Here is a summary of the OCR A Level Further Mathematics A (H245) specification (Version 1.7, February 2024).

1. Qualification Overview

• Title: OCR A Level Further Mathematics A
• Specification Code: H245
• First Assessment: 2019
• Awarding Body: Oxford Cambridge and RSA (OCR)
• Accreditation: Ofqual (QN603/1325/0)
• Type: Linear qualification (all exams in the same series)

2. Course Structure

• Mandatory Core: Pure Core (assessed in two papers: Y540 and Y541, each 25% of A Level)
• Optional Papers: Choose two from:
  1. Statistics (Y542)
  2. Mechanics (Y543)
  3. Discrete Mathematics (Y544)
  4. Additional Pure Mathematics (Y545)
• Each optional paper is 25% of the A Level.
• Total Papers: 4 (2 mandatory + 2 optional)
• Exam Duration: 90 minutes per paper

3. Content Areas

Pure Core (Mandatory)

• Proof by induction
• Complex numbers
• Matrices (2D and 3D transformations, determinants, inverses)
• Further vectors (lines, planes, vector products)
• Further algebra (roots of polynomials, partial fractions)
• Series (summation, method of differences)
• Hyperbolic functions
• Further calculus (Maclaurin series, improper integrals, polar coordinates)
• Differential equations (1st and 2nd order, SHM, damped oscillations)

Statistics (Optional)

• Probability (combinatorics)
• Discrete and continuous random variables
• Hypothesis tests and confidence intervals
• Chi-squared tests, non-parametric tests
• Correlation and regression

Mechanics (Optional)

• Dimensional analysis
• Work, energy, power
• Impulse and momentum
• Centre of mass
• Circular motion
• Further dynamics (variable force)

Discrete Mathematics (Optional)

• Mathematical preliminaries (sets, pigeonhole principle)
• Graphs and networks
• Algorithms (sorting, packing, complexity)
• Network algorithms (shortest path, travelling salesperson)
• Critical path analysis
• Linear programming and game theory

Additional Pure Mathematics (Optional)

• Sequences and series (recurrence relations)
• Number theory (modular arithmetic, Fermat’s little theorem)
• Group theory
• Further vectors (scalar triple product)
• Surfaces and partial differentiation
• Further calculus (arc length, surface area, reduction formulae)

4. Assessment Objectives (AOs)

• AO1: Use and apply standard techniques (50%)
• AO2: Reason, interpret and communicate mathematically (≥15%)
• AO3: Solve problems within mathematics and other contexts (≥15%)

5. Key Features

• Linear assessment
• Equal weighting across papers
• Use of technology encouraged (calculators, graphing tools, CAS)
• Formulae booklet provided in exams
• Synoptic assessment across papers
• Stretch and challenge questions for high achievers
• Co-teachable with AS Level Further Mathematics A (H235)

6. Practical Details

• Total Qualification Time: 360 hours
• Grading: A*–E
• Results: Available in June each year
• Retakes: Allowed for full qualification
• Special Considerations: Available via JCQ guidelines
• Private Candidates: Permitted

7. Appendices

• Mathematical notation and symbols
• Formulae and identities (provided in exam booklet)
• Statistical tables (critical values for χ², Wilcoxon tests, etc.)
• Summary of updates to the specification