FREE GCSE and iGCSE Maths and Lessons

ID	Lesson	Unit	GCSE/iGCSE Level
1	Expressions, equations, identities and formula	Algebra	Foundation, KS3
2	Simplifying Expressions	Algebra	Foundation, KS3
3	Change the subject of a Formula (Part 1)	Algebra	Foundation, KS3
4	Co-ordinates - reading and plotting in all quadrants	Algebra	Foundation, KS3
5	Substitute Numbers into Formula	Algebra	Foundation, KS3
6	Factorising Expressions	Algebra	Foundation, KS3
7	Substitute Numbers into Expressions	Algebra	Foundation, KS3
8	Expanding Single Brackets	Algebra	Foundation, KS3
9	Re-arranging & solving simple one step equations	Algebra	Foundation, KS3
10	Double Function Machines	Algebra	Foundation, KS3
11	Forming Expressions, Equations or Formula	Algebra	Foundation, Higher, KS4
12	Function Machines	Algebra	Foundation, KS3
13	Solve inequalities with one or two variables	Algebra	Foundation, Higher, KS4
14	Solving quadratic equations by factorising (Part 1)	Algebra	Foundation, Higher, KS4
15	Trial and Improvement to find approximate solutions of equations	Algebra	Foundation, Higher, KS4
16	Change the subject of a Formula (Part 2) - with powers	Algebra	Foundation, Higher, KS4
17	Find the gradient of a straight line graph using 2 co-ordinates	Algebra	Foundation, Higher, KS4
18	Finding the mid-point of a line	Algebra	Foundation, Higher, KS4
19	Find the length of a line (using Pythagoras)	Algebra	Foundation, Higher, KS4
20	Solve equations that include brackets	Algebra	Foundation, Higher, KS4
21	Functions (Part 3) - Inverse functions	Algebra	Higher, KS4
22	Factorising Quadratics into 2 Brackets with coefficients of x ² greater than 1	Algebra	Higher, KS4
23	Solve equations that include powers	Algebra	Foundation, Higher, KS4
24	Solving Fractional equations (Part 1) - Linear	Algebra	Foundation, Higher, KS4
25	Solve equations with unknown on both sides including negative numbers	Algebra	Foundation, Higher, KS4
26	Solve two step equations with unknown on one side and involving fractions	Algebra	Foundation, Higher, KS4
27	Use elimination to solve simultaneous equations	Algebra	Foundation, Higher, KS4
28	Use substitution to solve simultaneous equations	Algebra	Foundation, Higher, KS4
29	Using number sequences & describe a rule of a sequence	Algebra	Foundation, Higher, KS4
30	Find & use the nth term expression for a sequence	Algebra	Foundation, Higher, KS4
31	Using the nth term expression of a quadratic sequence	Algebra	Foundation, Higher, KS4
32	An Equation of a line - Gradient, Y-intercept and y=mx+c	Algebra	Foundation, Higher, KS4
33	Expanding Double Brackets	Algebra	Foundation, Higher, KS4
34	Drawing Straight Line Graphs	Algebra	Foundation, Higher, KS4
35	Factorising Quadratics into 2 Brackets	Algebra	Foundation, Higher, KS4
36	Drawing Straight Line Graphs to solve linear simultaneous equations on graphs	Algebra	Foundation, Higher, KS4
37	Inequalities on a Number Line	Algebra	Foundation, Higher, KS4
38	Solving quadratic inequalities	Algebra	Higher, KS4
39	Solving quadratic equations by factorising (Part 2) - with coefficients > 1	Algebra	Higher, KS4
40	Solving quadratic equations by using the formula	Algebra	Higher, KS4
41	Perpendicular gradients	Algebra	Higher, KS4
42	Equations of parallel and perpendicular lines	Algebra	Higher, KS4
43	Change the subject of a Formula (Part 3) - by factorising	Algebra	Higher, KS4
44	Factorising using the difference of two squares	Algebra	Higher, KS4
45	Find the equation of a straight line from gradient and co-ordinates	Algebra	Higher, KS4
46	Geometric sequence (Common Ratio)	Algebra	Higher, KS4
