OCRAS Level186 resources

OCR AS Level Further Mathematics A Past Papers

Download OCR AS Level Further Mathematics A (H235) past papers. Pure Core, plus optional Mechanics, Statistics, Discrete or Additional Pure components. 19 resources.

📅June 2017 – present📄186 resources available✅Free to download

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186 of 186 resources — page 1 of 2

June 2023

19 files

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Further Mathematics A – Question paper – Statistics

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Further Mathematics A – Question paper – Pure core 1

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Further Mathematics A – Question paper – Mechanics

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Further Mathematics A – Question paper – Discrete mathematics

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Further Mathematics A – Modified papers

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Further Mathematics A – Mark scheme – Statistics

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Further Mathematics A – Mark scheme – Mechanics

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Further Mathematics A – Mark scheme – Discrete mathematics

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Further Mathematics A – Examiners’ report – Statistics

Examiner Report

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Further Mathematics A – Examiners’ report – Mechanics

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Further Mathematics A – Examiners’ report – Pure core 1

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Further Mathematics A – Mark scheme – Additional pure mathematics

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Further Mathematics A – Examiners’ report – Additional pure mathematics

Examiner Report

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Further Mathematics A – Examiners’ report – Discrete mathematics

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Further Mathematics A – Question paper – Statistics

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Further Mathematics A – Question paper – Statistics answer book

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Further Mathematics A – Question paper – Pure core answer book

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Further Mathematics A – Question paper – Pure core

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Further Mathematics A – Question paper – Mechanics

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June 2022

18 files

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Further Mathematics A – Question paper – Statistics

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Further Mathematics A – Question Paper – Pure core 1

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📋

Further Mathematics A – Modified papers

Modified Paper

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Further Mathematics A – Question Paper – Discrete mathematics

Question Paper

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✅

Further Mathematics A – Mark scheme – Statistics

Mark Scheme

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✅

Further Mathematics A – Mark scheme – Mechanics

Mark Scheme

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✅

Further Mathematics A – Mark scheme – Discrete mathematics

Mark Scheme

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📊

Further Mathematics A – Examiners’ report – Mechanics

Examiner Report

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📊

Further Mathematics A – Examiners’ report – Pure core 1

Examiner Report

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📊

Further Mathematics A – Examiners’ report – Statistics

Examiner Report

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📊

Further Mathematics A – Examiners’ report – Additional pure mathematics

Examiner Report

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📊

Further Mathematics A – Examiners’ report – Discrete mathematics

Examiner Report

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📄

Further Mathematics A – Question paper – Statistics answer book

Question Paper

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Further Mathematics A – Question paper – Pure core answer book

Question Paper

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Further Mathematics A – Question paper – Statistics

Question Paper

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📄

Further Mathematics A – Question paper – Pure core

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Further Mathematics A – Question paper – Mechanics

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Further Mathematics A – Question paper – Mechanics answer book

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November 2021

16 files

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Further Mathematics A – Question paper – Statistics

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Further Mathematics A – Question paper – Pure core 1

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Further Mathematics A – Question paper – Mechanics

Question Paper

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📋

Further Mathematics A – Modified papers

Modified Paper

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📄

Further Mathematics A – Question paper – Discrete mathematics

Question Paper

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✅

Further Mathematics A – Mark scheme – Mechanics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Statistics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Pure core 1

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Additional pure mathematics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Discrete mathematics

Mark Scheme

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📄

Further Mathematics A – Question paper – Statistics answer book

Question Paper

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📄

Further Mathematics A – Question paper – Pure core answer book

Question Paper

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📄

Further Mathematics A – Question paper – Statistics

Question Paper

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📄

Further Mathematics A – Question paper – Pure core

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics answer book

Question Paper

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November 2020

17 files

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Further Mathematics A – Question paper – Statistics

Question Paper

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📄

Further Mathematics A – Question paper – Pure core 1

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics

Question Paper

Download

📄

Further Mathematics A – Question paper – Discrete mathematics

Question Paper

Download

✅

Further Mathematics A – Mark scheme – Statistics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Mechanics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Pure core 1

