Complete revision resources for A-level Maths!
This complete guide to A-level Maths is all you need to ace your A-level Maths exams.
Revision videos, practice questions and mark schemes are linked below to give you a complete free revision package.
Click here for our revision tips page, for the best advise to revision effectively!
Thanks to MathsGenie, PhysicsandMathsTutor, Dr Frost, Dr Austin Maths and Naiker Maths for their resources in this revision guide.
1. Algebraic Methods
This chapter reviews a lot of prior knowledge from GCSE Maths. This is essential practice for you because A-level maths requires a high skill level in algebra. Fluent algebraic manipulation is essential to high grades.
| Learning Objective | Revision Videos | Practice |
| Know and apply indices laws. | Revision Page: Laws of Indices | See revision page. |
| Be able to expand and factorise brackets. Including: Basic linear factors Quadratics Difference of 2 Squares | Algebra Playlist Factorising Quadratics Difference of 2 Squares Factorising Harder Quadratics | Difference of 2 Squares Transum Factorising Harder Quadratics Transum Mixed Algebra Practice from Addvance Maths |
| Understand how to manipulate surds and simplify surd expressions. | Surds Revision Page | See revision page. |
| Be able to rationalise the denominator of a fractional surd. | See above. | Dr Austin Maths: Surds Revision Grid Markscheme |
2. Quadratic Equations and Functions
Quadratic equations are one of the most common types of equations you will come across at A-level. Fluency with factoring, completing the square and solving is essential. You should also be very familiar with quadratic graphs.
3. Equations and Inequalities
Inequalities will come up often in later topics. Get used to them now!
| Learning Objective | Revision Videos | Practice |
| Be able to solve linear simultaneous equations. | Simultaneous Equations Video | Extension: Comparing Method of Solving Simultaneous Equations |
| Be able to solve simultaneous equations on graphs. | Simultaneous on a Graph Video | |
| Be able to solve equations on graphs, understanding that the points of intersection are the solutions. | Solving Equations using Graphs Video | |
| Be able to solve quadratic simultaneous equations. | Quadratic Simultaneous Equations Video | |
| Know how to solve linear inequalities. | Inequalities Video | |
| Know how to solve quadratic inequalities. | Quadratic Inequalities Video | |
| Understand regions and inequalities on graphs. | Inequalities Regions Video |
4. Graphs and Transformations
We use graphs a lot in A-level maths. Having a proper conceptual understanding of them is really important.
| Learning Objective | Revision Videos | Practice |
| Be familiar with cubic and quartic graphs, and know their features. | Cubic Graphs Revision Video | |
| Know the general shape and features of a reciprocal graph. | Reciprocal Graphs Video | |
| Solve problems involving points of intersection of two graphs. | Solving Equations using Graphs Video | |
| Know and understand that rules for graph transformations. | Graph Transformations Page | Mathsgenie Practice for all of Topci 4 Markscheme Naiker Maths: Practice Questions Markscheme |
5. Straight Line Graphs
| Learning Objective | Revision Videos | Practice |
| Be familiar with the equation of a straight line graph: y=mx+c | Straight Line Graphs Revision Page | |
| Be able to find the gradient of a straight line. | Gradients Video | |
| Know that parallel lines have the same gradient, but perpendicular graphs have the negative reciprocal gradient. | Video Coming Soon Perpendicular Bisectors Video | |
| Be able to solve problems and model scenarios using straight line graphs. | Video Coming Soon | Mathsgenie Practice for all of 5. Markscheme |
6. Circles
The equation y = mx + c is one of the most famous equations in all of maths.
| Learning Objective | Revision Videos | Practice |
| Understand how to find the midpoint between two points, and solve problems involving midpoints. | ||
| Be able to find the equation of a perpendicular bisector on a graph. | ||
| Know that the general form of a circle equation is (x-a)2+(y-b)2=r2 | Circle Equations Video | |
| Be able to solve problems involving circle equations and their graphs. | See Above | Mathsgenie: Circle Equations Markscheme NaikerMaths: Circle Questions Markscheme |
7. Algebraic Methods
Algebraic fluency means that you can smoothly and quickly rearrange, solve and manipulate algebraic expressions.
| Learning Objective | Revision Videos | Practice |
| Be able to simplify algebraic fractions. | Algebraic Fractions Video | |
| Be able to solve equations involving algebraic fractions. | See above. | |
| Divide polynomials using algebra. | ||
| Understand the factor theorem. | Mathsgenie: The Factor Theorem and Algebraic Division Markscheme for Above Dr Oliver Maths: Factor Theorem Dr Oliver Maths: Solutions | |
| Use mathematical proof to prove mathematical facts. | Algebraic Proof Video | |
| Understand various methods of proof. |
8. The Binomial Expansion
Some nice problem solving questions in this topic, but they can get quite tricky!
