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KS5 – Core Mathematics

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1 Adding indices when multiplying terms with the same bas… Indices

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Current lesson
2 Subtracting indices when dividing terms with the same b… Indices

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To be done
3 Multiplying indices when raising a power to a power Indices

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To be done
4 Multiplying indices when raising to more than one term Indices

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To be done
5 Terms raised to the power of zero Indices

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To be done
6 Negative Indices Indices

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To be done
7 Fractional indices Indices

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8 Complex fractions as indices Indices

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To be done
9 Introducing surds Surds

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10 Some rules for the operations with surds Surds

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11 Simplifying surds Surds

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12 Creating entire surds Surds

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13 Adding and subtracting like surds Surds

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14 Expanding surds Surds

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15 Conjugate binomials with surds Surds

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16 Rationalising the denominator Surds

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17 Rationalising binomial denominators Surds

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18 Graphing irrational roots Surds

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19 Simultaneous equations Equations

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20 Elimination method Equations

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21 Elimination method part 2 Equations

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22 Applications of simultaneous equations Equations

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23 Solving Inequalities. Inequalities

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24 Simplifying algebraic fractions. Simplifying

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25 Simplifying algebraic fractions using the index laws. Simplifying

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26 Algebraic fractions resulting in negative indices. Simplifying

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27 Cancelling binomial factors in algebraic fractions. Simplifying

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28 Common factor and the difference of two squares Factorising

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29 Factorising quadratic trinomials [monic] – Case 2. Factorising

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30 Factorising quadratic trinomials [monic] – Case 3. Factorising

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31 Factorising quadratic trinomials [monic] – Case 4. Factorising

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32 Factorisation of non-monic quadratic trinomials Factorising

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33 Factorisation of non-monic quadratic trinomials – moon … Factorising

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34 Difference of two squares Roots

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35 Quadratic equations with factorisation. Roots

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36 Solving quadratic equations. Roots

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37 Completing the square Roots

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38 Solving quadratic equations by completing the square Roots

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39 The quadratic formula Roots

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40 Problem solving with quadratic equations Roots

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41 Solving simultaneous quadratic equations graphically Roots

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42 Quadratic polynomials of the form y = ax. + bx + c. Graphs

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43 Graphing perfect squares: y=(a-x) squared Graphs

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44 Solve by graphing Graphs

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45 Graphing complex polynomials: quadratics with no real r… Graphs

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46 General equation of a circle: determine and graph the e… Graphs

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47 Graphing cubic curves Graphs

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48 Graphs of polynomials Graphs

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49 Introduction to polynomials Polynomials

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50 The sum, difference and product of two polynomials. Polynomials

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51 Polynomials and long division. Polynomials

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52 Polynomial equations Polynomials

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53 The factor theorem Factor theorem

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54 More on the factor theorem Factor theorem

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55 Complete factorisations using the factor theorem Factor theorem

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56 Expansions leading to the difference of two squares Factorising

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57 The remainder theorem. Remainder theorem

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58 More on remainder theorem Remainder theorem

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59 Absolute value equations Modulus

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60 Sum and difference of two cubes. Roots

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61 Sum and product of roots of quadratic equations Roots

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62 Sum and product of roots of cubic and quartic equations Roots

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63 Methods of approximating roots Roots

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64 Inductive and deductive reasoning Proofs

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65 Definition and use of counter examples Proofs

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66 Indirect proofs Proofs

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67 Mathematical induction Proofs

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68 Conditional statements (converse, inverse and contrapos… Proofs

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69 Use grids to enlarge/reduce 2D shapes Transformations

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70 Special transformations – reflections, rotations and en… Transformations

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71 Transformations – reflections Transformations

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72 The definition and concept of combined transformations … Transformations

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73 Distance formula. Coordinate geometry

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74 Mid-point formula Coordinate geometry

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75 Gradient Coordinate geometry

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76 Gradient formula. Coordinate geometry

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77 The straight line. Coordinate geometry

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78 Lines through the origin. Coordinate geometry

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79 General form of a line and the x and y Intercepts. Coordinate geometry

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80 Slope intercept form of a line. Coordinate geometry

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81 Point slope form of a line Coordinate geometry

