KS4 – Higher Mathematics – England
KS4 – Higher Mathematics
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| 1 | Multiplying 4-digit numbers by 3-digit numbers | Multiplication and division |
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| 2 | Multiplying 4-digit numbers by 4-digit number | Multiplication and division |
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| 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 3-D 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 semi-circle 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 non-collinear 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 right-angled 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 | Mid-point 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=(a-x) 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 non-monic quadratic trinomials | Factorising |
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| 222 | Factorisation of non-monic 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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To be done |
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