AQA A-Level Mathematics Revision Guide

• ⏰Duration: 2 hours

• 🏆Marks: 100 marks (33.3% of total grade)

• 📌Content: Paper 1 assesses only pure maths. Anything from the pure content of the specification can appear.

• Proof and mathematical argument (e.g. simple proofs, logical reasoning) 

• Algebra and functions - polynomials, surds, modulus, inverse functions, manipulating algebraic expressions/functions. 

• Coordinate geometry in the (x, y) plane - working with lines, curves, circles, etc. 

• Sequences and series - arithmetic sequences, geometric sequences, series, binomial expansion, etc. 

• Trigonometry - trig identities, equations, graphs, working in radians, trig functions, transformations. 

• Exponentials and logarithms - working with exponential and log functions, solving related equations. 

• Differentiation and integration - the usual calculus: derivatives, integrals.

• Numerical methods - methods for approximations (e.g. solving equations numerically). 

So Paper 1 is “pure maths only”, covering a wide range of fundamental and advanced maths topics. 

• ❓Question Types:  Paper 1 focuses entirely on pure maths skills and reasoning.

Common Question Types:

Short structured questions

• Clear method, usually 1–5 marks

• Tests core skills like differentiation, integration, solving equations or simplifying expressions

Multi-step problem-solving questions

• Linked parts (a), (b), (c)…

• Each step builds on the previous one

• Often mixes several topics (e.g. algebra + calculus)

Proof and explanation questions

• “Show that…”

• “Hence prove…”

• Requires clear logical steps and correct mathematical language

Graphical interpretation

• Sketching graphs

• Using graphs to solve equations

• Interpreting intersections, turning points, asymptotes

Application-style pure maths

• Pure maths set in a context (no statistics or mechanics yet)

• Requires selecting the right technique, not just calculation

📌 Key skill tested: algebraic accuracy + logical reasoning

• ⏰Duration: 2 hours

• 🏆Marks: 100 marks (33.3% of total grade)

• 📌Content: Pure maths content (from the same list as Paper 1) + Mechanics content

Mechanics Topics Included:

• Quantities and units (SI units and derived units: velocity, acceleration, force, moment, etc.) 

• Kinematics - motion in one or two dimensions: displacement, velocity, acceleration, projectile motion, etc. 

• Forces and Newton’s Laws - applying force, mass, acceleration; dynamics. 

• Moments - equilibrium, turning effects, lever arms, torque (moments) problems. 

Because Paper 2 includes both pure and mechanics portions, you need to be ready to switch between “pure maths thinking” and “physics-style modelling” within the same paper. 

• ❓Question Types:  Paper 2 is split between pure maths questions and mechanics questions.

Pure Maths Question Types

These are very similar to Paper 1:

• Short calculations

• Multi-part problems

• “Show that” questions

• Calculus and algebra combined

• Problem-solving using multiple techniques

Mechanics Question Types

Modelling questions

• Turning a real situation into equations

• Using simplifying assumptions

Diagram-based problems

• Drawing clear force diagrams or motion diagrams

• Identifying forces acting on particles

Calculation-heavy mechanics

• SUVAT equations

• Applying Newton’s laws

• Calculating forces, acceleration, tension

Explanation questions

• Explaining assumptions (e.g. “particle”, “smooth surface”)

• Interpreting results in context

📌 Key skill tested: translating real-world situations into maths

• ⏰Duration: 2 hours

• 🏆Marks: 100 marks (33.3% of total grade)

• 📌 Content: Pure maths content (same list as Paper 1) + Statistics content

Statistics Topics Included:

• Statistical sampling - understanding populations vs samples, sampling techniques (e.g. random sampling), critiquing sampling methods. 

• Data presentation and interpretation - histograms, scatter diagrams, regression lines (though heavy regression calculations may be excluded), understanding correlation vs causation, interpreting data. 

• Measures of location and spread (mean, median, standard deviation, outliers, interpreting summary statistics) 

• Probability - basic probability, events, Venn diagrams perhaps depending on context, probability calculations.

• Statistical distributions - e.g. binomial distribution, normal distribution (as per the spec). 

• Hypothesis testing - using statistical tests to make inferences, interpreting results, understanding what conclusions you can draw. 

So Paper 3 demands both “pure maths reasoning + calculation” and “statistics-style thinking and interpretation.” 

