1. DMO’L.St Thomas More C4: Starters Revise formulae and develop problem solving skills. 123456789 101112131415161718 19 2021 222324252627 28293031

2. DMO’L.St Thomas More Starter 1 Express in partial fractions. Hence find

3. DMO’L.St Thomas More Starter 1 Express in partial fractions. Hence

4. DMO’L.St Thomas More Starter 1 Back

5. DMO’L.St Thomas More Starter 2 Express in partial fractions. Hence find

6. DMO’L.St Thomas More Starter 2 Express in partial fractions. Hence

7. DMO’L.St Thomas More Starter 2 Back

8. DMO’L.St Thomas More Starter 3 Find the cartesian equation of the curve given by the parametric equations

9. DMO’L.St Thomas More Starter 3 Find a way to eliminate t Back

10. DMO’L.St Thomas More Starter 4 Find the cartesian equation of the curve given by the parametric equations

11. DMO’L.St Thomas More Starter 4 Find a way to eliminate t Back

12. DMO’L.St Thomas More Starter 5 Find the cartesian equation the curve given by the parametric equations

13. DMO’L.St Thomas More Starter 5 Find a way to eliminate t Back

14. DMO’L.St Thomas More Starter 6 Find the coordinates of the points where the following curves meet the x,y axes Back

15. DMO’L.St Thomas More Starter 7 Find the coordinates of the points where the following curves meet the x,y axes Back

16. DMO’L.St Thomas More Starter 8 Find dy / dx leaving your answer in terms of t. Back

17. DMO’L.St Thomas More Starter 9 Find dy / dx leaving your answer in terms of t. Back

18. DMO’L.St Thomas More Starter 10 Find the equation of the tangent to the curve defined by the following parametric equations at the point P where t =  / 2 At P t =  / 2 so that giving Back

19. DMO’L.St Thomas More Starter 11 Evaluate Back

20. DMO’L.St Thomas More Starter 12 Complete the table: Back

21. DMO’L.St Thomas More Starter 13 Complete the table: Back

22. DMO’L.St Thomas More Starter 14 Complete the table: Back

23. DMO’L.St Thomas More Starter 15 Evaluate Back

24. DMO’L.St Thomas More Starter 16 Evaluate Back

25. DMO’L.St Thomas More Starter 17 In each case find Back in terms of x and y

26. DMO’L.St Thomas More Starter 18 Find Back

27. DMO’L.St Thomas More Starter 19 Find Back

28. DMO’L.St Thomas More Starter 20 Find Back

29. DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers 00 0.5 0.2231 1 0.6931 1.5 1.1787 2 1.6094 2.5 1.9810 32.3026  5.6854

30. DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers 00 0.5 0.2231 1 0.6931 1.5 1.1787 2 1.6094 2.5 1.9810 32.3026  5.6854

31. DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers 00 0.5 0.2231 1 0.6931 1.5 1.1787 2 1.6094 2.5 1.9810 32.3026  5.6854

32. DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers 00 0.5 0.2231 1 0.6931 1.5 1.1787 2 1.6094 2.5 1.9810 32.3026  5.6854

33. DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers 00 0.5 0.2231 1 0.6931 1.5 1.1787 2 1.6094 2.5 1.9810 32.3026  5.6854 To 3 sig. fig. Back

34. DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01  / 12 1.1260 /6/6 1.2559 /4/4 1.4142 /3/3 1.6529  2.65293.7962

35. DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01  / 12 1.1260 /6/6 1.2559 /4/4 1.4142 /3/3 1.6529  2.65293.7962

36. DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01  / 12 1.1260 /6/6 1.2559 /4/4 1.4142 /3/3 1.6529  2.65293.7962

37. DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01  / 12 1.1260 /6/6 1.2559 /4/4 1.4142 /3/3 1.6529  2.65293.7962 To 3 sig. fig. Back

38. DMO’L.St Thomas More Region A is bounded by the curve with equation, the lines x = 1, x = 0 and the x -axis. The region A is rotated through 360 o about the x -axis Find the volume generated. Starter 23 Volume Back

39. DMO’L.St Thomas More Points A and B have position vectors i + j + k and 2i - 3j + 2k respectively. Find the vector equation of the straight line through A and B. Starter 24 AB = ( 2i - 3j + 2k) – (i + j + k)

40. DMO’L.St Thomas More Points A and B have position vectors i + j + k and 2i - 3j + 2k respectively. Find the vector equation of the straight line through A and B. Starter 24 AB = ( 2i - 3j + 2k) – (i + j + k) = i – 4j + k Hence, a vector equation is; r = i + j + k + (i – 4j + k) Back

41. DMO’L.St Thomas More angle Find the acute angle between the two lines with vector equations r = 2i + j + k +t(3i – 5j – k) and r = 7i + 4j + k +s(2i + j – 9k) Starter 25 Consider the angle between their direction vectors; a = (3i – 5j – k) and b = (2i + j – 9k) Cosine of angle Back

42. DMO’L.St Thomas More Starter 26 The direction vector of the line is a = i + j +k A line has vector equation r = 3i + 5j - k +t(i + j +k) Find the position vector of the point P, on the line, such that OP is perpendicular to the line. When t = OP  a

43. DMO’L.St Thomas More Starter 26 The direction vector of the line is a = i + j +k A line has vector equation r = 3i + 5j - k +t(i + j +k) Find the position vector of the point P, on the line, such that OP is perpendicular to the line. When t = OP  a  OP. a = 0

44. DMO’L.St Thomas More Starter 26 When t = OP  a  OP. a = 0 So P has position vector OP = 3i + 5j - k - 7 / 3 (i + j +k) Back

45. DMO’L.St Thomas More Starter 27 Find the of the tangent to the given curve at the point (1,0). Differentiate; At (1,0) Hence tangent is Back

46. DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos  and y = 8sin  (a)Find the gradient of the curve at P, the point where  =  / 4 (b)Find the equation of the tangent to the curve at P. (c)Find the coordinates of the point R where the tangent meets the x -axis. (d)Find the area of the region bounded by the curve, the tangent and the x -axis.

47. DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos  and y = 8sin  (a)Find the gradient of the curve at P, the point where  =  / 4 At P  =  / 4;

48. DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos  and y = 8sin  (b) Find the equation of the tangent to the curve at P. At P  =  / 4; Equation of tangent;

49. DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos  and y = 8sin  (c) Find the coordinates of the point R where the tangent meets the x -axis. At R y  =  0

50. DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos  and y = 8sin  (d) Find the area of the region bounded by the curve, the tangent and the x -axis. Back

51. DMO’L.St Thomas More Starter 29 Find the general solution of each differential equation: Back

52. DMO’L.St Thomas More The region R is bounded by the curve C, the x -axis and the lines x = -8 and x = 8. The parametric equations for C are x = t 3 and y = t 2 Find the area of R. Area under curve Starter 30

53. DMO’L.St Thomas More The region R is bounded by the curve C, the x -axis and the lines x = -8 and x = 8. The parametric equations for C are x = t 3 and y = t 2 The region R is rotated about the x -axis, find the volume generated. Volume Starter 30 Back

54. DMO’L.St Thomas More A curve has equation Find the coordinates of the points on the curve where Differentiate w.r.t. x Starter 31 What’s this? Sub. back Back