KS4 – Higher Mathematics – Wales
KS4 – Higher Mathematics
| # | TOPIC | TITLE | ||
|---|---|---|---|---|
| 1 | Initial Assessment | Initial Assessment | ||
| 2 | N Multiplication and division | Multiplying 4-digit numbers by 3-digit numbers | ||
| 3 | N Multiplication and division | Multiplying 4-digit numbers by 4-digit number | ||
| 4 | N Decimals | Multiplying decimals by 10, 100 and 1000 | ||
| 5 | N Multiplication and division | Repeated subtraction with divisors greater than 20 with… | ||
| 6 | N Multiplication and division | Repeated subtraction with divisors less than 35 with so… | ||
| 7 | N Multiplication and division | Repeated subtraction with divisors less than 55 with di… | ||
| 8 | N Multiplication and division | Repeated subtraction with divisors greater than 50 with… | ||
| 9 | N Multiplication and division | Using divide, multiply and subtraction in the bring dow… | ||
| 10 | N Decimals | Dividing decimals by 10, 100 and 1000 | ||
| 11 | N Simplifying | Directed numbers: addition and subtraction. | ||
| 12 | N Simplifying | Directed numbers: multiplication and division. | ||
| 13 | N Bidmas | Using Order of Operation procedures (BIDMAS) with Fract… | ||
| 14 | N Multiplication and division | Multiples and factors of whole numbers | ||
| 15 | N Multiples and factors | Highest common factor. | ||
| 16 | N Multiples and factors | Factors by grouping. | ||
| 17 | N Decimals | Rounding decimals | ||
| 18 | N Decimals | Decimals to three decimal places | ||
| 19 | N Decimals | Adding decimals with a different number of decimal plac… | ||
| 20 | N Decimals | Subtracting decimals with a different number of places | ||
| 21 | N Decimals | Multiplying decimals by whole numbers | ||
| 22 | N Decimals | Multiplication of decimals by decimals to two decimal p… | ||
| 23 | N Decimals | Dividing decimal fractions by whole numbers | ||
| 24 | N Decimals | Dividing numbers by a decimal fraction | ||
| 25 | N Fractions | Adding and subtracting fractions with different denomin… | ||
| 26 | N Fractions | Multiplying fractions by whole numbers | ||
| 27 | N Fractions | Fractions of whole numbers | ||
| 28 | N Fractions | Multiplying fractions | ||
| 29 | N Fractions | Multiplying mixed numbers (mixed numerals) | ||
| 30 | N Fractions | Finding reciprocals of fractions and mixed numbers (mix… | ||
| 31 | N Fractions | Dividing fractions | ||
| 32 | N Fractions | Dividing mixed numbers (mixed numerals) | ||
| 33 | N Indices | Adding indices when multiplying terms with the same bas… | ||
| 34 | N Indices | Subtracting indices when dividing terms with the same b… | ||
| 35 | N Indices | Multiplying indices when raising a power to a power | ||
| 36 | N Indices | Multiplying indices when raising to more than one term | ||
| 37 | N Indices | Terms raised to the power of zero | ||
| 38 | N Indices | Negative Indices | ||
| 39 | N Indices | Fractional indices | ||
| 40 | N Indices | Complex fractions as indices | ||
| 41 | N Percentages | Calculating Percentages and Fractions of Quantities | ||
| 42 | N Percentages | Introduction to percentages, including converting fract… | ||
| 43 | N Percentages | Changing fractions and decimals to percentages using te… | ||
| 44 | N Percentages | Changing percentages to fractions and decimals | ||
| 45 | N Percentages | One quantity as a percentage of another | ||
| 46 | N Percentages | Compound interest | ||
| 47 | N Approximation | Significant figures | ||
| 48 | N Speed | Average speed | ||
| 49 | N Standard form | Scientific notation with larger numbers | ||
| 50 | N Standard form | Scientific notation with small numbers | ||
