AQA A LEVEL MATHS 2021 PAPER 1 QP

1. Straight line equation formula y-y1 = m(x-x1) 2. Perpendicular straight lines m1 x m2 = -1 3. Log(a)b=c a^c=b 4. Log(10)x + Log(10)y = Log(10)xy 5. Log(10)x - Log(10)y = Log(10)x/y 6. kLog(10)x = Log(10)x^k 7. Displacement dy/dx = Velocity 8. Velocity dy/dx = Acceleration 9. Cos^2A + Sin^2A= 1 10. 1 + Tan^2A = Sec^2A 11. 1 + Cot^2A = Cosec^2A 12. 2SinAcosA = Sin2A 13. Cos^2A - Sin^2A = Cos2A 14. (2tanA)/(1-tan^2A) = Tan2A 15. A^x A^y = A^xy 16. A^x / A^y = A^x-y 17. (A^x)^y a^xy 18. Arc Length (radians) = r¸ 19. Sector Area (radians) = 1/2 r^2 ¸ 20. x^n dy/dx = nx^(n-1) 22. Coskx dy/dx = -kSinkx 23. e^(kx) dy/dx = ke^(kx) 24. lnx dy/dx = 1/x 25. f(x)+g(x) dy/dx = f'(x)+g'(x) 26. f(x)g(x) dy/dx = f'(x)g(x) + f(x)g'(x) 27. f(g(x)) dy/dx = f'(g(x))g'(x) 28. +x^n = (x^(n+1))/(n+1) +c 29. +Coskx = 1/k Sinkx +c 30. S+inkx = -1/k Coskx +c 31. +e^(kx) = 1/k e^(kx) +c 32. +1x/ = ln |x| +c 33. f+'(x)+g'(x) = f(x)+g(x) +c 34. +f'(g(x))g'(x) = f(g(x)) +c 35. Weight = Mass x g 36. Force = Mass x Acceleration 37. Midpoint of a line (X1+X2)/2 , (y1+y2)/2 38. Length of a straight line x2(-x1)^2+(y2-y1)^2 39. Gradient of a line Change in y/Change in x 40. Equation of a circle (x-a)^2 + (y-b)^2 = r^2 , Centre (a,b) & Radius is r 42. Cos(90-¸)= Sin¸ 43. Sin(90-¸)= Cos¸ 44. Sin¸C/ os¸= Tan¸ 45. Sine Rule SinA/a = SinB/b 46. Cosine Rule a^2 = b^2 + c^2 -2bcCosA OR CosA = (b^2 + c^2 -a^2)/2bc 47. Area of a triangle 1/2abSinC 48. Calculating sin values 180-1st value, then +/- 360 49. Calculating cos values 360-1st value, then +/- 360 50. Calculating tan values +/- 180 51. A=Pe^(r/100 x t) A= Final amount P= Amount invested r%= Annual interest rate t= Number of years invested 52. Converting from component form to mag- nitude-direction form (vectors) 53. Converting from magnitude-direction form to component form (vectors) Magnitude= i^2 + j^2 Direction= Tan¸=j/i rCosi¸ + rSin¸j 54. Unit vector= i/magnitude + j/magnitude 55. Speed= distance/time 56. Velocity= displacement/time 57. Acceleration= change in velocity/time 58. Area of a trapezium 1/2(a+b)h 59. Census Surveying every member of the population 60. Random Sample Sampling by taking a lottery or picking names out of a hat 61. Systematic Sample Sampling every 5th or 10th (or similar) item 62. Stratified Sample Taking a sample from each sub-section of the population so each group is represented in proportion 63. Cluster Sample Pick a few groups (e.g. class- es) 64. Quota Sample Opportunity Sample, but must fill a certain criteria (e.g. 10 from year 7, 10 from year 11...) 65. Opportunity/Convenience sample Ask the first people you meet 66. Probability of event happening = No. of ways event can occur / Total no. of ways event can occur 67. Formula for general term (arithmetic se- ries) Ak = a+(K-1)d 68. Sum of terms formula (arithmetic series) S=n/2 (a+l) 69. Last term formula (arithmetic series) l=a+(n-1)d 70. Formula for general term (geometric se- ries) ak= ar^(K-1) 71. Sequences & Series notations a= First Number d= Common difference (arith- metic) l= Last Number k= Position (what term it is) r= Common ratio (geometric) n= Number of terms 72. Chain Rule dy/dx= dy/du x du/dx E.g. y=(x+1)^2, Let u=x+1 so y=u^3, du/dx=1 And dy/du=3u^2 so dy/dx= 3u^2 x 1 = 3(x+1)^2 73. Product Rule dy/dx= V du/dx + U dv/dx 74. Quotient Rule dy/dx= (V du/dx - U dv/dx) / V^2 75. Cosec¸ = 1/Sin¸ 76. Sec¸ = 1/Cos¸ 77. Cot¸ = 1/Tan¸ 78. a^x dy/dx = a^x lna 79. Ln(f(x)) dy/dx = F'(x) / f(x)