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June 2009 Paper 3

June 2009 Paper 3. 1)a) P(walk) = 37 100. 2) a) 4x + 3y – 2x + 5y = 2x + 8y b) 2c + 4r Hint: make up values for c and r and work out what sum you would need to do. 3)a) y = 4x – 3 Your graph should be a straight line through all the points with no ‘corners’

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June 2009 Paper 3

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  1. June 2009 Paper 3

  2. 1)a) • P(walk) = 37 • 100

  3. 2) a) 4x + 3y – 2x + 5y = 2x + 8y b) 2c + 4r Hint: make up values for c and r and work out what sum you would need to do

  4. 3)a) y = 4x – 3 • Your graph should be a straight line through all the points with no ‘corners’ • On this exam you only got 1 mark for plotting your points if they were wrong

  5. 4)a) P = 4k – 10 P = 50 50 = 4k – 10 (1 mark) 60 = 4k k = 60 ÷ 4 k = 15 (1 mark) b) y = 4n – 3d n=2 d=5 y = 4x2 – 3x5 (1 mark) y = 8 – 15 y = -7 (1 mark)

  6. 5)a)

  7. 5)b) Translation 3 right and 1 down 3 (1 mark) (1 mark) -1

  8. 6) a) Opposite sides of a rectangle are equal b) 4x + 1 = 2x + 12 2x + 1 = 12 2x = 11 x = 5.5 c) Perimeter = 5.5 + 5.5 + 23 + 23 = 57cm

  9. 7) 322 x 48 = 15456 a) 3.22 x 4.8 = 15.456 b) 0.322 x 0.48 = 0.15456 c) 15456 ÷ 4.8 = 3220

  10. 8) a) 2x2 = 72 x2 = 36 x = 6 b) 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32 72 36 2 6 6 2 3 2 3

  11. 9)

  12. 9)

  13. There are 40 litres of water in a barrel. • The water flows out of the barrel at a rate of 125 millilitres per second. • 1 litre = 1000 millilitres. • Work out the time it takes for the barrel to empty completely. • 40 litres = 40 000 millilitres • 40 000 ÷ 125 = 320 seconds • (40 000 ÷ 125 = 40 x 8)

  14. a) 62.5 • 11)b) 63.5

  15. 12)

  16. 13) a) What type of magazines do you read? Sport Music Fashion One question 1 mark Tick box options – at least two options 1 mark

  17. 13) b) How many magazines have you read in the last month? 0 1-2 3+ Time period e.g. month, week, year 1 mark Tick box options – at least three non-overlapping options 1 mark

  18. 14) 6.8 x 191 0.051 7 x 200 (1 mark for at least 0.05 two of these) 1400 (1 mark) 0.05 28000 (1 mark) (Dividing by 0.05 is the same as multiplying by 20)

  19. 15)a) Write 64 000 in standard form • 6.4 x 104 • (b) Write 156 x 10-7 in standard form • 1.56 x 10-5

  20. 16)a) Factorise fully 4x2 – 6xy 2x(2x – 3y) b) Factorise x2 + 5x – 6 (x + 6)(x – 1)

  21. 17) Use upper bounds Join with a smooth curve

  22. 17)b) Median is ‘middle one’ 60th value Mark given for any value between 235 and 245

  23. 17)c) Men spent more money than women

  24. 18)a) Work out the size of angle AOD 54° (2 marks) tangent is perpendicular to a radius angles in a triangle add up to 180° (reasons not required)

  25. 18)b) Work out the size of angle ABC. Give a reason for your answer. 27° (2 marks) Angle at the centre is twice the angle at the circumference. (1 mark)

  26. 19)a) x = 2, y = 3

  27. 19b) Find an equation of the straight line which is parallel to the line y = ½x + 2 and passes through the point (0, 4) y = mx + c y = ½x + c y = ½x + 4

  28. 20)a) 3t + 1 < t + 12 2t + 1 < 12 2t < 11 t < 5.5

  29. 20)b) t is a whole number. Write down the largest value of t that satisfies 3t + 1 < t + 12 t < 5.5 largest value of t is 5

  30. 21) M is directly proportional to L3. When L = 2, M = 160 Find the value of M when L = 3 M = k x L3 160 = k x 23 160 = k x 8 160 = k 8 k = 20 M = 20 x L3 M = 20 x 33 M = 20 x 27 = 540

  31. 22)

  32. 23)a) 0.5 0.3 0.2 0.5 0.3 0.2 0.2 0.5 0.3 0.2

  33. 23)b) Work out the probability that Vishi will win both games. 0.5 x 0.5 = 0.25

  34. 24)a) AB = AC (sides of an equilateral triangle) AD = AD (common side) ADC = ADB = 90° Therefore ABD and ACD are congruent (RHS)

  35. 24)b) BD = DC (congruent triangles) BC = AB (equilateral triangles) Therefore BD = ½ AB

  36. 25) 1 + 1 = 1 u v f 1 + 1 = 1 (1 mark) 5/210/3 f 2 + 3 = 1 5 10 f 4 + 3 = 1 10 10 f 7 = 1 (1 mark) 10 f f = 7 (1 mark) 10

  37. 25) 1 + 1 = 1 u v f 1 = 1 - 1 u f v 1 = v - f u fv fv 1 = v - f u fv u = fv v - f

  38. 26) a) Find an equation of the translated curve. y = f(x – 4)

  39. 26) b) On the grid, sketch the graph of y = 3 cos (2x°) for values of x from 0 to 540

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