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82 Two point formula: equation of a line which joins a pai… Coordinate geometry

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83 Intercept form of a straight line: find the equation wh… Coordinate geometry

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84 Parallel lines: identify equation of a line parallel to… Coordinate geometry

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85 Perpendicular lines. Coordinate geometry

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86 Perpendicular distance Coordinate geometry

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87 Line through intersection of two given lines Coordinate geometry

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88 Angles between two lines Coordinate geometry

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89 Internal and external division of an interval Coordinate geometry

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90 Triangle inequality theorem Co-ordinate Geometry

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91 The equation of a circle: to find radii of circles Circles

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92 The semicircle: to select the equation given the semi c… Circles

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93 Binomial expansions Surds

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94 Binomial products. Binomial

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95 Binomial products with negative multiplier Binomial

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96 Binomial products [non-monic]. Binomial

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97 Squaring a binomial. [monic] Binomial

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98 Squaring a binomial [non-monic]. Binomial

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99 Binomial Theorem – Pascal’s Triangle Probability

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100 Differentiation from first principles. Differentiation

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101 Differentiation of y = x to the power of n. Differentiation

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102 Meaning of dy over dx – equations of tangents and norma… Differentiation

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103 Function of a function rule, product rule, quotient rul… Differentiation

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104 Increasing, decreasing and stationary functions. Differentiation

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105 First Derivative – turning points and curve sketching Differentiation

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106 The second derivative – concavity. Differentiation

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107 Curve sketching Differentiation

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108 Practical applications of maxima and minima Differentiation

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109 Limits Differentiation

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110 Integration – anti-differentiation, primitive function Integration

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111 Computation of an area Integration

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112 Computation of volumes of revolution Integration

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113 The Trapezium rule and Simpson’s rule Integration

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114 The arithmetic progression Series and sequences

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115 Finding the position of a term in an A.P. Series and sequences

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116 Given two terms of A.P., find the sequence. Series and sequences

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117 Arithmetic means Series and sequences

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118 The sum to n terms of an A.P. Series and sequences

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119 The geometric progression. Series and sequences

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120 Finding the position of a term in a G.P. Series and sequences

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121 Given two terms of G.P., find the sequence. Series and sequences

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122 Geometric means. Series and sequences

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123 The sum to n terms of a G.P. Series and sequences

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124 Sigma notation Series and sequences

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125 Limiting sum or sum to infinity. Series and sequences

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126 Recurring decimals and the infinite G.P. Series and sequences

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127 Superannuation. Series and sequences

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128 Time payments. Series and sequences

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129 Applications of arithmetic sequences Series and sequences

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130 Graphing the trigonometric ratios – I Sine curve. Trigonometry

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131 Graphing the trigonometric ratios – II Cosine curve. Trigonometry

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132 Graphing the trigonometric ratios – III Tangent curve. Trigonometry

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133 Graphing the trigonometric ratios – IV Reciprocal ratio… Trigonometry

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134 Trigonometric ratios. Trigonometry

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135 Using the calculator. Trigonometry

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136 Using the trigonometric ratios to find unknown length. … Trigonometry

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137 Using the trigonometric ratios to find unknown length. … Trigonometry

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138 Using the trigonometric ratios to find unknown length. … Trigonometry

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139 Unknown in the denominator. [Case 4]. Trigonometry

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140 Angles of elevation and depression. Trigonometry

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141 Trigonometric ratios in practical situations. Trigonometry

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142 Using the calculator to find an angle given a trigonome… Trigonometry

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143 Using the trigonometric ratios to find an angle in a ri… Trigonometry

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144 Trigonometric ratios of 30., 45. and 60. – exact ratios… Trigonometry

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145 The cosine rule to find an unknown side. [Case 1 SAS]. Trigonometry

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To be done
146 The cosine rule to find an unknown angle. [Case 2 SSS]. Trigonometry

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147 The sine rule to find an unknown side. Case 1. Trigonometry

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148 The sine rule to find an unknown angle. Case 2. Trigonometry

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149 The area formula Trigonometry

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150 Reciprocal ratios. Trigonometry

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151 Trigonometric identities Trigonometry