• ❓Question Types:  Paper 3 combines pure maths with statistics, and interpretation is especially important here.

Pure Maths Question Types

Again, similar to Papers 1 and 2:

• Multi-step algebra and calculus problems

• Graph work

• “Show that” and “hence” questions

• Problem-solving under time pressure

Statistics Question Types

Data interpretation

• Reading and interpreting tables, histograms, box plots

• Identifying trends, outliers and limitations

Calculation questions

• Mean, variance, standard deviation

• Probabilities using binomial or normal distributions

• Using calculator functions accurately

Hypothesis testing

• Stating hypotheses clearly

• Carrying out a test

• Writing conclusions in context

Written reasoning

• Explaining what results mean

• Commenting on assumptions or methods

• Justifying conclusions

📌 Key skill tested: combining maths with written interpretation

📑 Paper 1

• ⏰Duration: 1 hour 30 minutes




• 🏆Marks: 80 marks (50% of total grade)




• 📌Content: Paper 1 assesses a mixture of core Pure Mathematics and Mechanics content.

PURE MATHEMATICS

Proof

• Types of proof: deduction, exhaustion, disproof by counterexample.

Algebra and Functions

• Laws of indices (including rational indices)

• Manipulating surds and rationalising denominators

• Quadratic functions: roots, discriminant, solving equations, completing the square

• Simultaneous linear and quadratic equations

• Polynomials, factor theorem, algebraic manipulation

• Inequalities: linear and quadratic

• Graphs: sketching, transformations, intersections

• Functions: domain, range, composite and inverse functions

• Proportional relationships

Coordinate Geometry

• Equations of straight lines

• Equation and geometric properties of circles

• Using coordinate methods to solve geometric problems

Sequences and Series

• Arithmetic and geometric sequences

• Arithmetic and geometric series

• Binomial expansion for positive integer powers

Trigonometry

• Trigonometric definitions and exact values

• Trig identities (e.g. sin² + cos² = 1)

• Solving simple trigonometric equations

• Graphs of sine, cosine and tangent

Exponentials & Logarithms

• Exponential functions

• Laws of logarithms

• Solving exponential and logarithmic equations

• Modelling with exponentials

Differentiation

• Basic rules: powers, exponentials, trig

• Tangents, normals, stationary points

• Interpreting derivatives as rates of change

• Second derivative and nature of stationary points

Integration

• Basic integration (reverse differentiation)

• Definite integrals

• Areas under curves

Vectors

• Vector representation

• Vector algebra: magnitude, addition, subtraction, scalar multiples

• Vector geometry in 2D/3D

MECHANICS

Quantities and Units

• Displacement, velocity, acceleration, force

• SI units and dimensional reasoning

Kinematics

• Motion in a straight line

• Constant acceleration equations

• Velocity–time and displacement–time graphs

Forces and Newton’s Laws

• Types of forces

• Resultant force

• Newton’s laws applied to simple contexts

• Connected particles or bodies in simple cases

• ❓Question Types: Since Paper 1 covers Pure mathematics + Mechanics, typical question types include:

• Short-answer / single-mark questions: e.g. recall a formula, give an exact value (trig, indices, surds), do a simple calculation.

• Procedural / method questions: apply algebraic manipulation, solve equations or inequalities, simplify surds, factorise, complete the square, expand brackets, etc.

• Graph/sketch questions: sketch functions, transformations, circles or lines (coordinate geometry), interpret intercepts/gradients.

• Multi-step problems: combining several techniques - e.g. solve a quadratic inequality then interpret, or solve a kinematics problem using algebra and equations of motion.

• Calculus-based questions: differentiation/integration tasks - find derivative, find turning points, integrate for area under curve, apply to kinematics/mechanics (velocity, displacement, acceleration).

• Vector or mechanics problems: vector proofs/manipulations; mechanics questions involving forces, motion, using the correct formulae, units, modelling.




• Proof or reasoning questions: simple proofs or deductive reasoning (especially from the “Proof” topic).

Thus Paper 1 tends to combine shorter factual/calculation items with longer, multi-part applied or theoretical problems, sometimes requiring deeper reasoning or method plus accuracy plus interpretation.

