EDEXCEL A LEVEL FURTHER MATHS 2022 PAPER 2

1. integrate sinx -cosx + c 2. integrate cosx sinx + c 3. integrate sec^2 x tanx + c 4. integrate cosecxcotx -cosecx + c 5. integrate cosec^2x -cotx + c 6. integrate secxtanx secx + c 7. cosec^2 x = cot^2 x + 1 8. sec^2 x = tan^2 x + 1 9. sin^2 x 1 - cos^2 x 10. sin^2 x 1-cos2x/2 11. cos^2 x 1+cos2x/2 12. 1/x ln IxI + C 13. Differentiate sin x cos x 14. Differentiate tan x sec² x 15. Differentiate cot x - cosec² x 16. Differentiate sec x sec x tan x 17. Differentiate cos x - sin x 18. Differentiate cosec x - cosec x cot x 19. Differentiate sin 2x 2 cos 2x 20. Differentiate cot 3x - 3 cosec² 3x 21. Differentiate sin² x 2 sin x cos x 22. Differentiate cos 0.5x - 0.5 sin 0.5x 23. Differentiate sin x cos x cos 2x 24. Differentiate 2cos0.5x -sin0.5x 25. 1 + tan2¸ = sec2¸ 26. cot2¸ + 1 =cosec2¸ = cosec2¸ 27. Sin2¸ 2sin¸cos¸ 28. Cos2¸ cos²¸-sin²¸ 2cos²¸-1 1-2sin²¸ 29. Tan2¸ 2tan¸ / (1 -tan²¸) 30. How do you write a rational num- ber in a proof? a/b 31. What does y=|f(x)| do? Reflects values below the x-axis in the x-axis 32. What does y=f(|x|) do? Reflects values of xe0 in the y-axis 33. Arithmetic sequence formula a•+(n-1)d 34. Geometric sequence formula u™ = ar•{¹ 35. Convergent geometric series Convergent if |r|1 where r is the common ratio 36. Periodic sequences Sequence is periodic if terms repeat in a cycle 37. Vectors and angles If the vector a = xi + yj + zk makes an angle “¸ with the positive x-axis, then cos“¸() = x/(|a|) and similarly for the angles ¸agnd ¸z. 38. Radian to degree conversion 1 radian = 180°= À 39. Arc length l=r¸ 40. Area of a circle sector a=1/2 x r²¸ 41. Arcsin(x) Graph 42. State the domain of y = arcsinx -1 dx d 1 43. State the range of y = arcsinx -À/2yddÀ/2 44. Arccos(x) Graph 45. State the domain of y = arccosx -1 dx d 1 46. State the range of y = arccosx 0 dy dÀ 47. Arctan(x) Graph 48. State the domain of y = arctanx - x 49. State the range of y = arctanx -À/2 y À/2 50. Differentiating y = eOã dy/dx = keOã 51. Differentiating y = ln(x) dy/dx = 1/x 52. Differentiating y = aOã dy/dx = (aOã)kln(a) 53. The Chain Rule dy/dx = dy/du x du/dx 54. The Product Rule 55. The Quotient Rule 56. Differentiating parametric equa- tions 57. Implicit differentiation 58. Concave function f(x) concave if f''(x) d 0 for all values of x in that interval 59. Convex function f(x) concave if f''(x) e 0 for all values of x in that interval 60. Point of inflection Point at which f''(x) changes sign 61. +eã dx eã + c 62. + 1x/ dx ln(x) + c 63. +sin(x) dx -cos(x) + c 64. +cos(x) dx sin(x) + c 65. Integration by parts uv - + v(du/dx) dx 66. 1 + tan² ¸ 67. cot² ¸ + 1 68. tan ¸ 69. cot ¸ 70. tan² ¸ sec² ¸ - 1 71. 1 sec² ¸ -tan² ¸ 72. cot² ¸ csc² ¸ - 1 73. sin²¸+cos²¸=? 1 74. sec²x-1 tan²x 75. sec²x-tan²x 1 76. sin²x 1-cos²x 77. cos²x 1-sin²x 78. cot²x+1 csc²x 79. csc²x-cot²x 1 80. Pulley is smooth - no friction - therefore tension is uniform 81. String is inextensible - acceleration is constant 82. string is light - mass is negligable 83. linear regression - do not extrapolate data - should not use the linear regression line to find a value of x for a given y 84. experiment - repeatable process - rise to number of outcomes 85. event A collection of one or more outcomes of an experiment 86. sample space the set of all possible outcomes 87. Mutually exclusive events P(A or B) = P(A) + P(B) - cannot occur at same time , no overlap 88. independent events P(A and B) = P(A) x P(B) 89. Probability mass function for B(n,p) 90. Model using binomial distribu- tion when: P(X = r) = (nCr)p^r(1-p)^n-r - fixed number of trials - two possible outcomes - fixed probability of success - trials are independent of eachother 91. product moment correlation Describes the linear correlation between two variables and takes a value between -1 - 1 -1 - strong negative correlation 0 no linear correlation 1 strong positive correlation 92. Explain why a linear model may be appropriate to describe the relationship between x and y. As the points lie reasonably close to a straight line 93. Reliable estimate when interpolation is used 94. What to remember when you want to find the area above the curve that goes be,on the x-axis: 95. Why is drawing a diagram im- portant when trying to find the area travelled from a quadratic equation for velocity on a dis- tance-time diagram Flip the numbers on the integral bracket (so smaller thing subtracts bigger thing) When integrating, you may want to find the area above the curve, if it goes below the x-axis. You won't realise which parts you need to break it up into without a diagram.