KS4 – Higher Mathematics – England
KS4 – Higher Mathematics
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1  Multiplying 4digit numbers by 3digit numbers  Multiplication and division 
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Current lesson  
2  Multiplying 4digit numbers by 4digit number  Multiplication and division 
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To be done  
3  Multiplying decimals by 10, 100 and 1000  Decimals 
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4  Repeated subtraction with divisors greater than 20 with…  Multiplication and division 
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5  Repeated subtraction with divisors less than 35 with so…  Multiplication and division 
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6  Repeated subtraction with divisors less than 55 with di…  Multiplication and division 
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7  Repeated subtraction with divisors greater than 50 with…  Multiplication and division 
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8  Using divide, multiply and subtraction in the bring dow…  Multiplication and division 
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9  Dividing decimals by 10, 100 and 1000  Decimals 
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10  Directed numbers: addition and subtraction.  Simplifying 
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11  Directed numbers: multiplication and division.  Simplifying 
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12  Using Order of Operation procedures (BIDMAS) with Fract…  Bidmas 
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13  Multiples and factors of whole numbers  Multiplication and division 
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14  Highest common factor.  Multiples and factors 
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15  Factors by grouping.  Multiples and factors 
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16  Rounding decimals  Decimals 
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17  Decimals to three decimal places  Decimals 
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18  Adding decimals with a different number of decimal plac…  Decimals 
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19  Subtracting decimals with a different number of places  Decimals 
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20  Multiplying decimals by whole numbers  Decimals 
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21  Multiplication of decimals by decimals to two decimal p…  Decimals 
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22  Dividing decimal fractions by whole numbers  Decimals 
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23  Dividing numbers by a decimal fraction  Decimals 
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24  Adding and subtracting fractions with different denomin…  Fractions 
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25  Multiplying fractions by whole numbers  Fractions 
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26  Fractions of whole numbers  Fractions 
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27  Multiplying fractions  Fractions 
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28  Multiplying mixed numbers (mixed numerals)  Fractions 
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29  Finding reciprocals of fractions and mixed numbers (mix…  Fractions 
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30  Dividing fractions  Fractions 
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31  Dividing mixed numbers (mixed numerals)  Fractions 
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32  Adding indices when multiplying terms with the same bas…  Indices 
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33  Subtracting indices when dividing terms with the same b…  Indices 
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34  Multiplying indices when raising a power to a power  Indices 
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35  Multiplying indices when raising to more than one term  Indices 
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36  Terms raised to the power of zero  Indices 
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37  Negative Indices  Indices 
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38  Fractional indices  Indices 
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39  Complex fractions as indices  Indices 
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40  Calculating Percentages and Fractions of Quantities  Percentages 
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41  Introduction to percentages, including converting fract…  Percentages 
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42  Changing fractions and decimals to percentages using te…  Percentages 
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43  Changing percentages to fractions and decimals  Percentages 
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44  One quantity as a percentage of another  Percentages 
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45  Compound interest  Percentages 
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46  Significant figures  Approximation 
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47  Average speed  Speed 
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48  Scientific notation with larger numbers  Standard form 
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49  Scientific notation with small numbers  Standard form 
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50  Changing scientific notation to numerals  Standard form 
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51  Number sets and their members  Sets 
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52  Properties of real numbers using addition and multiplic…  Real numbers 
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53  Introducing surds  Surds 
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54  Some rules for the operations with surds  Surds 
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55  Simplifying surds  Surds 
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56  Creating entire surds  Surds 
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57  Adding and subtracting like surds  Surds 
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58  Expanding surds  Surds 
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59  Conjugate binomials with surds  Surds 
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60  Rationalising the denominator  Surds 
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61  Rationalising binomial denominators  Surds 
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62  Compare and convert formal units of measurement  Problem solving 
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63  Estimate, measure and compare the capacity of container…  Capacity 
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64  Areas of rectangles and parallelograms  Problem solving 
