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I. Numbers (1)
(34)
1. Surds
(34)
II. Quadratic functions
(235)
2. Quadratic functions, graphs
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3. Factorisation of quadratic functions
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III. Polynomials
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10. Division of polynomials
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11. The factor and remainder theorems
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12. Factorisation of polynomials
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13. Factorisation and roots of polynomials
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IV. Graphs of polynomials
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19. Translations and graphs
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V. Coordinate geometry (1)
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21. Parallel and perpendicular lines
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22. Coordinate geometry of a circle
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23. The tangent
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24. The normal
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25. Intersection points (1)
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26. Intersection points (2)
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VI. Differentiation (1)
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27. The derivative
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28. Differentiation of simple functions
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29. Differentiation of polynomials
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30. Finding gradients, tangents and normals
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31. Monotonicity
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32. Local extrema, stationary points, critical points
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33. Finding local extrema
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34. Finding maximum and minimum values
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35. Second-order derivatives
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VII. Integration (1)
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36. The anti-derivative
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37. Integrating
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38. The definite integral
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39. Area under the curve
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40. Laws of indices – rational exponents
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50. General angles
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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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59. Measuring the circle
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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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72. Inverse 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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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
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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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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
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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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Finding the area
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Finding the area of the region
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Finding the length of the stretched band
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Measuring the circle
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Measuring the circle
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Miscellaneous exercises
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The area of a sector
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The area of a sector
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The area of a segment
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The length of an arc
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The length of an arc
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The length of an arc – finding the angle
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Three circles
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Three circles – finding the arcs
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Three circles – finding the area
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Two circles
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Two circles and a line
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Two circles and a line
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Resources: 1 – 20 Total: 20
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