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I. Numbers (1)
(34)
1. Surds
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II. Quadratic functions
(235)
2. Quadratic functions, graphs
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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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35. Second-order derivatives
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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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54. Simple trigonometric equations
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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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69. Inverse function
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70. The modulus function
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XVII. Exponentials and logarithms
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75. The natural exponential function
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81. Integration of selected functions
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82. Integration methods (1)
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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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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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Resources: 1 – 25 Total: 97
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A fraction and its decomposition
Whiteboard exercise
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A fraction and its decomposition
Student activity
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A polynomial and its different divisors
Whiteboard exercise
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A rational expression and its simpler form
Animation
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A rational function
Student activity
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A simple trick
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Algebraic division
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Algebraic division
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Algorithm of polynomial division
Whiteboard exercise
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Algorithm of polynomial division
Student activity
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Arbitrary denominator
Whiteboard exercise
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Arbitrary denominators
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Asymptotes of a rational function
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Asymptotes of a simple rational function
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Asymptotic behaviour
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Asymptotic behaviour
Simulation
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Building rational expressions
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Can the rational expression be simplified?
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Completing the decomposition
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Constant rational function
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Decomposing a rational expression into partial fractions
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Decomposing an expression with a polynomial in the denominator
Whiteboard exercise
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Decomposing by factorising the denominator
Animation
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Decomposing rational expressions
Whiteboard exercise
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Decomposing rational expressions into partial fractions
Student activity
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Resources: 1 – 25 Total: 97
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