FREE GCSE and iGCSE Maths and Lessons

Maths School Skills and Exam Question Problem Solving Workbooks

Our workbooks provide students the appropriate skills and problem solving practice students need to succeed in examinations.

ID Lesson Skills Workbooks Problem Solving Workbooks Unit Level Lesson Content
1

Expressions, equations, identities and formula

AlgebraFoundation, KS3
2

Simplifying Expressions

AlgebraFoundation, KS3
3

Change the subject of a Formula (Part 1)

AlgebraFoundation, KS3
4

Co-ordinates - reading and plotting in all quadrants

AlgebraFoundation, KS3
5

Substitute Numbers into Formula

    AlgebraFoundation, KS3
6

Factorising Expressions

    AlgebraFoundation, KS3
7

Substitute Numbers into Expressions

    AlgebraFoundation, KS3
8

Expanding Single Brackets

    AlgebraFoundation, KS3
9

Re-arranging & solving simple one step equations

AlgebraFoundation, KS3
10

Double Function Machines

AlgebraFoundation, KS3
11

Forming Expressions, Equations or Formula

    AlgebraFoundation, Higher, KS4
12

Function Machines

AlgebraFoundation, KS3
13

Solve inequalities with one or two variables

AlgebraFoundation, Higher, KS4
14

Solving quadratic equations by factorising (Part 1)

AlgebraFoundation, Higher, KS4
15

Trial and Improvement to find approximate solutions of equations

AlgebraFoundation, Higher, KS4
16

Change the subject of a Formula (Part 2) - with powers

AlgebraFoundation, Higher, KS4
17

Find the gradient of a straight line graph using 2 co-ordinates

AlgebraFoundation, Higher, KS4
18

Finding the mid-point of a line

AlgebraFoundation, Higher, KS4
19

Find the length of a line (using Pythagoras)

AlgebraFoundation, Higher, KS4
20

Solve equations that include brackets

AlgebraFoundation, Higher, KS4
21

Functions (Part 3) - Inverse functions

AlgebraHigher, KS4
22

Factorising Quadratics into 2 Brackets with coefficients of x² greater than 1

AlgebraHigher, KS4
23

Solve equations that include powers

AlgebraFoundation, Higher, KS4
24

Solving Fractional equations (Part 1) - Linear

AlgebraFoundation, Higher, KS4
25

Solve equations with unknown on both sides including negative numbers

AlgebraFoundation, Higher, KS4
26

Solve two step equations with unknown on one side and involving fractions

    AlgebraFoundation, Higher, KS4
27

Use elimination to solve simultaneous equations

AlgebraFoundation, Higher, KS4
28

Use substitution to solve simultaneous equations

AlgebraFoundation, Higher, KS4
29

Using number sequences & describe a rule of a sequence

AlgebraFoundation, Higher, KS4
30

Find & use the nth term expression for a sequence

AlgebraFoundation, Higher, KS4
31

Using the nth term expression of a quadratic sequence

AlgebraFoundation, Higher, KS4
32

An Equation of a line - Gradient, Y-intercept and y=mx+c

AlgebraFoundation, Higher, KS4
33

Expanding Double Brackets

AlgebraFoundation, Higher, KS4
34

Drawing Straight Line Graphs

AlgebraFoundation, Higher, KS4
35

Factorising Quadratics into 2 Brackets

AlgebraFoundation, Higher, KS4
36

Drawing Straight Line Graphs to solve linear simultaneous equations on graphs

AlgebraFoundation, Higher, KS4
37

Inequalities on a Number Line

AlgebraFoundation, Higher, KS4
38

Solving quadratic inequalities

AlgebraHigher, KS4
39

Solving quadratic equations by factorising (Part 2) - with coefficients > 1

AlgebraHigher, KS4
40

Solving quadratic equations by using the formula

AlgebraHigher, KS4
41

Perpendicular gradients

AlgebraHigher, KS4
42

Equations of parallel and perpendicular lines

AlgebraHigher, KS4
43

Change the subject of a Formula (Part 3) - by factorising

AlgebraHigher, KS4
44

Factorising using the difference of two squares

AlgebraHigher, KS4
45

Find the equation of a straight line from gradient and co-ordinates

AlgebraHigher, KS4
46

Geometric sequence (Common Ratio)

