Paper 1 and Paper 3 revision checklist for A Level Math

A good revision checklist is a list of things you can do, not a list of chapter titles. This guide gives a checklist for Pure Mathematics 1 and Pure Mathematics 3, topic by topic, written as questions to ask yourself. Tick a line only if you could do it now, without notes, on a question you have not seen before.

How to use the checklist

1. Go through a topic and answer each line honestly.
2. Mark anything you hesitated over. These are the lines to revise first.
3. Revise the marked lines, then attempt topical questions on them. Do not move on until the questions come out.
4. Come back in a week and test the same lines again.

Paper 1: Pure Mathematics 1

Quadratics and functions

• Can you complete the square and use it to find the vertex and range?
• Can you use the discriminant to decide the number of roots and to find a range of values for a parameter?
• Do you know when a function is one-one, how to find an inverse, and how to find a composite function?
• Can you describe and sketch transformations of a graph?

Coordinate geometry and circles

• Can you find gradients, midpoints, lengths and the equation of a line, including perpendicular lines?
• Can you find the centre and radius of a circle from its equation, and the equation of a tangent?
• Can you find where a line meets a curve or a circle and interpret the number of solutions?

Circular measure and trigonometry

• Can you work in radians, including arc length, sector area and the area of a segment?
• Can you solve trigonometric equations in a given interval, using identities where needed?
• Do you know the graphs of the basic trigonometric functions and their transformations?

Series

• Can you expand a binomial with a positive whole-number power and find a specific term?
• Do you know the formulae for arithmetic and geometric progressions, including the sum to infinity and when it exists?

Differentiation and integration

• Can you find stationary points and decide their nature?
• Can you find the equation of a tangent or normal, and set up a rates of change question?
• Can you integrate, find a constant from a point, and find an area under a curve or between a curve and a line?
• Can you find a volume of revolution?

Paper 3: Pure Mathematics 3

Algebra

• Can you solve equations and inequalities involving a modulus?
• Can you use the factor and remainder theorems?
• Can you split a fraction into partial fractions, including repeated factors?
• Can you expand a binomial with a negative or fractional power and say when the expansion is valid?

Logarithmic and exponential functions

• Can you solve equations in which the unknown is a power?
• Can you use logarithms to reduce a relationship to a straight line and read off the constants?

Trigonometry

• Do you know the reciprocal functions, the compound angle formulae and the double angle formulae?
• Can you write a sum of sine and cosine in a single trigonometric form and use it to solve equations or find greatest and least values?

Differentiation and integration

• Can you differentiate products, quotients, implicit and parametric functions?
• Can you integrate by substitution, by parts and using partial fractions?
• Can you solve a first-order differential equation by separating the variables and interpret it in context?

Numerical solution of equations

• Can you show that a root lies in an interval by a sign change?
• Can you set up an iterative formula and use it to a required accuracy?

Vectors and complex numbers

• Can you work with lines in three dimensions, including angles, intersections and skew lines?
• Can you work with complex numbers in cartesian and modulus-argument forms, solve polynomial equations and sketch loci?