| 51 | N Standard form | Changing scientific notation to numerals | ||
| 52 | N Sets | Number sets and their members | ||
| 53 | N Real numbers | Properties of real numbers using addition and multiplic… | ||
| 54 | N Surds | Introducing surds | ||
| 55 | N Surds | Some rules for the operations with surds | ||
| 56 | N Surds | Simplifying surds | ||
| 57 | N Surds | Creating entire surds | ||
| 58 | N Surds | Adding and subtracting like surds | ||
| 59 | N Surds | Expanding surds | ||
| 60 | N Surds | Conjugate binomials with surds | ||
| 61 | N Surds | Rationalising the denominator | ||
| 62 | N Surds | Rationalising binomial denominators | ||
| 63 | M Problem solving | Compare and convert formal units of measurement | ||
| 64 | M Capacity | Estimate, measure and compare the capacity of container… | ||
| 65 | M Problem solving | Areas of rectangles and parallelograms | ||
| 66 | M Problem solving | Finding the area of a triangle and other composite shap… | ||
| 67 | M Problem solving | Area of a trapezium. | ||
| 68 | M Problem solving | Area of a rhombus. | ||
| 69 | M Problem solving | Area of a circle. | ||
| 70 | M Problem solving | Area of regular polygons and composite figures. | ||
| 71 | M Surface area | Surface area of a cube/rectangular prism. | ||
| 72 | M Surface area | Surface area of a triangular/trapezoidal prism. | ||
| 73 | M Surface area | Surface area of a cylinder and sphere. | ||
| 74 | M Surface area | Surface area of pyramids | ||
| 75 | M Surface area | Surface area of cones | ||
| 76 | M Surface area | Surface area of composite solids | ||
| 77 | M Volume | Introducing the formula for volume. | ||
| 78 | M Volume | Using the cubic metre to measure volume. | ||
| 79 | M Volume | Solving Problems about Volume – Part 1. | ||
| 80 | M Volume | Solving Problems about Volume – Part 2. | ||
| 81 | M Volume | Finding the volume of prisms | ||
| 82 | M Volume | Volume of a cylinder and sphere. | ||
| 83 | M Volume | Volume of pyramids and cones. | ||
| 84 | M Volume | Composite solids. | ||
| 85 | M Problem solving | Problems with length. | ||
| 86 | M Problem solving | Problems with mass. | ||
| 87 | M Problem solving | Problems with area. | ||
| 88 | M Problem solving | Problems with volume/capacity. | ||
| 89 | G Triangles | Using the prefix to determine polygons | ||
| 90 | G 3D shapes | Recognise and name prisms according to spatial properti… | ||
| 91 | G 3D shapes | Recognise and name pyramids according to spatial proper… | ||
| 92 | G 3D shapes | Recognise nets for prisms, pyramids, cubes and cones | ||
| 93 | G 3D shapes | Viewing 3-D shapes. | ||
| 94 | G 3D shapes | Constructing models. | ||
| 95 | G Angles | Adjacent angles | ||
| 96 | G Angles | Complementary and supplementary angles | ||
| 97 | G Angles | Vertically opposite angles | ||
| 98 | G Angles | Angles at a Point. | ||
| 99 | G Angles | Parallel Lines. | ||
| 100 | G Angles | Additional questions involving parallel lines | ||
| 101 | G Angles | Angle sum of a triangle | ||
| 102 | G Angles | Exterior angle theorem | ||
| 103 | G Angles | To determine angle labelling rules, naming angles accor… | ||
| 104 | G Angles | More difficult exercises involving parallel lines | ||
| 105 | AS Series and sequences | Further difficult exercises involving formal reasoning | ||
| 106 | G Angles | Angles of regular polygons | ||
| 107 | G Angles | Complementary angle results. | ||
| 108 | G Angles | Bearings – the compass. | ||
| 109 | G Angles | Theorem – Equal arcs on circles of equal radii subtend … | ||
| 110 | G Angles | Theorem – The perpendicular from the centre of a circle… | ||
| 111 | G Angles | Theorem – Equal chords in equal circles are equidistant… | ||
