A-Level Further Mathematics (OCR)

Course Overview 课程介绍

OCR A-Level 进阶数学 A，纯核必修 + 两门选修，覆盖复数、矩阵、微分方程等高阶主题。

OCR A-Level Further Mathematics A (H245) is a linear two-year course taken alongside A-Level Mathematics. OCR A-Level has moved to a linear structure since 2015, so all exams are taken at the end of the course. It is built from two mandatory Pure Core papers (Y540 and Y541) plus two optional papers chosen from Statistics (Y542), Mechanics (Y543), Discrete mathematics (Y544) and Additional Pure mathematics (Y545). The course introduces complex numbers, matrices, polar coordinates, hyperbolic functions and differential equations, and is highly valued by top-tier mathematics, engineering and physics programmes.

Key Facts 基本信息

Exam Board (考试局)	Oxford, Cambridge and RSA Examinations (OCR)
Specification Code (代码)	H235 (AS) / H245 (A-Level)
Structure (结构)	Linear (since 2017); AS is a standalone qualification and does not count towards A-Level
Grading (评分)	A* - E (A* only for full A-Level)
Exam Papers (试卷)	A-Level: Pure Core Y540/Y541 + 2 options · AS: Pure Core Y531 + 2 options
Coursework (课程作业)	No coursework, all external exams

AS / Year 1 Syllabus AS 阶段章节

ASPure Core (Y531): Proof, Complex Numbers and Matrices

Proof by induction, complex numbers and their arithmetic, Argand diagrams, matrices and their operations, transformations of the plane
ASPure Core (Y531): Further Vectors and Further Algebra

Further vectors, equations of lines and planes, roots of polynomials, further algebra and series
ASOption: Statistics (Y532)

Probability, discrete random variables, the Poisson distribution, bivariate data and correlation, hypothesis testing
ASOption: Mechanics (Y533)

Dimensional analysis, work, energy and power, impulse and momentum, motion in a circle
ASOption: Discrete Mathematics (Y534) / Additional Pure (Y535)

Y534: graphs and networks, algorithms, linear programming. Y535: number theory, recurrence relations, groups

A2 / Year 2 Syllabus A2 阶段章节

A2Pure Core (Y540/Y541): Series, Hyperbolic Functions and Further Calculus

Method of differences, Maclaurin series, hyperbolic functions, further calculus including improper integrals and volumes of revolution
A2Pure Core (Y540/Y541): Polar Coordinates and Differential Equations

Polar coordinates and their curves, first and second order differential equations including simple harmonic motion and damping
A2Option: Statistics (Y542)

Continuous random variables, linear combinations of random variables, hypothesis tests, chi-squared tests, non-parametric tests, regression
A2Option: Mechanics (Y543)

Centre of mass, circular motion, further dynamics and kinematics, collisions and elasticity
A2Option: Discrete (Y544) / Additional Pure (Y545)

Y544: network algorithms, critical path analysis, game theory, simplex. Y545: further sequences, groups, surfaces and partial differentiation, further calculus

Exam Structure (OCR H245) 考试结构

Pure Core 1 (Y540)	A-Level · Mandatory · 1h30m · 75 marks · 25%
Pure Core 2 (Y541)	A-Level · Mandatory · 1h30m · 75 marks · 25%
Options (choose any two)	A-Level · Statistics Y542 / Mechanics Y543 / Discrete Y544 / Additional Pure Y545 · each 1h30m · 75 marks · 25%
AS Pure Core (Y531)	AS · Mandatory · 1h15m · 75 marks · 33⅓%
AS Options (choose any two)	AS · Y532/Y533/Y534/Y535 · each 1h15m · 60 marks · 33⅓%

Suitable Majors & Pathway 适用专业与衔接

顶尖数学、工程、物理与计算机专业的强加分项，部分名校将其列为推荐或必修。

A-Level Further Mathematics is highly valued, and frequently required or strongly recommended, by top-tier mathematics, engineering, physics and computer science programmes at universities such as Cambridge, Oxford, Imperial and Warwick. It provides essential preparation for the pace and rigour of quantitative degrees, covering abstract and applied topics (complex numbers, matrices, differential equations) that bridge A-Level Mathematics and university study.