1. Core Content Across All Exam Boards

Regardless of the exam board, A-Level Mathematics consists of Pure Mathematics and Applied Mathematics, which is divided into Statistics and Mechanics.

Pure Mathematics (Common Topics)

• Proof: Methods of proof, including direct proof, proof by contradiction, and proof by induction (though induction is not in all specifications).
• Algebra and Functions: Quadratic equations, polynomial division, binomial expansion, and exponentials/logarithms.
• Coordinate Geometry: Straight-line equations, circles, and parametric equations.
• Sequences and Series: Arithmetic and geometric progressions, sigma notation.
• Trigonometry: Radians, trigonometric identities, sine/cosine rules, and trigonometric equations.
• Differentiation and Integration: Rules of differentiation, chain/product/quotient rules, integration by substitution and parts.
• Numerical Methods: Newton-Raphson method, iterative methods.
• Vectors: 3D vectors, scalar products.

Statistics (Common Topics)

• Data Representation: Histograms, cumulative frequency, box plots.
• Probability: Conditional probability, independent/dependent events.
• Statistical Distributions: Binomial and normal distributions.
• Hypothesis Testing: Use of critical regions, p-values.

Mechanics (Common Topics)

• Kinematics: SUVAT equations, motion graphs, projectiles.
• Forces and Newton’s Laws: Resolving forces, equilibrium, friction.
• Moments: Turning effects of forces.
• Connected Particles: Pulley systems, tension in strings.
• Work, Energy, and Power: Kinetic energy, potential energy, conservation of energy.

2. Differences in Content and Approach

Each board has slight variations in content depth and emphasis.

AQA

• Content Breakdown:
  • Pure Mathematics (2/3 of the syllabus)
  • Statistics and Mechanics (1/3 split equally)
• Key Features:
  • More structured and traditional layout.
  • Questions are generally direct and less context-based.
  • No numerical methods in statistics (unlike some other boards).
  • Statistics uses large data sets (e.g. analysing real-world data).
  • Mechanics is relatively standard with clear applications.

Edexcel

• Content Breakdown:
  • Pure Mathematics (2/3 of the syllabus)
  • Statistics and Mechanics (1/3 split equally)
• Key Features:
  • Consistent exam structure: Every year follows a predictable format.
  • Questions tend to be formulaic, with clear mark schemes.
  • Greater emphasis on modelling in Mechanics.
  • Uses large data sets, requiring students to interpret real-world data.
  • Statistics is more focused on probability distributions.
  • Mechanics includes projectiles and inclined planes more extensively.

OCR A

• Content Breakdown:
  • Pure Mathematics (2/3 of the syllabus)
  • Statistics and Mechanics (1/3 split equally)
• Key Features:
  • Closely follows the government-set syllabus without extra content.
  • More challenging algebraic manipulation compared to Edexcel and AQA.
  • Statistics includes a greater focus on hypothesis testing.
  • Mechanics has more emphasis on connected particles and forces.
  • Large data set included, but less central than in Edexcel.
  • Slightly more problem-solving focus in Mechanics.

OCR B (MEI)

• Content Breakdown:
  • Pure Mathematics (2/3 of the syllabus)
  • Statistics and Mechanics (1/3 split equally)
• Key Features:
  • Unique approach: OCR B (MEI) is designed to develop mathematical thinking and problem-solving.
  • Includes a Comprehension Paper: Students analyse and interpret unfamiliar mathematical content.
  • More focus on real-world applications, with questions presented in context.
  • Greater emphasis on numerical methods (e.g. iterative methods appear more frequently).
  • Mechanics has more modelling and interpretation, with less emphasis on direct formula application.
  • Statistics has a broader range of statistical techniques, including more work with distributions and hypothesis testing.

3. Unique Features of Each Board

The above gives a broad overview of the unique features of exam board, but in terms of detailed specific content, the following is a good guide for what to expect.

AQA

• Has infinite sums of iterative sequences.
• Does not have any Normal approximation to the binomial distribution.
• Only has moments problems in 1-d. Whilst this is not specified in the syllabus, no exam question has yet come up with a moments problem with forces at an angle.

OCR A

• The normal approximation to the binomial distribution is somewhat light-touch with no continuity correction required.
• Has area between a curve and the y-axis, unlike the other boards.
• Contains a subtopic of approximating upper and lower bounds of areas with rectangles.
• Unlike AQA and OCR B, has moments problems in 2-d, including ladders resting against walls and forces at an angle.

OCR B

• Like AQA, only has moments problems in 1d.
• In stats, the mean and variance of linear combinations of discrete random variables is examinable.
• Like Edexcel, the normal approximation to the binomial distribution requires a continuity correction to be used.

Edexcel

• Like OCR B, in the normal approximation to the binomial distribution, a continuity correction is requires.
• Linear coding in stats is directly examinable and the effect it has on the standard deviation and mean of a distribution.
• The discrete uniform distribution is included unlike any of the other boards.
• Box plots identify outliers as crosses.
• Like OCR, moments in 2-d is examinable, including ladder problems and forces at an angle.

4. Which Syllabus Should You Choose?

• AQA: Best for students who prefer a structured and traditional approach with clear question styles.
• Edexcel: Suitable for those who like predictability and a formulaic approach, with less focus on tricky algebra.
• OCR A: Great for students who enjoy challenging algebra and problem-solving, with a stronger statistics focus.
• OCR B (MEI): Ideal for students who like context-based questions, real-world applications, and numerical methods.

Final Thoughts

All A-Level Maths syllabuses broadly cover the same fundamental content aligning in about 95% of the content, but their approaches in how they do so differ. If you’re choosing between them, consider:

• Your strengths (e.g., algebra, statistics, mechanics).
• The type of exam you prefer (structured vs real-world).
• What you are hoping to achieve (your goals will definitely shape your choice).