| 112 | G Angles | Theorem – The angle at the centre of a circle is double… | ||
| 113 | G Angles | Theorem – Angles in the same segment of a circle are eq… | ||
| 114 | G Angles | Theorem – The angle of a semi-circle is a right angle. | ||
| 115 | G Angles | Theorem – The opposite angles of a cyclic quadrilateral… | ||
| 116 | G Angles | Theorem – The exterior angle at a vertex of a cyclic qu… | ||
| 117 | G Angles | Theorem – The tangent to a circle is perpendicular to t… | ||
| 118 | G Angles | Theorem – Tangents to a circle from an external point a… | ||
| 119 | G Angles | Theorem – The angle between a tangent and a chord throu… | ||
| 120 | G Angles | Theorem – The products of the intercepts of two interse… | ||
| 121 | G Angles | Theorem – The square of the length of the tangent from … | ||
| 122 | G Angles | Theorem – If the opposite angles in a quadrilateral are… | ||
| 123 | G Angles | Theorem – If an interval subtends equal angles at two p… | ||
| 124 | G Angles | Theorem – When circles touch, the line of the centres p… | ||
| 125 | G Angles | Theorem – Any three non-collinear points lie on a uniqu… | ||
| 126 | G Construction | Geometric constructions | ||
| 127 | G Construction | To identify collinear points, coplanar lines and points… | ||
| 128 | G Construction | Angle bisector construction and its properties (Stage 2… | ||
| 129 | G Construction | Circumcentre and incentre (Stage 2) | ||
| 130 | G Construction | Orthocentre and centroids (Stage 2) | ||
| 131 | G Construction | Constructions and loci – single condition | ||
| 132 | G Construction | Constructions and loci – multiple conditions | ||
| 133 | G Triangles | Spatial properties of quadrilaterals | ||
| 134 | G Similar shapes | Similar triangles | ||
| 135 | G Similar shapes | Using similar triangles to calculate lengths | ||
| 136 | G Similar shapes | Special triangles | ||
| 137 | G Transformations | Use grids to enlarge/reduce 2D shapes | ||
| 138 | G Transformations | Special transformations – reflections, rotations and en… | ||
| 139 | G Transformations | Transformations – reflections | ||
| 140 | G Transformations | Geometry transformations without matrices: reflection (… | ||
| 141 | G Transformations | Geometry transformations without matrices: translation … | ||
| 142 | G Transformations | Geometry transformations without matrices: rotation (St… | ||
| 143 | G Transformations | Geometry transformations without matrices: dilation or … | ||
| 144 | G Transformations | The definition and concept of combined transformations … | ||
| 145 | G Triangles | Recognise and name triangles | ||
| 146 | G Quadrilaterals | Midsegments of Triangles | ||
| 147 | G Triangles | Congruent triangles, Test 1 and 2 | ||
| 148 | G Triangles | Congruent triangles, Test 3 and 4 | ||
| 149 | G Triangles | Proofs and congruent triangles. | ||
| 150 | G Triangles | Examples involving overlapping triangles | ||
| 151 | G Pythagoras | Find the hypotenuse | ||
| 152 | G Pythagoras | Pythagorean triples | ||
| 153 | G Pythagoras | Find the hypotenuse Part 2 | ||
| 154 | G Pythagoras | Calculating a leg of a right-angled triangle | ||
| 155 | G Pythagoras | Proofs of Pythagoras theorem | ||
| 156 | G Trigonometry | Graphing the trigonometric ratios – I Sine curve. | ||
| 157 | G Trigonometry | Graphing the trigonometric ratios – II Cosine curve. | ||
| 158 | G Trigonometry | Graphing the trigonometric ratios – III Tangent curve. | ||
| 159 | G Trigonometry | Graphing the trigonometric ratios – IV Reciprocal ratio… | ||
| 160 | G Trigonometry | Trigonometric ratios. | ||