AlgebraHigher, KS4
47

Solving quadratic equations by completing the square

AlgebraHigher, KS4
48

Completing the square of quadratic expressions (Part 1)

AlgebraHigher, KS4
49

Completing the square of quadratic expressions (Part 2) - with higher coefficients of x^2

AlgebraHigher, KS4
50

Working with Algebraic Fractions (Part 1 - Adding and Subtracting)

AlgebraHigher, KS4
51

Working with Algebraic Fractions (Part 2 - Simplifying by Factorising)

AlgebraHigher, KS4
52

Working with Algebraic Fractions (Part 3 - Multiplying and Dividing)

AlgebraHigher, KS4
53

Find the nth term expression for a quadratic sequence

AlgebraHigher, KS4
54

Circle equations in the form x² + y² = r²

AlgebraHigher, KS4
55

Equation of a Tangent to a circle

AlgebraHigher, KS4
56

Iteration

AlgebraHigher, KS4
57

Solving Quadratic Simultaneous Equations

AlgebraHigher, KS4
58

Turning Points

AlgebraHigher, KS4
59

Triple Brackets

GeometryFoundation, KS3
60

Solving Fractional Equations (Part 2) - Quadratic

AlgebraHigher, KS4
61

Solve quadratic and linear graphs simultaneously

AlgebraHigher, KS4
62

Exponential Growth and Decay

AlgebraHigher, KS4
63

Finding an exponential equation from a graph

AlgebraHigher, KS4
64

Proofs

AlgebraHigher, KS4
65

Functions (Part 1) - notation

AlgebraHigher, KS4
66

Functions (Part 2) - Composite functions

AlgebraHigher, KS4
67

Nets, plans and elevations

GeometryFoundation, KS3
68

Symmetry and rotational symmetry of shapes

GeometryFoundation, KS3
69

Angles in Triangles and Quadrilaterals

GeometryFoundation, KS3
70

Area of Parallelograms

GeometryFoundation, KS3
71

Area of Trapeziums

GeometryFoundation, KS3
72

Area of Rectangles

GeometryFoundation, KS3
73

Area of Compound Shapes

GeometryFoundation, KS3
74

Area of Triangles

GeometryFoundation, KS3
75

Missing angles in right angles, straight lines and around a point

GeometryFoundation, Higher, KS4
76

Parallel and Perpendicular Lines

GeometryFoundation, Higher, KS3
77

Types of angles

    GeometryFoundation, KS3
78

Types of triangles

GeometryFoundation, KS3
79

Circles - know the parts of a circle

GeometryFoundation, KS3
80

Perimeter of shapes

GeometryFoundation, KS3
81

Types of quadrilaterals

    GeometryFoundation, KS3
82

Basic congruent shapes

GeometryFoundation, KS3
83

Pythagoras Theorem

    GeometryFoundation, Higher, KS4
84

Understand and use translations, using vectors and describing translations

GeometryFoundation, Higher, KS4
85

Reflections and describing reflections in mirror lines

GeometryFoundation, Higher, KS4
86

Calculate the length of an arc and area of a sector

GeometryFoundation, Higher, KS4
87

Find the surface area of shapes of cubes and cuboids by using the formulae for rectangles

GeometryFoundation, Higher, KS4
88

Enlargements - Scale Factors

GeometryFoundation, Higher, KS4
89

Enlargements - Enlargements from a point

GeometryFoundation, Higher, KS4
90

Enlargements - Describing enlargements (including finding the centre - positive scale factors)

GeometryFoundation, Higher, KS4
91

Find the Surface Area of Prisms and Cylinders

GeometryFoundation, Higher, KS4
92

Find the Volume of Prisms and Cylinders

    GeometryFoundation, Higher, KS4
93

Rotations and describing rotations

GeometryFoundation, Higher, KS4
94

Solve simple vector problems

GeometryFoundation, Higher, KS4
95

Use the formula to calculate the volume of a cuboid

GeometryFoundation, Higher, KS4
96

Calculate the sum of interior angles in a polygon and external angles add up to 360 degrees, and how shapes tessellate