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Additional pure mathematics

Mark Scheme

Download

✅

Further Mathematics A – Mark scheme – Discrete mathematics

Mark Scheme

Download

📊

Further Mathematics A – Examiners’ report

Examiner Report

Download

📊

Further Mathematics A – Examiners’ report

Examiner Report

Download

📄

Further Mathematics A – Question paper – Statistics answer book

Question Paper

Download

📄

Further Mathematics A – Question paper – Pure core answer book

Question Paper

Download

📄

Further Mathematics A – Question paper – Statistics

Question Paper

Download

📄

Further Mathematics A – Question paper – Pure core

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics answer book

Question Paper

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June 2019

19 files

📄

Further Mathematics A – Question paper – Statistics

Question Paper

Download

📄

Further Mathematics A – Question Paper – Pure core 1

Question Paper

Download

📄

Further Mathematics A – Question paper – Discrete mathematics

Question Paper

Download

✅

Further Mathematics A – Mark scheme – Mechanics

Mark Scheme

Download

📋

Further Mathematics A – Modified papers

Modified Paper

Download

✅

Further Mathematics A – Mark scheme – Statistics

Mark Scheme

Download

📊

Further Mathematics A – Examiners’ report – Mechanics

Examiner Report

Download

✅

Further Mathematics A – Mark scheme – Additional pure mathematics

Mark Scheme

Download

📊

Further Mathematics A – Examiners’ report – Pure core 1

Examiner Report

Download

✅

Further Mathematics A – Mark scheme – Discrete mathematics

Mark Scheme

Download

📊

Further Mathematics A – Examiners’ report – Statistics

Examiner Report

Download

📊

Further Mathematics A – Examiners’ report – Discrete mathematics

Examiner Report

Download

📊

Further Mathematics A – Examiners’ report – Additional pure mathematics

Examiner Report

Download

📄

Further Mathematics A – Question paper – Statistics answer book

Question Paper

Download

📄

Further Mathematics A – Question paper – Pure core answer book

Question Paper

Download

📄

Further Mathematics A – Question paper – Statistics

Question Paper

Download

📄

Further Mathematics A – Question paper – Pure core

Question Paper

Download

📄

Further Mathematics A – Question paper – Mechanics

Question Paper

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📄

Further Mathematics A – Question paper – Mechanics answer book

Question Paper

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June 2018

4 files

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Further Mathematics A – Question paper – Statistics answer booklet

Question Paper

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Further Mathematics A – Question paper – Pure core answer booklet

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Further Mathematics A – Question paper – Statistics

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Further Mathematics A – Question paper – Mechanics

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No date

6 files

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Further Mathematics A – Statistics

Sample Assessment Materials

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Further Mathematics A – Pure core 1

Sample Assessment Materials

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Further Mathematics A – Mechanics

Sample Assessment Materials

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📝

Further Mathematics A – Additional pure mathematics

Sample Assessment Materials

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Further Mathematics A – Discrete mathematics

Sample Assessment Materials

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📝

Further Mathematics A – Statistics

Sample Assessment Materials

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Unknown

1 file

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Further Mathematics A – Question paper – Additional pure mathematics

Question Paper

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Pure Core Extended with Optional Applied Specialisms at AS Further Maths

OCR AS Level Further Mathematics A (H235) extends the content of AS Mathematics into deeper algebraic, geometric, and applied territory, and is typically studied alongside AS or A-Level Mathematics. The qualification is assessed by two papers: Pure Core (mandatory) and one optional paper chosen from Additional Pure, Mechanics, Statistics, or Discrete Mathematics. Paper 1: Pure Core (H235/01, 1 hour 30 minutes, 75 marks) covers content that goes beyond AS Mathematics A. Topics include complex numbers (the Argand diagram, modulus-argument form, De Moivre's theorem at introductory level), matrices (2×2 and 3×3 matrix operations, determinants, inverse matrices, transformations in the plane), further calculus (integration by parts, integration by substitution, arc length and surface area of revolution), series (Maclaurin series for standard functions), and proof by induction. The optional Paper 2 allows specialisation. Mechanics (H235/02B) covers further kinematics (variable acceleration using calculus, projectiles on inclined planes), circular motion, work, energy and power, and simple harmonic motion. Statistics (H235/02C) covers discrete and continuous probability distributions beyond the binomial, including the normal distribution, statistical inference using the normal distribution, and chi-squared contingency table tests. Discrete Mathematics (H235/02D) covers graph theory (traversability, spanning trees), algorithms (sorting, shortest path, linear programming), and networks. Additional Pure Mathematics (H235/02A) extends the Pure Core with further complex numbers, hyperbolic functions, differential equations, and vectors in three dimensions.