| 161 | G Trigonometry | Using the calculator. | ||
| 162 | G Trigonometry | Using the trigonometric ratios to find unknown length. … | ||
| 163 | G Trigonometry | Using the trigonometric ratios to find unknown length. … | ||
| 164 | G Trigonometry | Using the trigonometric ratios to find unknown length. … | ||
| 165 | G Trigonometry | Unknown in the denominator. [Case 4]. | ||
| 166 | G Trigonometry | Angles of elevation and depression. | ||
| 167 | G Trigonometry | Trigonometric ratios in practical situations. | ||
| 168 | G Trigonometry | Using the calculator to find an angle given a trigonome… | ||
| 169 | G Trigonometry | Using the trigonometric ratios to find an angle in a ri… | ||
| 170 | G Trigonometry | Trigonometric ratios of 30., 45. and 60. – exact ratios… | ||
| 171 | G Trigonometry | The cosine rule to find an unknown side. [Case 1 SAS]. | ||
| 172 | G Trigonometry | The cosine rule to find an unknown angle. [Case 2 SSS]. | ||
| 173 | G Trigonometry | The sine rule to find an unknown side. Case 1. | ||
| 174 | G Trigonometry | The sine rule to find an unknown angle. Case 2. | ||
| 175 | G Trigonometry | The area formula | ||
| 176 | G Trigonometry | Reciprocal ratios. | ||
| 177 | G Trigonometry | Angles of any magnitude | ||
| 178 | G Trigonometry | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | ||
| 179 | G Coordinate geometry | Distance formula. | ||
| 180 | G Coordinate geometry | Mid-point formula | ||
| 181 | G Coordinate geometry | Gradient | ||
| 182 | G Coordinate geometry | Gradient formula. | ||
| 183 | G Coordinate geometry | The straight line. | ||
| 184 | G Coordinate geometry | Lines through the origin. | ||
| 185 | G Coordinate geometry | General form of a line and the x and y Intercepts. | ||
| 186 | AS Series and sequences | General sequences. | ||
| 187 | AS Series and sequences | Finding Tn given Sn. | ||
| 188 | A Simplifying | Algebraic expressions. | ||
| 189 | A Simplifying | Simplifying Algebraic expressions: combining addition a… | ||
| 190 | A Simplifying | Simplifying algebraic expressions: multiplication | ||
| 191 | A Simplifying | Simplifying algebraic expressions: division | ||
| 192 | A Simplifying | Expanding algebraic expressions: multiplication | ||
| 193 | A Simplifying | Expanding algebraic expressions: negative multiplier | ||
| 194 | A Simplifying | Expanding and simplifying algebraic expressions | ||
| 195 | A Simplifying | Simplifying algebraic fractions using the index laws. | ||
| 196 | A Simplifying | Algebraic fractions resulting in negative indices. | ||
| 197 | A Simplifying | Cancelling binomial factors in algebraic fractions. | ||
| 198 | A Simplifying | Products in simplification of algebraic expressions | ||
| 199 | A Simplifying | Algebraic Expressions – Larger expansions. | ||
| 200 | A Simplifying | Simplifying algebraic fractions. | ||
| 201 | A Inequalities | Simplifying absolute values | ||
| 202 | A Graphs | Quadratic polynomials of the form y = ax. + bx + c. | ||
| 203 | A Graphs | Graphing perfect squares: y=(a-x) squared | ||
| 204 | A Graphs | Solve by graphing | ||
| 205 | A Graphs | Graphing cubic curves | ||
| 206 | A Equations | Solving equations containing addition and subtraction | ||
| 207 | A Equations | Solving equations containing multiplication and divisio… | ||
| 208 | A Equations | Solving two step equations | ||
| 209 | A Equations | Solving equations containing binomial expressions | ||
| 210 | A Equations | Equations involving grouping symbols. | ||
| 211 | A Equations | Equations involving fractions. | ||
| 212 | A Inequalities | Solving for the variable | ||
| 213 | A Equations | Simultaneous equations | ||
