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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
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9. Algebraic manipulation of polynomials
(42)
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
(29)
IV. Graphs of polynomials
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14. Sketching graphs
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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
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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
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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)
(239)
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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VIII. Numbers (2)
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40. Laws of indices – rational exponents
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IX. Graph transformations
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X. Sequences and 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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64. Derivatives of powers with rational exponent
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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
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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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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
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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 – 19 Total: 19
A system of simultaneous equations
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Are there any solutions?
Student activity
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Equations with one variable
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Equations with one variable
Whiteboard exercise
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Finding an approximate solution of the equation
Animation
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General equations with one variable
Student activity
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General equations with one variable
Whiteboard exercise
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Graphical solution of equations (2)
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Graphical solution of equations (2)
Whiteboard presentation
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Is the route safe?
Animation
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Long Range Navigation
Whiteboard exercise
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Long Range Navigation
Student activity
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LORAN
Animation
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Parallel lines
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Solving a system of simultaneous equations
Student activity
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Solving a system of simultaneous equations
Whiteboard exercise
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Systems of more complicated equations
Whiteboard exercise
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Systems of more complicated equations
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The number of solutions
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Resources: 1 – 19 Total: 19
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