Skip to main content

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