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65  Finding the area of a triangle and other composite shap…  Problem solving 
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66  Area of a trapezium.  Problem solving 
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67  Area of a rhombus.  Problem solving 
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68  Area of a circle.  Problem solving 
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69  Area of regular polygons and composite figures.  Problem solving 
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70  Surface area of a cube/rectangular prism.  Surface area 
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71  Surface area of a triangular/trapezoidal prism.  Surface area 
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72  Surface area of a cylinder and sphere.  Surface area 
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73  Surface area of pyramids  Surface area 
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74  Surface area of cones  Surface area 
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75  Surface area of composite solids  Surface area 
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76  Introducing the formula for volume.  Volume 
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77  Using the cubic metre to measure volume.  Volume 
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78  Solving Problems about Volume – Part 1.  Volume 
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79  Solving Problems about Volume – Part 2.  Volume 
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80  Finding the volume of prisms  Volume 
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81  Volume of a cylinder and sphere.  Volume 
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82  Volume of pyramids and cones.  Volume 
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83  Composite solids.  Volume 
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84  Problems with length.  Problem solving 
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85  Problems with mass.  Problem solving 
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86  Problems with area.  Problem solving 
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87  Problems with volume/capacity.  Problem solving 
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88  Using the prefix to determine polygons  Triangles 
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89  Recognise and name prisms according to spatial properti…  3D shapes 
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90  Recognise and name pyramids according to spatial proper…  3D shapes 
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91  Recognise nets for prisms, pyramids, cubes and cones  3D shapes 
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92  Viewing 3D shapes.  3D shapes 
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93  Constructing models.  3D shapes 
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94  Adjacent angles  Angles 
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95  Complementary and supplementary angles  Angles 
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96  Vertically opposite angles  Angles 
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97  Angles at a Point.  Angles 
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98  Parallel Lines.  Angles 
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99  Additional questions involving parallel lines  Angles 
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100  Angle sum of a triangle  Angles 
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101  Exterior angle theorem  Angles 
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102  To determine angle labelling rules, naming angles accor…  Angles 
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103  More difficult exercises involving parallel lines  Angles 
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104  Further difficult exercises involving formal reasoning  Series and sequences 
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105  Angles of regular polygons  Angles 
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106  Complementary angle results.  Angles 
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107  Bearings – the compass.  Angles 
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108  Theorem – Equal arcs on circles of equal radii subtend …  Angles 
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109  Theorem – The perpendicular from the centre of a circle…  Angles 
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110  Theorem – Equal chords in equal circles are equidistant…  Angles 
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111  Theorem – The angle at the centre of a circle is double…  Angles 
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112  Theorem – Angles in the same segment of a circle are eq…  Angles 
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113  Theorem – The angle of a semicircle is a right angle.  Angles 
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114  Theorem – The opposite angles of a cyclic quadrilateral…  Angles 
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115  Theorem – The exterior angle at a vertex of a cyclic qu…  Angles 
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116  Theorem – The tangent to a circle is perpendicular to t…  Angles 
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117  Theorem – Tangents to a circle from an external point a…  Angles 
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118  Theorem – The angle between a tangent and a chord throu…  Angles 
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119  Theorem – The products of the intercepts of two interse…  Angles 
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120  Theorem – The square of the length of the tangent from …  Angles 
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121  Theorem – If the opposite angles in a quadrilateral are…  Angles 
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122  Theorem – If an interval subtends equal angles at two p…  Angles 
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123  Theorem – When circles touch, the line of the centres p…  Angles 
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124  Theorem – Any three noncollinear points lie on a uniqu…  Angles 
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125  Geometric constructions  Construction 
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126  To identify collinear points, coplanar lines and points…  Construction 
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127  Angle bisector construction and its properties (Stage 2…  Construction 
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128  Circumcentre and incentre (Stage 2)  Construction 
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129  Orthocentre and centroids (Stage 2)  Construction 
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130  Constructions and loci – single condition  Construction 
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131  Constructions and loci – multiple conditions  Construction 