'Number'Foundation, Higher, KS4
97

Circles - calculate the circumference of a circle

GeometryFoundation, Higher, KS4
98

Circles - calculate the area of a circle

GeometryFoundation, Higher, KS4
99

Understand vector notation, and be able to add, subtract and multiply vectors

GeometryFoundation, Higher, KS4
100

Compound Measure - Speed

GeometryFoundation, Higher, KS4
101

Compound Measure - Pressure

GeometryFoundation, Higher, KS4
102

Compound Measure - Density

GeometryFoundation, Higher, KS4
103

Vertically opposite angles

GeometryFoundation, Higher, KS4
104

Angles on Parallel Lines - Alternate angles

GeometryFoundation, Higher, KS4
105

Angles on Parallel Lines - Co-interior angles

GeometryFoundation, Higher, KS4
106

Angles on Parallel Lines - Corresponding angles

GeometryFoundation, Higher, KS4
107

Converting units

GeometryFoundation, Higher, KS4
108

Interior and exterior angles and deducing the number of sides of a regular polygon, given one of its angles

GeometryFoundation, Higher, KS4
109

Understand trigonometric relationships in right angled triangles and use it to find missing sides in 2D problems

GeometryFoundation, Higher, KS4
110

Use trigonometry to find the angle between 2 lines

GeometryFoundation, Higher, KS4
111

Algebra in Shapes

GeometryFoundation, Higher, KS4
112

Speed / Distance & Time Graphs

GeometryFoundation, Higher, KS4
113

Conversion Graphs

GeometryFoundation, Higher, KS4
114

Constructions - Perpendiculars

GeometryFoundation, Higher, KS4
115

Constructions - Angle Bisectors

GeometryFoundation, Higher, KS4
116

Loci

GeometryFoundation, Higher, KS4
117

Similar shapes / similarity

GeometryFoundation, Higher, KS4
118

Scale drawings

GeometryFoundation, Higher, KS4
119

Calculate the area of a segment using Sine

GeometryHigher, KS4
120

Apply Pythagoras theorem and Trigonometry in 3D problems

GeometryHigher, KS4
121

Find the surface area of cones

GeometryHigher, KS4
122

Find the volume of cones

GeometryHigher, KS4
123

Finding the surface area of pyramids

GeometryHigher, KS4
124

Find the volume of pyramids

GeometryHigher, KS4
125

Find the volumes of frustums

GeometryHigher, KS4
126

Enlargements - using a negative scale factor

GeometryHigher, KS4
127

Enlargements - Finding the centre of enlargements (including negatives)

GeometryHigher, KS4
128

Understand how to solve more complex vector problems

GeometryHigher, KS4
129

Find the surface area and volume of spheres and hemispheres

GeometryHigher, KS4
130

Calculate the area of a triangle using A = ½ab SinC formula

GeometryHigher, KS4
131

Circle Theorems Rules - Part 1 to 3. Angles at the centre, cyclic quadrilaterals and angles in a semi circle

GeometryHigher, KS4
132

Circle Theorems Rules - Part 4 to 6. Angles subtended by the same arc, Tangents and Alternate segment theorem

GeometryHigher, KS4
133

Circle Theorems Proof - Part 1 : Angles at the centre

GeometryHigher, KS4
134

Circle Theorems Proof - Part 2 : Cyclic quadrilaterals

GeometryHigher, KS4
135

Circle Theorems Proof - Part 3 : Angles in a semi circle

GeometryHigher, KS4
136

Circle Theorems Proof - Part 4 : Angles subtended by the same arc

GeometryHigher, KS4
137

Circle Theorems Proof - Part 5 : Tangents

GeometryHigher, KS4
138

Circle Theorems Proof - Part 6 : Alternate segment theorem

GeometryHigher, KS4
139

Use the cosine rule to solve 2D problems

GeometryHigher, KS4
140

Use the sine rule to solve 2D problems

GeometryHigher, KS4
141

Find the angle of elevation and the angle of depression

GeometryHigher, KS4
142

To be able to calculate / know exact trig ratios

    GeometryHigher, KS4
143

Surface Area of Compound 3D Shapes

GeometryHigher, KS4
144

Volume of Compound 3D Shapes

GeometryHigher, KS4
145

Converting units of area and volume

    GeometryHigher, KS4
146

Bearings

    GeometryFoundation, Higher, KS4
147

Similarity in shapes (Area and Volume)

