KS5 – Core Mathematics – England
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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4  Multiplying indices when raising to more than one term  Indices 
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5  Terms raised to the power of zero  Indices 
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6  Negative Indices  Indices 
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7  Fractional indices  Indices 
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8  Complex fractions as indices  Indices 
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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 nonmonic quadratic trinomials  Factorising 
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33  Factorisation of nonmonic 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=(ax) 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  Midpoint 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  Coordinate 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 [nonmonic].  Binomial 
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97  Squaring a binomial. [monic]  Binomial 
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98  Squaring a binomial [nonmonic].  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 – antidifferentiation, 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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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  Rowechelon 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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To be done 