – 11 (x + 3)2 = x2 + 6x + 9

  44. 26) White then black = 7/11 x 4/10 = 28/110 Black then white = 4/11 x 7/10 = 28/110 One of each = 56/110 (or equivalent) W 6/10 W 7/11 B 4/10 W 7/10 4/11 B 3/10 B

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

  46. 27)a)

  47. 27)b)

  48. 28)a) Area = ½ x 10.5 x 8.3 x sin 62 = 38.474... cm2

  49. 28)b) QR2 = 10.52 + 8.32 – 2x10.5x8.3xcos62 QR2 = 97.311111 QR = 9.8646... cm

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