47	Solving quadratic equations by completing the square	Algebra	Higher, KS4
48	Completing the square of quadratic expressions (Part 1)	Algebra	Higher, KS4
49	Completing the square of quadratic expressions (Part 2) - with higher coefficients of x^2	Algebra	Higher, KS4
50	Working with Algebraic Fractions (Part 1 - Adding and Subtracting)	Algebra	Higher, KS4
51	Working with Algebraic Fractions (Part 2 - Simplifying by Factorising)	Algebra	Higher, KS4
52	Working with Algebraic Fractions (Part 3 - Multiplying and Dividing)	Algebra	Higher, KS4
53	Find the nth term expression for a quadratic sequence	Algebra	Higher, KS4
54	Circle equations in the form x² + y² = r²	Algebra	Higher, KS4
55	Equation of a Tangent to a circle	Algebra	Higher, KS4
56	Iteration	Algebra	Higher, KS4
57	Solving Quadratic Simultaneous Equations	Algebra	Higher, KS4
58	Turning Points	Algebra	Higher, KS4
59	Triple Brackets	Algebra	Foundation, KS3
60	Solving Fractional Equations (Part 2) - Quadratic	Algebra	Higher, KS4
61	Solve quadratic and linear graphs simultaneously	Algebra	Higher, KS4
62	Exponential Growth and Decay	Algebra	Higher, KS4
63	Finding an exponential equation from a graph	Algebra	Higher, KS4
64	Proofs	Algebra	Higher, KS4
65	Functions (Part 1) - notation	Algebra	Higher, KS4
66	Functions (Part 2) - Composite functions	Algebra	Higher, KS4
67	Nets, plans and elevations	Geometry	Foundation, KS3
68	Symmetry and rotational symmetry of shapes	Geometry	Foundation, KS3
69	Angles in Triangles and Quadrilaterals	Geometry	Foundation, KS3
70	Area of Parallelograms	Geometry	Foundation, KS3
71	Area of Trapeziums	Geometry	Foundation, KS3
72	Area of Rectangles	Geometry	Foundation, KS3
73	Area of Compound Shapes	Geometry	Foundation, KS3
74	Area of Triangles	Geometry	Foundation, KS3
75	Missing angles in right angles, straight lines and around a point	Geometry	Foundation, Higher, KS4
76	Parallel and Perpendicular Lines	Geometry	Foundation, Higher, KS3
77	Types of angles	Geometry	Foundation, KS3
78	Types of triangles	Geometry	Foundation, KS3
79	Circles - know the parts of a circle	Geometry	Foundation, KS3
80	Perimeter of shapes	Geometry	Foundation, KS3
81	Types of quadrilaterals	Geometry	Foundation, KS3
82	Basic congruent shapes	Geometry	Foundation, KS3
83	Pythagoras Theorem	Geometry	Foundation, Higher, KS4
84	Understand and use translations, using vectors and describing translations	Geometry	Foundation, Higher, KS4
85	Reflections and describing reflections in mirror lines	Geometry	Foundation, Higher, KS4
86	Calculate the length of an arc and area of a sector	Geometry	Foundation, Higher, KS4
87	Find the surface area of shapes of cubes and cuboids by using the formulae for rectangles	Geometry	Foundation, Higher, KS4
88	Enlargements - Scale Factors	Geometry	Foundation, Higher, KS4
89	Enlargements - Enlargements from a point	Geometry	Foundation, Higher, KS4
90	Enlargements - Describing enlargements (including finding the centre - positive scale factors)	Geometry	Foundation, Higher, KS4
91	Find the Surface Area of Prisms and Cylinders	Geometry	Foundation, Higher, KS4
92	Find the Volume of Prisms and Cylinders	Geometry	Foundation, Higher, KS4
93	Rotations and describing rotations	Geometry	Foundation, Higher, KS4
94	Solve simple vector problems	Geometry	Foundation, Higher, KS4
95	Use the formula to calculate the volume of a cuboid	Geometry	Foundation, 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	Geometry	Foundation, Higher, KS4
98	Circles - calculate the area of a circle	Geometry	Foundation, Higher, KS4
99	Understand vector notation, and be able to add, subtract and multiply vectors	Geometry	Foundation, Higher, KS4