| Learning Objective | Revision Videos | Practice |
| Understand how to use binomial expansion, and be able to expand brackets efficiently. | Binomial Expansion Video | |
| Solve problems using the binomial theorem. | Binomial Expansion Problems Video | Mathsgenie: The Binomial Expansion Markscheme for Above |
| Estimate calculations using an appropriate binomial expansion. | Binomial Approximations |
9. Trigonometric Ratios
Trigonometry is a very useful topic in engineering, science and computer design.
| Learning Objective | Revision Videos | Practice |
| Revision: Revise all of GCSE SOHCAHTOA and Pythagoras Theorem. | Trigonometry Revision Page | |
| Be able to use the sine and cosine rules to solve problems involving non-right angle triangles. | Sine Rule Video Cosine Rule Video | |
| Be able to use the formula for the area of a triangle with sine to solve problems. | Area of a Triangle with Sine Video | |
| Know the graphs of sine, cosine and tan. | Sin, Cos and Tan graphs Video | |
| Know how to transform trigonometric graphs. | Transformations of Trigonometric Graphs Video Modelling with Trig Graphs Video |
10. Trigonometric Identities and Equations
Getting tricky now! Solving trig equations can be confusing at times – practice will make perfect.
| Learning Objective | Revision Videos | Practice |
| Be able to solve basic trigonometric equations. | ||
| Know the exact trigonometric values, and the special triangles. | Special Triangles Video | |
| Know the trig identities, and use them to solve problems. | Trigonometric Identities Video | |
| Be able to use a CAST diagram to calculate repeated solutions to trigonometric equations. | Introduction to CAST Diagrams Solving Trig Equations Using Trig | MathsGenie: Solving Trigonometric Equations Markscheme |
11. Vectors
Best to start by revising the Vectors topic from GCSE…
| Learning Objective | Revision Videos | Practice |
| Understand vector notation. | Vector Notation Video | |
| Understand the concept of vector magnitude, and be able to calculate the magnitude of a vector. | Video Coming Soon | |
| Be able to apply vector facts to solve vector problems. | Video Coming Soon | |
| Be able to model with vectors. | Video Coming Soon | MathsGenie: Vectors Markscheme |
12. Differentiation
My favourite topic from all of A-level!
| Learning Objective | Revision Videos | Practice |
| Understand how to differentiate from first principles. | Differentiation from First Principles Video | MathsGenie: Differentiation from First Principles MarkScheme |
| Be able to differentiate using the power rule. | Differentiation Video | MathsGenie: Differentiation Questions Markscheme |
| Use differentiation to find the gradient of a curve at a particular coordinate. | See below | |
| Use differentiation to find the equation of a tangent of a curve at a coordinate. | Finding the Equation of Tangent Video | Naiker Maths: Tangent Questions Markscheme |
| Use differentiation to find the equation of a normal of a curve at a coordinate. | See above | |
| Understand the concept of a second derivative. | Second Derivative Video | |
| Analyse a curve to see whether it is increasing or decreasing at a particular point. | See above | |
| Find the coordinates of stationary points using differentiation. | Maximum and Minimums Video | |
| Be able to model using differentiation. | Coming Soon | NaikerMaths: Modelling with Differentiation Markscheme |
13. Integration
The opposite of differentiation…
| Learning Objective | Revision Videos | Practice |
| Be able to integrate using the reverse power rule. | Introduction to Integration Video | Transum: Integration MathsGenie: Integration Markscheme |
| Be able to find the equation of a function from the equation of a gradient using integration. | Coming Soon | |
| Use integration to find areas beneath and between curves. | Integration: Finding Areas Video | Naiker Maths: Integration and Areas Markscheme |
14. Exponentials and Logarithms
Here, we look deeper at solving equations with indices. Have you already mastered the laws of indices? If not, best to start there.
| Learning Objective | Revision Videos | Practice |
| Understand the general shape an exponential graph. | Coming Soon | |
| Use exponential equations to model real life situations. | Modelling with Exponentials Video | |
| Understand the concept of a logarithm. | Coming Soon | Transum: Logarithms MathsGenie: Exponentials and Logarithms Questions Markscheme |
| Know the laws of logarithms and how to use them to solve equations involving exponents. | Coming Soon | |
| Understand how to use logarithms to model non-linear data. | Coming Soon |
Addvance Maths 