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132  Spatial properties of quadrilaterals  Triangles 
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133  Similar triangles  Similar shapes 
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134  Using similar triangles to calculate lengths  Similar shapes 
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135  Special triangles  Similar shapes 
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136  Use grids to enlarge/reduce 2D shapes  Transformations 
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137  Special transformations – reflections, rotations and en…  Transformations 
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138  Transformations – reflections  Transformations 
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139  Geometry transformations without matrices: reflection (…  Transformations 
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140  Geometry transformations without matrices: translation …  Transformations 
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141  Geometry transformations without matrices: rotation (St…  Transformations 
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142  Geometry transformations without matrices: dilation or …  Transformations 
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143  The definition and concept of combined transformations …  Transformations 
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144  Recognise and name triangles  Triangles 
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145  Midsegments of Triangles  Quadrilaterals 
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146  Congruent triangles, Test 1 and 2  Triangles 
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147  Congruent triangles, Test 3 and 4  Triangles 
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148  Proofs and congruent triangles.  Triangles 
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149  Examples involving overlapping triangles  Triangles 
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150  Find the hypotenuse  Pythagoras 
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151  Pythagorean triples  Pythagoras 
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152  Find the hypotenuse Part 2  Pythagoras 
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153  Calculating a leg of a rightangled triangle  Pythagoras 
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154  Proofs of Pythagoras theorem  Pythagoras 
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155  Graphing the trigonometric ratios – I Sine curve.  Trigonometry 
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156  Graphing the trigonometric ratios – II Cosine curve.  Trigonometry 
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157  Graphing the trigonometric ratios – III Tangent curve.  Trigonometry 
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158  Graphing the trigonometric ratios – IV Reciprocal ratio…  Trigonometry 
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159  Trigonometric ratios.  Trigonometry 
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160  Using the calculator.  Trigonometry 
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161  Using the trigonometric ratios to find unknown length. …  Trigonometry 
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162  Using the trigonometric ratios to find unknown length. …  Trigonometry 
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163  Using the trigonometric ratios to find unknown length. …  Trigonometry 
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164  Unknown in the denominator. [Case 4].  Trigonometry 
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165  Angles of elevation and depression.  Trigonometry 
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166  Trigonometric ratios in practical situations.  Trigonometry 
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167  Using the calculator to find an angle given a trigonome…  Trigonometry 
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168  Using the trigonometric ratios to find an angle in a ri…  Trigonometry 
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169  Trigonometric ratios of 30., 45. and 60. – exact ratios…  Trigonometry 
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170  The cosine rule to find an unknown side. [Case 1 SAS].  Trigonometry 
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171  The cosine rule to find an unknown angle. [Case 2 SSS].  Trigonometry 
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172  The sine rule to find an unknown side. Case 1.  Trigonometry 
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173  The sine rule to find an unknown angle. Case 2.  Trigonometry 
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174  The area formula  Trigonometry 
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175  Reciprocal ratios.  Trigonometry 
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176  Angles of any magnitude  Trigonometry 
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177  Trigonometric ratios of 0°, 90°, 180°, 270° and 360°  Trigonometry 
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178  Distance formula.  Coordinate geometry 
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179  Midpoint formula  Coordinate geometry 
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180  Gradient  Coordinate geometry 
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181  Gradient formula.  Coordinate geometry 
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182  The straight line.  Coordinate geometry 
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183  Lines through the origin.  Coordinate geometry 
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184  General form of a line and the x and y Intercepts.  Coordinate geometry 
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185  General sequences.  Series and sequences 
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186  Finding Tn given Sn.  Series and sequences 
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187  Algebraic expressions.  Simplifying 
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188  Simplifying Algebraic expressions: combining addition a…  Simplifying 
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189  Simplifying algebraic expressions: multiplication  Simplifying 
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190  Simplifying algebraic expressions: division  Simplifying 
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191  Expanding algebraic expressions: multiplication  Simplifying 
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192  Expanding algebraic expressions: negative multiplier  Simplifying 
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193  Expanding and simplifying algebraic expressions  Simplifying 
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194  Simplifying algebraic fractions using the index laws.  Simplifying 