100	Compound Measure - Speed	Geometry	Foundation, Higher, KS4
101	Compound Measure - Pressure	Geometry	Foundation, Higher, KS4
102	Compound Measure - Density	Geometry	Foundation, Higher, KS4
103	Vertically opposite angles	Geometry	Foundation, Higher, KS4
104	Angles on Parallel Lines - Alternate angles	Geometry	Foundation, Higher, KS4
105	Angles on Parallel Lines - Co-interior angles	Geometry	Foundation, Higher, KS4
106	Angles on Parallel Lines - Corresponding angles	Geometry	Foundation, Higher, KS4
107	Converting units	Geometry	Foundation, Higher, KS4
108	Interior and exterior angles and deducing the number of sides of a regular polygon, given one of its angles	Geometry	Foundation, Higher, KS4
109	Understand trigonometric relationships in right angled triangles and use it to find missing sides in 2D problems	Geometry	Foundation, Higher, KS4
110	Use trigonometry to find the angle between 2 lines	Geometry	Foundation, Higher, KS4
111	Algebra in Shapes	Geometry	Foundation, Higher, KS4
112	Speed / Distance & Time Graphs	Geometry	Foundation, Higher, KS4
113	Conversion Graphs	Geometry	Foundation, Higher, KS4
114	Constructions - Perpendiculars	Geometry	Foundation, Higher, KS4
115	Constructions - Angle Bisectors	Geometry	Foundation, Higher, KS4
116	Loci	Geometry	Foundation, Higher, KS4
117	Similar shapes / similarity	Geometry	Foundation, Higher, KS4
118	Scale drawings	Geometry	Foundation, Higher, KS4
119	Calculate the area of a segment using Sine	Geometry	Higher, KS4
120	Apply Pythagoras theorem and Trigonometry in 3D problems	Geometry	Higher, KS4
121	Find the surface area of cones	Geometry	Higher, KS4
122	Find the volume of cones	Geometry	Higher, KS4
123	Finding the surface area of pyramids	Geometry	Higher, KS4
124	Find the volume of pyramids	Geometry	Higher, KS4
125	Find the volumes of frustums	Geometry	Higher, KS4
126	Enlargements - using a negative scale factor	Geometry	Higher, KS4
127	Enlargements - Finding the centre of enlargements (including negatives)	Geometry	Higher, KS4
128	Understand how to solve more complex vector problems	Geometry	Higher, KS4
129	Find the surface area and volume of spheres and hemispheres	Geometry	Higher, KS4
130	Calculate the area of a triangle using A = ½ab SinC formula	Geometry	Higher, KS4
131	Circle Theorems Rules - Part 1 to 3. Angles at the centre, cyclic quadrilaterals and angles in a semi circle	Geometry	Higher, KS4
132	Circle Theorems Rules - Part 4 to 6. Angles subtended by the same arc, Tangents and Alternate segment theorem	Geometry	Higher, KS4
133	Circle Theorems Proof - Part 1 : Angles at the centre	Geometry	Higher, KS4
134	Circle Theorems Proof - Part 2 : Cyclic quadrilaterals	Geometry	Higher, KS4
135	Circle Theorems Proof - Part 3 : Angles in a semi circle	Geometry	Higher, KS4
136	Circle Theorems Proof - Part 4 : Angles subtended by the same arc	Geometry	Higher, KS4
137	Circle Theorems Proof - Part 5 : Tangents	Geometry	Higher, KS4
138	Circle Theorems Proof - Part 6 : Alternate segment theorem	Geometry	Higher, KS4
139	Use the cosine rule to solve 2D problems	Geometry	Higher, KS4
140	Use the sine rule to solve 2D problems	Geometry	Higher, KS4
141	Find the angle of elevation and the angle of depression	Geometry	Higher, KS4
142	To be able to calculate / know exact trig ratios	Geometry	Higher, KS4
143	Surface Area of Compound 3D Shapes	Geometry	Higher, KS4
144	Volume of Compound 3D Shapes	Geometry	Higher, KS4
145	Converting units of area and volume	Geometry	Higher, KS4
146	Bearings	Geometry	Foundation, Higher, KS4
147	Similarity in shapes (Area and Volume)	Geometry	Higher, KS4