📑 Paper 2

• ⏰Duration: 1 hour 30 minutes 




• 🏆Marks: 80 marks (50% of total grade) 




• 📌Content: Paper 2 includes the same core Pure content that is in paper 1 (Proof through to Integration) plus all Statistics topics.

STATISTICS

Statistical Sampling

• Types of sampling (random, systematic, stratified, etc.)

• Advantages and disadvantages

• Understanding population vs. sample

Data Presentation and Interpretation

• Interpreting charts, diagrams and tables

• Measures of central tendency and spread

• Correlation and regression in basic forms

• Outliers and data features

• Using and interpreting large data sets (conceptually)

Probability

• Basic probability rules

• Mutually exclusive and independent events

• Combined events

• Tree diagrams and Venn diagrams

Statistical Distributions

• Discrete distributions appropriate for AS level

• The binomial distribution: notation, conditions, probability calculations

Statistical Hypothesis Testing

• Basic concepts of hypothesis testing

• Formulating hypotheses

• Using the binomial distribution for tests

• Interpreting significance and conclusions

• ❓Question Types:  Paper 2 mixes Pure mathematics (like some of Paper 1) with Statistics, so you get a different mix of question types:

• Short-answer / fact recall: formula recall, definitions, basic probability/frequency statements.




• Procedural questions (pure maths): algebra, functions, sequences/series, trig, logs/exponentials, calculus (as in Paper 1) — e.g. solve equations, simplify expressions, differentiate/integrate, series expansion.




• Data-handling and interpretation questions: given data sets/tables/graphs/histograms or charts — summarise data (mean, median, mode, range, identify outliers), interpret scatter diagrams, frequency distributions, etc.




• Probability questions: simple event probability, combined events (independent/conditional), use of tree diagrams or set notation, probability calculations.




• Statistical distribution questions: discrete distributions (e.g. binomial), compute probabilities under distribution models, expectations, variances if applicable.




• Statistical hypothesis testing questions: forming hypotheses (null/alternative), carrying out binomial tests or similar, interpreting significance, drawing conclusions, commenting on context.




• Multi-step / problem-solving questions combining pure maths + statistics: e.g. apply algebra to model a data set; use probability + algebra; interpret outcomes; apply context (word problems).




• Reasoning/justification questions: explaining why a method/approach is valid, commenting on assumptions or limitations (especially in modelling or statistics).

Because of the inclusion of statistics, Paper 2 often mixes mathematical calculation with data interpretation, probability reasoning and contextual modelling - in addition to “pure” math questions.

✨Here are some top tips to make your revision more effective:

1. Master the Core Skills 🧠

Pure maths is the foundation. Make sure you’re confident with:

• Algebraic manipulation

• Differentiation and integration

• Trigonometric identities

• Functions and graphs

These ideas appear everywhere.

2. Learn the Exam Style 📝

Both AS and A Level Maths has a very recognisable question format.
Do this to get familiar:

• Work through past papers (full papers under timed conditions!)

• Try topic-by-topic questions to strengthen weak areas

• Check mark schemes to understand phrasing and structure

You will find the links to past papers on this page!

3. Use Your Formula Booklet Effectively 📘

Know:

• What’s given

• What’s not given

• How each formula is applied

Students often waste time trying to memorise things they don’t need to!

4. For Statistics 📊

Focus on:

• Using your calculator efficiently (normal distribution especially!)

• Understanding the meaning of hypotheses and conclusions

• Practising interpretation questions (very common!)

5. For Mechanics ⚙️

Success comes from:

• Drawing clear diagrams

• Identifying forces correctly

• Breaking problems into small steps

• Knowing standard modelling assumptions

6. Review Mistakes the Right Way 🔄

Don’t just redo the question - instead:

• Diagnose why you made the mistake

• Summarise it in a notebook (“silly mistake log”)

• Redo the question a week later to check you’ve fixed the issue

7. Build Exam Stamina ⏱️

Three 2-hour papers require:

• Timed practice

• Prioritising easy marks

• Knowing when to move on

Speed + accuracy = success.

8. Stay Positive and Look After Yourself 🌱

Breaks, rest, and balanced revision are essential - not optional.
A clear brain solves maths better than a tired one!

🎉 Final Thoughts

A Level Maths may look demanding, but with the right strategy, it becomes completely manageable. Focus on understanding, practise consistently and build your exam technique. You’ve got this! 💪