GeometryHigher, KS4
148

Congruence

GeometryHigher, KS4
149

Graph Transformations

GeometryHigher, KS4
150

Trigonometric Graphs

GeometryHigher, KS4
151

Graph Types

GeometryHigher, KS4
152

Numbers in and from Words and Place value

NumberFoundation, KS3
153

Ordering Integers

NumberFoundation, KS3
154

Ordering Fractions, Decimals and Percentages

NumberFoundation, KS3
155

Multiplying and dividing by Powers of 10

NumberFoundation, KS3
156

Adding whole and decimal numbers

NumberFoundation, KS3
157

Number operations (BIDMAS)

NumberFoundation, KS3
158

Simple Percentages

NumberFoundation, KS3
159

Converting between Fractions and Decimals

NumberFoundation, KS3
160

Converting between Decimals and Percentages

NumberFoundation, KS3
161

Converting between improper fractions and mixed numbers

NumberFoundation, KS3
162

Converting between Fractions & Percentages

NumberFoundation, KS3
163

Division using the bus stop method (including decimals)

NumberFoundation, KS3
164

Basic Venn Diagrams

NumberFoundation, Higher, KS3
165

Factors and Highest Common Factor

NumberFoundation, KS3
166

Multiples and Lowest Common Multiple

NumberFoundation, KS3
167

Multiplication using standard methods

NumberFoundation, KS3
168

Indices notations, powers and roots

    NumberFoundation, KS3
169

Rounding to Integers (whole numbers), 10s, hundreds and decimal places

NumberFoundation, KS3
170

Estimating by rounding to significant figures

    NumberFoundation, KS3
171

Equivalent Fractions & Simplifying Fractions

NumberFoundation, KS3
172

Subtracting whole and decimal Numbers

NumberFoundation, KS3
173

Negative numbers

NumberFoundation, KS3
174

Money Problems

NumberFoundation, Higher, KS3
175

Types of Numbers

NumberFoundation, Higher, KS3
176

Using a Calculator

NumberFoundation, Higher, KS3
177

Add and Subtract Fractions

NumberFoundation, Higher, KS3
178

Increasing and Decreasing by a Percentage

NumberFoundation, Higher, KS3
179

Percentages of a quantity with multiplier (leading to increasing and decreasing)

NumberFoundation, Higher, KS3
180

Compound Interest

NumberFoundation, Higher, KS4
181

Similar or related calculations

NumberFoundation, Higher, KS3
182

Simple Interest

NumberFoundation, Higher, KS3
183

One number as a percentage of another

    NumberFoundation, Higher, KS4
184

Standard Form

NumberFoundation, Higher, KS4
185

Using Venn Diagrams to find LCM and HCF

NumberFoundation, Higher, KS4
186

Reverse Percentage Calculations

NumberFoundation, Higher, KS4
187

Multiplying and Dividing Fractions

NumberFoundation, Higher, KS3
188

Multiplying and Dividing Decimals

NumberFoundation, KS3
189

Fractions of quantities

NumberFoundation, Higher, KS3
190

Negative Indices

    NumberFoundation, Higher, KS4
191

Unitary Ratios- calculating best value

NumberFoundation, Higher, KS4
192

Ratios

NumberFoundation, Higher, KS4
193

Combining Ratios

NumberFoundation, Higher, KS4
194

Recurring Decimals

NumberFoundation, Higher, KS4
195

Calculating Harder Percentages without a calculator

NumberFoundation, Higher, KS3
196

Exchange rates

NumberFoundation, Higher, KS4
197

Product of Prime Factors

NumberFoundation, Higher, KS4
198

Reciprocals

NumberFoundation, Higher, KS4
199

Laws of Indices

NumberFoundation, Higher, KS4
200

Time Tables

NumberFoundation, Higher, KS4
201

Fractional (combined with negative) Indices

NumberHigher, KS4
202

Accuracy with Bounds

NumberHigher, KS4
203

Finding upper and lower bounds with problems

    NumberHigher, KS4
204

Converting numbers to use laws of indices

NumberHigher, KS4
205

Calculations with Surds - expanding brackets

NumberHigher, KS4
206

Rationalising the denominator (surds)