148	Congruence	Geometry	Higher, KS4
149	Graph Transformations	Geometry	Higher, KS4
150	Trigonometric Graphs	Geometry	Higher, KS4
151	Graph Types	Geometry	Higher, KS4
152	Numbers in and from Words and Place value	Number	Foundation, KS3
153	Ordering Integers	Number	Foundation, KS3
154	Ordering Fractions, Decimals and Percentages	Number	Foundation, KS3
155	Multiplying and dividing by Powers of 10	Number	Foundation, KS3
156	Adding whole and decimal numbers	Number	Foundation, KS3
157	Number operations (BIDMAS)	Number	Foundation, KS3
158	Simple Percentages	Number	Foundation, KS3
159	Converting between Fractions and Decimals	Number	Foundation, KS3
160	Converting between Decimals and Percentages	Number	Foundation, KS3
161	Converting between improper fractions and mixed numbers	Number	Foundation, KS3
162	Converting between Fractions & Percentages	Number	Foundation, KS3
163	Division using the bus stop method (including decimals)	Number	Foundation, KS3
164	Basic Venn Diagrams	Number	Foundation, Higher, KS3
165	Factors and Highest Common Factor	Number	Foundation, KS3
166	Multiples and Lowest Common Multiple	Number	Foundation, KS3
167	Multiplication using standard methods	Number	Foundation, KS3
168	Indices notations, powers and roots	Number	Foundation, KS3
169	Rounding to Integers (whole numbers), 10s, hundreds and decimal places	Number	Foundation, KS3
170	Estimating by rounding to significant figures	Number	Foundation, KS3
171	Equivalent Fractions & Simplifying Fractions	Number	Foundation, KS3
172	Subtracting whole and decimal Numbers	Number	Foundation, KS3
173	Negative numbers	Number	Foundation, KS3
174	Money Problems	Number	Foundation, Higher, KS3
175	Types of Numbers	Number	Foundation, Higher, KS3
176	Using a Calculator	Number	Foundation, Higher, KS3
177	Add and Subtract Fractions	Number	Foundation, Higher, KS3
178	Increasing and Decreasing by a Percentage	Number	Foundation, Higher, KS3
179	Percentages of a quantity with multiplier (leading to increasing and decreasing)	Number	Foundation, Higher, KS3
180	Compound Interest	Number	Foundation, Higher, KS4
181	Similar or related calculations	Number	Foundation, Higher, KS3
182	Simple Interest	Number	Foundation, Higher, KS3
183	One number as a percentage of another	Number	Foundation, Higher, KS4
184	Standard Form	Number	Foundation, Higher, KS4
185	Using Venn Diagrams to find LCM and HCF	Number	Foundation, Higher, KS4
186	Reverse Percentage Calculations	Number	Foundation, Higher, KS4
187	Multiplying and Dividing Fractions	Number	Foundation, Higher, KS3
188	Multiplying and Dividing Decimals	Number	Foundation, KS3
189	Fractions of quantities	Number	Foundation, Higher, KS3
190	Negative Indices	Number	Foundation, Higher, KS4
191	Unitary Ratios- calculating best value	Number	Foundation, Higher, KS4
192	Ratios	Number	Foundation, Higher, KS4
193	Combining Ratios	Number	Foundation, Higher, KS4
194	Recurring Decimals	Number	Foundation, Higher, KS4
195	Calculating Harder Percentages without a calculator	Number	Foundation, Higher, KS3
196	Exchange rates	Number	Foundation, Higher, KS4
197	Product of Prime Factors	Number	Foundation, Higher, KS4
198	Reciprocals	Number	Foundation, Higher, KS4
199	Laws of Indices	Number	Foundation, Higher, KS4
200	Time Tables	Number	Foundation, Higher, KS4
201	Fractional (combined with negative) Indices	Number	Higher, KS4
202	Accuracy with Bounds	Number	Higher, KS4
203	Finding upper and lower bounds with problems	Number	Higher, KS4
204	Converting numbers to use laws of indices	Number	Higher, KS4
205	Calculations with Surds - expanding brackets	Number	Higher, KS4
