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I. Numbers (1)
(34)
1. Surds
(34)
II. Quadratic functions
(235)
2. Quadratic functions, graphs
(45)
3. Factorisation of quadratic functions
(46)
4. Quadratic equations
(40)
5. Simultaneous equations
(29)
6. Inequalities
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7. Quadratic inequalities
(45)
III. Polynomials
(195)
8. Presentation of polynomials
(37)
9. Algebraic manipulation of polynomials
(42)
10. Division of polynomials
(26)
11. The factor and remainder theorems
(26)
12. Factorisation of polynomials
(35)
13. Factorisation and roots of polynomials
(29)
IV. Graphs of polynomials
(125)
14. Sketching graphs
(22)
15. Graphical solution of equations (1)
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16. Graphical solution of equations (2)
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17. Graphical solution of inequalities (1)
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18. Graphical solution of inequalities (2)
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19. Translations and graphs
(19)
V. Coordinate geometry (1)
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20. Equation of a straight line
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21. Parallel and perpendicular lines
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22. Coordinate geometry of a circle
(37)
23. The tangent
(19)
24. The normal
(22)
25. Intersection points (1)
(19)
26. Intersection points (2)
(20)
VI. Differentiation (1)
(239)
27. The derivative
(25)
28. Differentiation of simple functions
(28)
29. Differentiation of polynomials
(25)
30. Finding gradients, tangents and normals
(32)
31. Monotonicity
(26)
32. Local extrema, stationary points, critical points
(23)
33. Finding local extrema
(27)
34. Finding maximum and minimum values
(28)
35. Second-order derivatives
(25)
VII. Integration (1)
(113)
36. The anti-derivative
(29)
37. Integrating
(23)
38. The definite integral
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39. Area under the curve
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VIII. Numbers (2)
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40. Laws of indices – rational exponents
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IX. Graph transformations
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41. Transformations of graphs (1)
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42. Transformations of graphs (2)
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X. Sequences and series
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43. Sequences
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44. Arithmetic sequence
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45. Arithmetic series
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46. Geometric sequence
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47. Geometric series
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48. Infinite convergent geometric series
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49. The binomial expansion
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XI. Trigonometry (1)
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50. General angles
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51. General angles, angle measures
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52. Basic trigonometric functions
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53. Graphs of trigonometric functions
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54. Simple trigonometric equations
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55. Solving simple trigonometric equations
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56. The area of a triangle
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57. The sine rule
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58. The cosine rule
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59. Measuring the circle
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XII. Exponentials and logarithms
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60. Exponential functions
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61. The logarithm
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62. Basic exponential equations
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63. Exponential inequalities
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XIII. Differentiation (2)
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64. Derivatives of powers with rational exponent
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XIV. Integration (2)
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65. Integrals of powers with rational exponent
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66. Approximation of the area under a curve
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XV. Functions
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67. Functions – basic notions
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68. Composition of functions
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69. Inverse function
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70. The modulus function
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71. Transformation of graphs
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XVI. Trigonometry (3)
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72. Inverse trigonometric functions
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73. Other trigonometric functions
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74. Identities for trigonometric functions
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XVII. Exponentials and logarithms
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75. The natural exponential function
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76. The natural logarithmic function
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XVIII. Differentiation (3)
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77. Derivatives of exponential and logarithmic functions
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78. Derivatives of trigonometric functions
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79. Differentiation rules (1)
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80. Differentiation rules (2)
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XIX. Integration (3)
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81. Integration of selected functions
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82. Integration methods (1)
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83. Integration methods (2)
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84. Volumes of revolution
(28)
XX. Numerical methods
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85. Zeros of a function
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86. Approximate solution of equations
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87. Numerical integration – mid-ordinate rule
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88. Numerical integration – Simpson's rule
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XXI. Rational functions
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89. Rational expressions
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90. Rational functions
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91. Algebraic division
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92. Partial fractions
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XXII. Coordinate geometry (2)
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93. Equations of curves
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94. Parametric equations of curves
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XXIII. Sequences and series
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95. Binomial series
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96. Expansion of rational functions
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XXIV. Trigonometry (3)
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97. Trigonometric functions of the sum and difference of angles (1)
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98. Trigonometric functions of the sum and difference of angles (2)
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99. Double-angle formulas
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XXV. Exponentials and logarithms
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100. Exponential growth and decay
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XXVI. Differentiation and integration
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101. Differential equations
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102. Equations with separable variables
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103. Implicit differentiation
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104. Parametric differentiation
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105. Tangents and normals for implicitly or parametrically defined curves
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106. Integration using partial fractions
(20)
XXVII. Vectors
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107. Vectors
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108. Algebraic operations on vectors
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109. Position vectors
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110. Vector equations of lines in 2-D
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111. Vector equations of lines in 3-D
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112. The scalar product (1)
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113. The scalar product (2)
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114. Perpendicular distance from a point to a line
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Resources: 1 – 25 Total: 27
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A case study
Whiteboard exercise
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A case study
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A special case
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Does a function have an extremum?
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Extrema at critical points
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Finding extrema
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Finding extrema
Animation
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Finding extrema
Whiteboard exercise
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Finding extrema at critical points
Student activity
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Finding extrema at critical points
Whiteboard exercise
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Finding extrema at critical points
Whiteboard exercise
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Finding extrema at points with no derivative
Animation
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Finding extrema at points with no derivative
Student activity
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Finding extrema at stationary points
Whiteboard exercise
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Finding extrema at stationary points
Student activity
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Finding extrema of the modulus function
Whiteboard exercise
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Finding local extrema
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Finding local extrema
Class activity
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Finding local extrema
Student activity
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How to recognise an extremum
Student activity
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How to recognise an extremum
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Local extrema
Animation
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Local extrema
Student activity
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Local extrema and critical points
Student activity
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Local extrema and critical points
Whiteboard exercise
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Resources: 1 – 25 Total: 27
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