Exam Paper Structure

Paper 1Calculator ✓

Pure Core

⏱ 1 hour 30 minutes🎯 75 marks📊 50%% of grade

Complex numbersMatrices and transformationsFurther calculusSeries and Maclaurin expansionsProof by induction

Paper 2Calculator ✓

Optional component (Mechanics / Statistics / Discrete / Additional Pure)

⏱ 1 hour 30 minutes🎯 75 marks📊 50%% of grade

Variable acceleration and circular motion (Mechanics)Normal distribution and chi-squared tests (Statistics)Graph theory and algorithms (Discrete)Differential equations and vectors (Additional Pure)

Key Information

Exam Board	OCR
Specification Code	H235
Qualification	AS Level
Grading Scale	A–E
Assessment Type	2 written papers (Pure Core + 1 optional)
Number Of Papers	2
Exam Duration	1 hour 30 minutes per paper
Total Marks	150 (75 + 75)
Calculator Status	Calculator allowed in both papers
Available Sessions	June 2017 – present
Total Resources	19

Key Topics in Further Mathematics A

Topics you need to know

Complex numbers and the Argand diagramMatrix operations and transformationsProof by mathematical inductionFurther integration techniquesSimple harmonic motionNormal distribution and inferenceGraph theory and network algorithms

Exam Command Words

Command word	What the examiner expects
Show that	Derive the stated result with complete algebraic working
Find the exact value	Express the answer in surd or fractional form — not as a decimal
Prove by induction	Establish the result for all n using the four-step induction structure
Sketch	Draw a diagram showing key features — not to scale, but proportionally reasonable

Typical Grade Boundaries

Grade	Approximate mark needed
A	65–80%
B	53–64%
C	41–52%
D	29–40%
E	18–28%

⚠️ OCR AS Further Mathematics A grade boundaries vary by session and optional component.

Mastering Complex Numbers, Matrix Transformations, and Proof by Induction

Complex number questions in Pure Core typically follow one of three patterns: algebraic manipulation (expanding, simplifying, or finding roots of quadratic equations with complex solutions), Argand diagram geometry (plotting loci such as circles, half-lines, and perpendicular bisectors), or modulus-argument conversions (converting between Cartesian and polar form). For loci questions, translate the inequality or equation into geometric language before attempting to sketch — for example, |z − 3| < 2 describes all complex numbers within distance 2 of the point (3, 0) in the Argand plane. Matrix transformation questions require you to know the standard 2×2 matrices for rotation, reflection, and enlargement off the top of your head. Rotation anticlockwise by θ about the origin has matrix [[cos θ, −sin θ], [sin θ, cos θ]]. Reflection in the line y = x has matrix [[0, 1], [1, 0]]. Composite transformations are applied right-to-left: if matrix A is applied first, then B, the combined transformation is BA (not AB). This ordering confuses many students. Proof by induction follows a rigid four-step structure that must be presented in full for full marks: (1) Base case — show the statement holds for the starting value (usually n = 1). (2) Inductive hypothesis — assume the statement holds for n = k. (3) Inductive step — use the assumption for n = k to prove the statement for n = k + 1. (4) Conclusion — state that since the base case holds and the inductive step is proved, the result holds for all n ≥ 1 by induction. Every step must be explicitly present. Marks are awarded for each step in the OCR mark scheme.

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OCR AS Level Further Mathematics A Past Papers

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June 2023

June 2022

November 2021

November 2020

June 2019

June 2018

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Pure Core Extended with Optional Applied Specialisms at AS Further Maths

Exam Paper Structure

Key Information

Key Topics in Further Mathematics A

Exam Command Words

Typical Grade Boundaries

Mastering Complex Numbers, Matrix Transformations, and Proof by Induction

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