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Problem-Solving Essentials: Improve Skills in Calculus

Revise formulae and enhance problem-solving abilities with St. Thomas More's starter exercises. Practice partial fractions, parametric equations, curves, and more.

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Problem-Solving Essentials: Improve Skills in Calculus

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  1. C4: Starters 1 2 3 4 5 6 7 8 9 Revise formulae and develop problem solving skills. 10 11 12 13 14 15 16 17 18 20 21 19 22 23 24 25 26 27 28 29 30 31 DMO’L.St Thomas More

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  29. Starter 21 Use the trapezium rule with 6 strips to estimate DMO’L.St Thomas More

  30. Starter 21 Use the trapezium rule with 6 strips to estimate DMO’L.St Thomas More

  31. Starter 21 Use the trapezium rule with 6 strips to estimate DMO’L.St Thomas More

  32. Starter 21 Use the trapezium rule with 6 strips to estimate DMO’L.St Thomas More

  33. Starter 21 Use the trapezium rule with 6 strips to estimate Back To 3 sig. fig. DMO’L.St Thomas More

  34. Starter 22 Use the trapezium rule with 4 strips to estimate DMO’L.St Thomas More

  35. Starter 22 Use the trapezium rule with 4 strips to estimate DMO’L.St Thomas More

  36. Starter 22 Use the trapezium rule with 4 strips to estimate DMO’L.St Thomas More

  37. Starter 22 Use the trapezium rule with 4 strips to estimate Back To 3 sig. fig. DMO’L.St Thomas More

  38. Starter 23 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 360o about the x-axis Find the volume generated. Volume Back DMO’L.St Thomas More

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

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

  41. Starter 25 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) Consider the angle between their direction vectors; a = (3i – 5j – k)and b =(2i + j – 9k) Cosine of angle angle Back DMO’L.St Thomas More

  42. Starter 26 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. The direction vector of the line is a = i + j +k When t = lOP a DMO’L.St Thomas More

  43. Starter 26 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. The direction vector of the line is a = i + j +k When t = lOP a  OP. a = 0 DMO’L.St Thomas More

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

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

  46. Starter 28 • A curve has parametric equations x = 4cosq and y = 8sinq. • Find the gradient of the curve at P, the point where q = p/4 • Find the equation of the tangent to the curve at P. • Find the coordinates of the point R where the tangent meets the x-axis. • Find the area of the region bounded by the curve, the tangent and the x-axis. DMO’L.St Thomas More

  47. Starter 28 • A curve has parametric equations x = 4cosq and y = 8sinq. • Find the gradient of the curve at P, the point where q = p/4 At P q = p/4; DMO’L.St Thomas More

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

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

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

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