NumberHigher, KS4
207

Percentage errors in Bounds

NumberHigher, KS4
208

Error Intervals and Truncating

NumberHigher, KS4
209

Manipulation and Simplification of Surds (Multiply and Divide Rules)

NumberHigher, KS4
210

Direct and Inverse Proportional Change

NumberHigher, KS4
211

Converting Recurring Decimals to Fractions

NumberHigher, KS4
212

Bar charts

StatisticsFoundation, KS3
213

Frequency Tables & Grouping Data

StatisticsFoundation, Higher, KS3
214

Calculate median

StatisticsFoundation, Higher, KS3
215

Calculate mean, mode and range (averages)

    StatisticsFoundation, Higher, KS3
216

Completing and using two-way tables

StatisticsFoundation, Higher, KS3
217

Dual bar charts

StatisticsFoundation, KS3
218

Pictograms

StatisticsFoundation, KS3
219

Frequency polygons

StatisticsFoundation, Higher, KS4
220

Stem and leaf diagrams

StatisticsFoundation, Higher, KS3
221

Probability and relative frequency

StatisticsFoundation, Higher, KS3
222

Sample spaces and probability

StatisticsFoundation, Higher, KS3
223

Combinations

StatisticsFoundation, Higher, KS3
224

Questionnaires

StatisticsFoundation, KS3
225

Cumulative frequency tables and graphs

StatisticsFoundation, Higher, KS3
226

Mean calculations

StatisticsFoundation, Higher, KS4
227

Estimating the mean from grouped frequency tables

StatisticsFoundation, Higher, KS4
228

Find the modal class from a grouped frequency tables

StatisticsFoundation, Higher, KS4
229

Find the median class from a grouped frequency tables

StatisticsFoundation, Higher, KS4
230

Calculate mean from a frequency table

StatisticsFoundation, Higher, KS4
231

Calculate the median from frequency tables

StatisticsFoundation, Higher, KS4
232

Calculate the mode from frequency tables

StatisticsFoundation, Higher, KS4
233

Stratified sampling

StatisticsFoundation, Higher, KS4
234

Line graphs

StatisticsFoundation, Higher, KS4
235

Lines of best fit

StatisticsFoundation, Higher, KS4
236

Pie charts

StatisticsFoundation, Higher, KS3
237

Scatter graphs & correlation

StatisticsFoundation, Higher, KS4
238

Quartiles

StatisticsHigher, KS4
239

Mutually exclusive events

        StatisticsHigher, KS4
240

Probability AND/OR Rules

StatisticsFoundation, Higher, KS4
241

Venn diagrams

        StatisticsFoundation, Higher, KS4
242

Probability trees

StatisticsHigher, KS4
243

Box plots (from raw data, or when given the median and quartiles)

StatisticsHigher, KS4
244

Histograms with unequal class intervals, using frequency density

StatisticsHigher, KS4
245

Interpreting histograms/frequency density diagrams

StatisticsHigher, KS4
246

Measuring and drawing angles with a protractor

GeometryFoundation, KS3
247

Inequalites notation

NumberFoundation, KS3
248

Measuring with scales

GeometryFoundation, KS3
249

Sum of an arithmetic series (iGCSE)

NumberHigher, igcse
250

Differentiation (Part 1) for iGCSE)

AlgebraHigher, igcse
251

Differentiation (Part 2) for iGCSE)

AlgebraHigher, igcse
252

Differentiation (Part 3) for iGCSE)

AlgebraHigher, igcse
253

Intersecting chords and secants (for iGCSE)

GeometryHigher, igcse
254

Constructing triangles with a protractor, ruler and compasses

GeometryFoundation, KS3
255

Using a ruler to measure and draw accurate lines

GeometryFoundation, KS3
256

Time and analogue clocks

NumberFoundation, Higher, KS4
257

Inequalities on graphs

    AlgebraHigher, KS4
258

Frequency Trees

StatisticsFoundation, Higher, KS4
259

Combining ratios and fractions

NumberHigher, KS4
260

Area under a curve and gradient of a curve

AlgebraHigher, KS4

Maths School Skills and Exam Question Problem Solving Workbooks

Our workbooks provide students the appropriate skills and problem solving practice students need to succeed in examinations.

Maths School

FREE
VIEW