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195  Algebraic fractions resulting in negative indices.  Simplifying 
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196  Cancelling binomial factors in algebraic fractions.  Simplifying 
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197  Products in simplification of algebraic expressions  Simplifying 
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198  Algebraic Expressions – Larger expansions.  Simplifying 
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199  Simplifying algebraic fractions.  Simplifying 
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200  Simplifying absolute values  Inequalities 
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201  Quadratic polynomials of the form y = ax. + bx + c.  Graphs 
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202  Graphing perfect squares: y=(ax) squared  Graphs 
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203  Solve by graphing  Graphs 
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204  Graphing cubic curves  Graphs 
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205  Solving equations containing addition and subtraction  Equations 
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206  Solving equations containing multiplication and divisio…  Equations 
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207  Solving two step equations  Equations 
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208  Solving equations containing binomial expressions  Equations 
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209  Equations involving grouping symbols.  Equations 
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210  Equations involving fractions.  Equations 
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211  Solving for the variable  Inequalities 
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212  Simultaneous equations  Equations 
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213  Elimination method  Equations 
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214  Elimination method part 2  Equations 
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215  Applications of simultaneous equations  Equations 
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216  Expansions leading to the difference of two squares  Factorising 
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217  Common factor and the difference of two squares  Factorising 
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218  Factorising quadratic trinomials [monic] – Case 2.  Factorising 
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219  Factorising quadratic trinomials [monic] – Case 3.  Factorising 
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220  Factorising quadratic trinomials [monic] – Case 4.  Factorising 
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221  Factorisation of nonmonic quadratic trinomials  Factorising 
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222  Factorisation of nonmonic quadratic trinomials – moon …  Factorising 
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223  Substitution into algebraic expressions.  Simplifying 
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224  Equations resulting from substitution into formulae.  Formulae 
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225  Changing the subject of the formula.  Formulae 
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226  Simplifying easy algebraic fractions.  Factorising 
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227  Factorisation of algebraic fractions including binomial…  Factorising 
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228  Solving Inequalities.  Inequalities 
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229  Solving and graphing inequalities  Inequalities 
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230  Inequalities on the number plane.  Inequalities 
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231  Difference of two squares  Roots 
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232  Quadratic trinomials [monic] – Case 1.  Roots 
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233  Introduction to quadratic equations.  Roots 
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234  Quadratic equations with factorisation.  Roots 
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235  Solving quadratic equations.  Roots 
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236  The quadratic formula  Roots 
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237  Problem solving with quadratic equations  Roots 
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238  Solving simultaneous quadratic equations graphically  Roots 
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239  Vectors  Matrices 
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240  The range.  Scatter diagrams 
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241  The mode  Probability 
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242  The mean  Probability 
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243  The median  Probability 
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244  Calculating the median from a frequency distribution  Probability 
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245  Calculating mean, mode and median from grouped data  Averages 
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246  Range as a measure of dispersion  Averages 
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247  Measures of spread  Averages 
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248  Measures of spread: the interquartile range  Averages 
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249  Pie and bar graphs.  Pie charts 
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250  Scatter Diagrams  Scatter diagrams 
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251  Stem and Leaf Plots along with Box and Whisker Plots  Scatter diagrams 
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252  Cumulative frequency  Probability 
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253  Frequency histograms and polygons  Scatter diagrams 
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254  Line graphs.  Pie charts 
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255  Frequency distribution table  Scatter diagrams 
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256  Relative frequency  Scatter diagrams 
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257  Probability of Simple Events  Probability 
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258  Rolling a pair of dice  Probability 
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259  Experimental probability  Probability 
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260  Tree diagrams – not depending on previous outcomes  Probability 
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261  Tree diagrams – depending on previous outcomes  Probability 
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262  Exam – KS4 – Maths – Higher  Review of all course work 
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