EXERCISES will include over 2000 practise questions covering the complete AS and A-level specifications. VIDEOS links through to excellent resources at www.mathsgenie.co.uk, where there are also more banks of practise questions and practise papers.
AS Pure Maths
TOPICS
VIDEOS
EXERCISES
SOLUTIONS
2. ALGEBRA
Solutions 2
Solutions 3
Solutions 4
Solutions 5
Solutions 6
3. FUNCTIONS
Solutions 7
Solutions 8
Solutions 9
Solutions 10
6. TRIGONOMETRY
14. Sine and cosine rules
15. Area of triangle
16. Graphs in degrees & exact values
17. Trigonometric identities
18. Trigonometric equations
Solutions 14
Solutions 15
Solutions 16
Solutions 17
Solutions 18
7. EXPONENTIALS & LOGARITHMS
19. Exponential function
20. Gradient of e^kx
21. Laws of logarithms
22. Exponential equations
23. Reduction to linear form
24. Modelling using exponentials
Solutions 19
Solutions 20
Solutions 21
Solutions 22
Solutions 23
Solutions 24
8. DIFFERENTIATION
25. The gradient function
26. Second derivatives
27. Differentiation from 1st principles
28. Differentiation of x^n
29. Tangents and Normals
30. Stationary points
Solutions 25
Solutions 26
Solutions 27
Solutions 28
Solutions 29
Solutions 30
9. INTEGRATION
31. Differentiation in reverse
32. Indefinite integrals of x^n
33. Definite integrals & areas
Solutions 31
Solutions 32
Solutions 33
10. VECTORS
34. Vectors in 2 dimensions
35. Magnitude and direction
36. Operations on vectors
37. Position vectors
38. Forces as vectors
Solutions 34
Solutions 35
Solutions 36
Solutions 37
Solutions 38
A-Level Pure Maths
TOPICS
VIDEOS
EXERCISES
SOLUTIONS
3. FUNCTIONS
43. The Modulus Function
44. Modulus equations
45. Function vocabulary
46. Inverse functions
47. Composite functions
48. Graph Transformations
Solutions 43
Solutions 44
Solutions 45
Solutions 46
Solutions 47
Solutions 48
5. SEQUENCES & SERIES
50. The binomial expansion
51. Increasing, decreasing, periodic
52. Arithmetic sequences
53. Geometric sequences
Solutions 50
Solutions 51
Solutions 52
Solutions 53
6. TRIGONOMETRY
54. Radians
55. Small angle approximations
56. Graphs in radians & exact values
57. Reciprocal functions
58. Inverse functions
59. Trigonometric identities
60. Double angle formulae
61. R-formulae
62. Trigonometric equations in radians
63. Proofs involving trig functions
Solutions 54
Solutions 55
Solutions 56
Solutions 57
Solutions 58
Solutions 59
Solutions 60
Solutions 61
Solutions 62
Solutions 63
7. DIFFERENTIATION
64. Second derivatives
65. Sine & cos from 1st principles
66. Points of inflection
67. Product rule
68. Quotient rule
69. Chain rule
70. Implicit differentiation
71. Parametric differentation
72. Differential equations
Solutions 64
Solutions 65
Solutions 66
Solutions 67
Solutions 68
Solutions 69
Solutions 70
Solutions 71
Solutions 72
8. INTEGRATION
73. Integration of e^kx
74. Integration of 1/x
75. Integration of sinx & cosx
76. Use of trigonometric identities
77. Areas between curves & lines
78. Integration as limit of a sum
79. Integration by substitution
80. Integration by parts
81. Integration using partial fractions
82. Interpreting differential equations
83. Differential equations with separable variables
Solutions 73
Solutions 74
Solutions 75
Solutions 76
Solutions 77
Solutions 78
Solutions 79
Solutions 80
Solutions 81
Solutions 82
Solutions 83
8. NUMERICAL METHODS
84. Cobweb & Staircase diagrams
85. Newton-Raphson method
86. Recurrence relations
87. The trapezium rule
88. Rectangle sum limits
Solutions 84
Solutions 85
Solutions 86
Solutions 87
Solutions 88