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152 Angles of any magnitude Trigonometry

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153 Trigonometric ratios of 0°, 90°, 180°, 270° and 360° Trigonometry

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154 Using one ratio to find another. Trigonometry

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155 Solving trigonometric equations – Type I. Trigonometry

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156 Solving trigonometric equations – Type II. Trigonometry

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157 Solving trigonometric equations – Type III. Trigonometry

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158 Plotting polar coordinates and converting polar to rect… Trigonometry

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159 Converting rectangular coordinates to polar form Trigonometry

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160 Write and graph points in polar form with negative vect… Trigonometry

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161 Sin(A+B) etc sum and difference identities (Stage 2) Trigonometry

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162 Double angle formulas (Stage 2) Trigonometry

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163 Half angle identities (Stage 2) Trigonometry

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164 t Formulas (Stage 2) Trigonometry

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165 The exponential function. Exponentials

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166 Logarithmic functions. Logarithms

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167 Powers of 2. Logarithms

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168 Equations of type log x to the base 3 = 4. Logarithms

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169 Equations of type log 32 to the base x = 5. Logarithms

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170 Laws of logarithms. Logarithms

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171 Using the log laws to expand logarithmic expressions. Logarithms

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172 Using the log laws to simplify expressions involving lo… Logarithms

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173 Using the log laws to find the logarithms of numbers. Logarithms

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174 Equations involving logarithms. Logarithms

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175 Using logarithms to solve equations. Logarithms

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176 Change of base formula Logarithms

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177 The graph of the logarithmic curve Logarithms

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178 Working with log curves. Logarithms

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179 Definition, domain and range Functions

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180 Notation and evaluations Functions

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181 More on domain and range Functions

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182 Domain and range from graphical representations Functions

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183 Evaluating and graphing piecewise functions Functions

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184 Functions combinations Functions

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185 Composition of functions Functions

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186 Inverse functions Functions

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187 Rational functions Part 1 Functions

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188 Rational functions Part 2 Functions

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189 Parametric equations (Stage 2) Functions

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190 Polynomial addition etc in combining and simplifying fu… Functions

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191 Parametric functions (Stage 2) Functions

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192 Vectors Matrices

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193 Average speed Speed

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194 Using subscripted variables Speed

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195 Uniform motion with equal distances Speed

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196 Uniform motion adding the distances Speed

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197 Uniform motion with unequal distances Speed

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198 Uniform motion of all types Speed

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199 Motion under gravity – objects in vertical motion Speed

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200 Introducing initial velocity Speed

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201 Newton’s method of approximation Approximation

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202 Imaginary numbers and standard form Complex numbers

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203 Complex numbers – multiplication and division Complex numbers

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204 Plotting complex number and graphical representation Complex numbers

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205 Absolute value Complex numbers

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206 Trigonometric form of a complex number Complex numbers

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207 Multiplication and division of complex numbers in trig … Complex numbers

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208 DeMoivre’s theorem (Stage 2) Complex numbers

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209 The nth root of real and complex numbers (Stage 2) Complex numbers

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210 Fundamental theorem of algebra (Stage 2) Complex numbers

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211 Basic concepts – Matrices Matrices

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212 Addition and subtraction of matrices Matrices

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213 Scalar matrix multiplication Matrices

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214 Multiplication of one matrix by another matrix Matrices

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215 Translation in the number plane Matrices

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216 Translation by matrix multiplication Matrices

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217 Number of solutions (Stage 2) Matrices

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218 2 vector addition in 2 and 3D (stage 2) Matrices

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219 Optimal solutions (Stage 2) – Vectors Matrices

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220 Linear systems with matrices (Stage 2) Matrices

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221 Row-echelon form (Stage 2) Matrices

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222 Gauss Jordan elimination method (Stage 2) Matrices

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223 The parabola: to describe properties of a parabola from… Parabola

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224 The rectangular hyperbola. Conic sections

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225 Introduction to conic sections and their general equati… Conic sections

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226 The parabola x. = 4ay Conic sections

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227 Circles Conic sections

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228 Ellipses Conic sections

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229 Hyperbola Conic sections

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230 Exam – KS5 – Maths – Core Review of all course work

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