206	Rationalising the denominator (surds)	Number	Higher, KS4
207	Percentage errors in Bounds	Number	Higher, KS4
208	Error Intervals and Truncating	Number	Higher, KS4
209	Manipulation and Simplification of Surds (Multiply and Divide Rules)	Number	Higher, KS4
210	Direct and Inverse Proportional Change	Number	Higher, KS4
211	Converting Recurring Decimals to Fractions	Number	Higher, KS4
212	Bar charts	Statistics	Foundation, KS3
213	Frequency Tables & Grouping Data	Statistics	Foundation, Higher, KS3
214	Calculate median	Statistics	Foundation, Higher, KS3
215	Calculate mean, mode and range (averages)	Statistics	Foundation, Higher, KS3
216	Completing and using two-way tables	Statistics	Foundation, Higher, KS3
217	Dual bar charts	Statistics	Foundation, KS3
218	Pictograms	Statistics	Foundation, KS3
219	Frequency polygons	Statistics	Foundation, Higher, KS4
220	Stem and leaf diagrams	Statistics	Foundation, Higher, KS3
221	Probability and relative frequency	Statistics	Foundation, Higher, KS3
222	Sample spaces and probability	Statistics	Foundation, Higher, KS3
223	Combinations	Statistics	Foundation, Higher, KS3
224	Questionnaires	Statistics	Foundation, KS3
225	Cumulative frequency tables and graphs	Statistics	Foundation, Higher, KS3
226	Mean calculations	Statistics	Foundation, Higher, KS4
227	Estimating the mean from grouped frequency tables	Statistics	Foundation, Higher, KS4
228	Find the modal class from a grouped frequency tables	Statistics	Foundation, Higher, KS4
229	Find the median class from a grouped frequency tables	Statistics	Foundation, Higher, KS4
230	Calculate mean from a frequency table	Statistics	Foundation, Higher, KS4
231	Calculate the median from frequency tables	Statistics	Foundation, Higher, KS4
232	Calculate the mode from frequency tables	Statistics	Foundation, Higher, KS4
233	Stratified sampling	Statistics	Foundation, Higher, KS4
234	Line graphs	Statistics	Foundation, Higher, KS4
235	Lines of best fit	Statistics	Foundation, Higher, KS4
236	Pie charts	Statistics	Foundation, Higher, KS3
237	Scatter graphs & correlation	Statistics	Foundation, Higher, KS4
238	Quartiles	Statistics	Higher, KS4
239	Mutually exclusive events	Statistics	Higher, KS4
240	Probability AND/OR Rules	Statistics	Foundation, Higher, KS4
241	Venn diagrams	Statistics	Foundation, Higher, KS4
242	Probability trees	Statistics	Higher, KS4
243	Box plots (from raw data, or when given the median and quartiles)	Statistics	Higher, KS4
244	Histograms with unequal class intervals, using frequency density	Statistics	Higher, KS4
245	Interpreting histograms/frequency density diagrams	Statistics	Higher, KS4
246	Measuring and drawing angles with a protractor	Geometry	Foundation, KS3
247	Inequalites notation	Number	Foundation, KS3
248	Measuring with scales	Geometry	Foundation, KS3
249	Sum of an arithmetic series (iGCSE)	Number	Higher, igcse
250	Differentiation (Part 1) for iGCSE)	Algebra	Higher, igcse
251	Differentiation (Part 2) for iGCSE)	Algebra	Higher, igcse
252	Differentiation (Part 3) for iGCSE)	Algebra	Higher, igcse
253	Intersecting chords and secants (for iGCSE)	Geometry	Higher, igcse
254	Constructing triangles with a protractor, ruler and compasses	Geometry	Foundation, KS3
255	Using a ruler to measure and draw accurate lines	Geometry	Foundation, KS3
256	Time and analogue clocks	Number	Foundation, Higher, KS4
257	Inequalities on graphs	Algebra	Higher, KS4
258	Frequency Trees	Statistics	Foundation, Higher, KS4
259	Combining ratios and fractions	Number	Higher, KS4
260	Area under a curve and gradient of a curve	Algebra	Higher, KS4