| 214 | A Equations | Elimination method | ||
| 215 | A Equations | Elimination method part 2 | ||
| 216 | A Equations | Applications of simultaneous equations | ||
| 217 | A Factorising | Expansions leading to the difference of two squares | ||
| 218 | A Factorising | Common factor and the difference of two squares | ||
| 219 | A Factorising | Factorising quadratic trinomials [monic] – Case 2. | ||
| 220 | A Factorising | Factorising quadratic trinomials [monic] – Case 3. | ||
| 221 | A Factorising | Factorising quadratic trinomials [monic] – Case 4. | ||
| 222 | A Factorising | Factorisation of non-monic quadratic trinomials | ||
| 223 | A Factorising | Factorisation of non-monic quadratic trinomials – moon … | ||
| 224 | A Simplifying | Substitution into algebraic expressions. | ||
| 225 | A Formulae | Equations resulting from substitution into formulae. | ||
| 226 | A Formulae | Changing the subject of the formula. | ||
| 227 | A Factorising | Simplifying easy algebraic fractions. | ||
| 228 | A Factorising | Factorisation of algebraic fractions including binomial… | ||
| 229 | A Inequalities | Solving Inequalities. | ||
| 230 | A Inequalities | Solving and graphing inequalities | ||
| 231 | A Inequalities | Inequalities on the number plane. | ||
| 232 | A Roots | Difference of two squares | ||
| 233 | A Roots | Quadratic trinomials [monic] – Case 1. | ||
| 234 | A Roots | Introduction to quadratic equations. | ||
| 235 | A Roots | Quadratic equations with factorisation. | ||
| 236 | A Roots | Solving quadratic equations. | ||
| 237 | A Roots | The quadratic formula | ||
| 238 | A Roots | Problem solving with quadratic equations | ||
| 239 | A Roots | Solving simultaneous quadratic equations graphically | ||
| 240 | A Matrices | Vectors | ||
| 241 | S Scatter diagrams | The range. | ||
| 242 | S Probability | The mode | ||
| 243 | S Probability | The mean | ||
| 244 | S Probability | The median | ||
| 245 | S Probability | Calculating the median from a frequency distribution | ||
| 246 | S Averages | Calculating mean, mode and median from grouped data | ||
| 247 | S Averages | Range as a measure of dispersion | ||
| 248 | S Averages | Measures of spread | ||
| 249 | S Averages | Measures of spread: the interquartile range | ||
| 250 | S Pie charts | Pie and bar graphs. | ||
| 251 | S Scatter diagrams | Scatter Diagrams | ||
| 252 | S Scatter diagrams | Stem and Leaf Plots along with Box and Whisker Plots | ||
| 253 | S Probability | Cumulative frequency | ||
| 254 | S Scatter diagrams | Frequency histograms and polygons | ||
| 255 | S Pie charts | Line graphs. | ||
| 256 | P Scatter diagrams | Frequency distribution table | ||
| 257 | P Scatter diagrams | Relative frequency | ||
| 258 | P Probability | Probability of Simple Events | ||
| 259 | P Probability | Rolling a pair of dice | ||
| 260 | P Probability | Experimental probability | ||
| 261 | P Probability | Tree diagrams – not depending on previous outcomes | ||
| 262 | P Probability | Tree diagrams – depending on previous outcomes | ||
| 263 | End of Course Assessment | End of Course Assessment |
Other courses in this curriculum
- KS2 - Year 5 Mathematics - Wales
- KS2 - Year 6 Mathematics - Wales
- KS3 - Year 7 Mathematics - Wales
- KS3 - Year 8 Mathematics - Wales
- KS3 - Year 9 Mathematics - Wales
- KS4 - Foundation Mathematics - Wales
- KS5 - Core Mathematics - Wales
- KS5 - Statistics Mathematics - Wales
- OCR - GCSE Revision Foundation Mathematics - Wales
- OCR - GCSE Revision Higher Mathematics - Wales
- WJEC - GCSE Revision Foundation Mathematics - Wales
- WJEC - GCSE Revision Higher Mathematics - Wales
