A-Level Year 2 Maths Revision Guide

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.

1. Algebraic Methods

Learning Objective	Revision Videos	Practice
Understand how to prove mathematical statements using proof by contradiction.
Manipulate and simplify algebraic fractions.
Be able to split algebraic fractions into partial fractions.
Know how to use algebraic division to solve problems.

2. Functions and Graphs

Learning Objective	Revision Videos	Practice
Understand the modulus function.
Understand the concept of a mapping, and how this links to mathematical functions.
Be able to combine functions to make composite functions.
Understand the concept of inverse functions, and be able to find an inverse functions algebraically.
Know the effect of modulus on a function’s graph.
Understand how to combine graph transformations.
Solve equations with modulus symbols.

3. Equations and Inequalities

Learning Objective	Revision Videos	Practice
Be able to solve linear simultaneous equations.
Be able to solve simultaneous equations on graphs.
Be able to solve quadratic simultaneous equations.
Know how to solve linear inequalities.
Know how to solve quadratic inequalities.
Understand regions and inequalities on graphs.

4. Graphs and Transformations

Learning Objective	Revision Videos	Practice
Be familiar with cubic and quartic graphs, and know their features.
Know the general shape and features of a reciprocal graph.
Solve problems involving points of intersection of two graphs.
Know and understand that rules for graph transformations.

5. Straight Line Graphs

Learning Objective	Revision Videos	Practice
Be familiar with the equation of a straight line graph: y=mx+c
Be able to find the gradient of a straight line.
Know that parallel lines have the same gradient, but perpendicular graphs have the negative reciprocal gradient.
Be able to solve problems and model scenarios using straight line graphs.

6. Circles

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
Be able to solve problems involving circle equations and their graphs.

7. Algebraic Methods

Learning Objective	Revision Videos	Practice
Be able to simplify algebraic fractions.
Be able to solve equations involving algebraic fractions.
Divide polynomials using algebra.
Understand the factor theorem.
Use mathematical proof to prove mathematical facts.
Understand various methods of proof.

8. The Binomial Expansion

Learning Objective	Revision Videos	Practice
Understand how to use binomial expansion, and be able to expand brackets efficiently.
Solve problems using the binomial theorem.
Estimate calculations using an appropriate binomial expansion.

9. Trigonometric Ratios

Learning Objective	Revision Videos	Practice
Revision: Revise all of GCSE SOHCAHTOA and Pythagoras Theorem.
Be able to use the sine and cosine rules to solve problems involving non-right angle triangles.
Be able to use the formula for the area of a triangle with sine to solve problems.
Know the graphs of sine, cosine and tan.
Know how to transform trigonometric graphs.

10. Trigonometric Identities and Equations

Learning Objective	Revision Videos	Practice
Be able to solve basic trigonometric equations.
Know the exact trigonometric values, and the special triangles.
Know the trig identities, and use them to solve problems.
Be able to use a CAST diagram to calculate repeated solutions to trigonometric equations.

11. Vectors

Learning Objective	Revision Videos	Practice
Understand vector notation.
Understand the concept of vector magnitude, and be able to calculate the magnitude of a vector.
Be able to apply vector facts to solve vector problems.
Be able to model with vectors.

12. Differentiation

Learning Objective	Revision Videos	Practice
Understand how to differentiate from first principles.
Be able to differentiate using the power rule.
Use differentiation to find the gradient of a curve at a particular coordinate.
Use differentiation to find the equation of a tangent of a curve at a coordinate.
Use differentiation to find the equation of a normal of a curve at a coordinate.
Understand the concept of a second derivative.
Analyse a curve to see whether it is increasing or decreasing at a particular point.
Find the coordinates of stationary points using differentiation.
Be able to model using differentiation.

13. Integration

Learning Objective	Revision Videos	Practice
Be able to integrate using the reverse power rule.
Be able to find the equation of a function from the equation of a gradient using integration.
Use integration to find areas beneath and between curves.

14. Exponentials and Logarithms

Learning Objective	Revision Videos	Practice
Understand the general shape an exponential graph.
Use exponential equations to model real life situations.
Understand the concept of a logarithm.
Know the laws of logarithms and how to use them to solve equations involving exponents.
Understand how to use logarithms to model non-linear data.