CIE A-Level Further Maths (9231) Topic Questions – Your Key to Scoring an A*

Getting an A* in CIE A-Level Further Maths (9231) may seem like a tough challenge, but with the right tools and strategies, it’s absolutely achievable. At Exam Papers Practice, we’ve developed a collection of topic-wise questions to help students prepare more efficiently and effectively. Whether you’re revising for an upcoming test or preparing for the final exam, our resources are designed to guide you step-by-step to top performance.

Here you will find all CIE A Level Further Maths Topic questions to revise by topic and exam board with mark scheme and video solution

Algebra & Functions

Evaluate Limits Using L'Hopital's Rule

Evaluate Limits Using Maclaurin's Series

Finding Maclaurin's Series

Graphs of Modulus and Reciprocals

Inequalities of Polynomials

Limits of Rational Polynomials

Modulus Equations and Inequalities

Oblique Asymptotes and Range of Rational Functions

Root Relationshhips (Quartics)

Root Relationships (Quadratics)

Sketching Rational Graphs

Solving Rational Inequalities Algebraically

Using Common Maclaurin's Series

Using Common Series

Calculus

Arc Length of Curves

Differentiating Inverse Trigonometric Functions

Improper Intergrals

Integrating Using Inverse Trigonometry

Mean Value of a Function

Partial Fraction Integration

Reduction Formula

Surface Area of Revolution

Two Limit Rules

Volume of Revolution

Complex Numbers

Add, Subtract and Multiply

Argrand Diagrams

Complex Conjugate Pairs

Complex Solutions to Quadratics

De Moivre's Theorem

Euler's Identiy and Exponential Form

Forms of a Complex Number

Loci of Complex Numbers

Modulus and Argument

Modulus and Argument Form

Modulus & Argument Multiplication

Nth Root of a Complex Number

Rationalize Complex Numbers

Summing Using De Moivre's

Differential Equations

Auxiliary Equation

Coupled Differential Equations

Hooke's Law and Simple Harmonic Motion

Integrating Fator

Second Order Homogeneous ODEs

Second Order Inhomogeneous ODEs

Simple Harmonic Motion with Damping

Hyperbolic Functions

Differentiating Hyperbolic Trigonometric Functions

Hyperbolic Trigonometric Functions

Hyperbolic Trigonometric Identities

Integrating Hyperbolic Trigonometric Functions

Integrating Using Inverse Hyperbolic Trigonometry

Inverse Hyperbolic Trigonometric Functions

Reciprocal Hyperbolic Trigonometric functions

Matrices

Basics of Matrices

Cayley Hamilton Theorem

Determinant Factorization

Determinant of 2x2 Matrices

Determinant of 3x3 Matrices

Eigen Values and Eigen Factors

Invariant Points and Lines

Inverse of 2x2 Matrices

Inverse of 3x3 Matrices

Matrix Diagonalization

Matrix Transforms in 2D

Matrix Transforms in 3D

Multiple Matrix Transforms

Multiplying Matrices

Singularities

Solving Simultaneous Equations

Numerical Methods

Euler's Step Method

Improved Euler's Method

Mid Ordinate Rule

Simpson's Rule

Polar Coordinates

Area Under a Polar

Polar Coordinates

Sketching Polar Curves

Tangents to Polar Curves

Proof

Method of Differences

Proof by Induction (Divisibility)

Proof by Induction (Matrices)

Proof by Induction (Sequences)

Proof by Induction (Series)

Vectors

Angle Between Lines

Angle Between Two Planes

Angle Between Lines and Planes

Distance Between a Line and Point

Distance Between a Plane and Point

Distance Between Two Lines

Equation of a Line

Equation of a Plane

Intersection of Lines and Planes

Intersection of Lines

Scalar Product

Using the Vector Product

Vector Product

Other Useful Questions That Find Useful to the Course

Complex Numbers 1a & b

Complex Numbers 1b & c

Complex Numbers 1d

Matrices (Arithmetic 2x2 Inverse)

Matrices (Simultaneous Equations 3x3 Inverse)

Poisson Distribution

Algorithms on Graphs (MST and Shortest Paths)

Matrix Transformations

Matrix Transformations (Invariance)

Discrete Random Variables

Complex Numbers (Roots of Equations)

Route Inspection

Poisson (Binomial)

Roots of Polynomials

Roots of Polynomials (Inc Transformation of Roots)

Linear Programming

Proof by Induction

Chi Square Testing (Goodness of Fit)

Vector Lines (Intersections & Angles)

Vector Lines (Planes & Distances)

Chi Squared Tests (Contingency Tables)

Critical Path Analysis

Volumes of Revolution

Why Topic-Based Practice is Crucial

Further Mathematics is advanced and packed with challenging concepts like complex numbers, matrices, differential equations, and more. With so many topics to cover, it’s easy to feel overwhelmed. This is where topic-based practice becomes essential.

Instead of jumping randomly between past papers, focusing on individual topics lets you:

  • Master one concept at a time.

  • Identify weak areas quickly.

  • Build confidence gradually.

  • Make revision more manageable.

Our website, Exam Papers Practice, offers a full breakdown of CIE A-Level Further Maths (9231) questions arranged by topic. This way, you can target your studies and improve faster.

What’s Inside Our Topic Questions?

Our CIE A-Level Further Maths (9231) Topic Questions are organized to follow the syllabus closely. Each topic includes:

  • A collection of real past exam questions.

  • Clear topic labels (e.g., “Complex Numbers”, “Matrices”).

  • Progressive difficulty to challenge you as you improve.

  • Space for working solutions.

We also include mark schemes, so you can compare your answers with what examiners expect — an excellent way to polish your technique and boost your accuracy.

Smart Tips to Get an A* in CIE A-Level Further Maths (9231)

Alongside using our topic-based resources, try these study techniques to maximize your results:

1. Understand the Syllabus

Before diving into questions, download the 9231 syllabus from the official Cambridge website. It outlines all topics, learning objectives, and what you’re expected to know. This ensures your revision is complete and focused.

2. Use Topic Questions to Build Foundation

Start with easy-to-moderate questions from each topic. Don’t rush into solving the hardest questions. Build a solid understanding first.

Example: If you’re studying Matrices, begin with basic operations and work your way up to transformations and determinants.

3. Practice Daily, Even If It’s Just 30 Minutes

Consistency beats cramming. Even short, regular study sessions with our CIE A-Level Further Maths (9231) Topic Questions can lead to huge improvements.

4. Make a Revision Schedule

Break your revision time by topic. For instance:

  • Monday: Complex Numbers

  • Tuesday: Matrices

  • Wednesday: Differential Equations

  • Thursday: Mechanics

  • Friday: Review and Mixed Practice

This keeps your study balanced and avoids burnout.

5. Use the Mark Scheme Wisely

After solving a question, don’t just check if your final answer is correct. Compare your working steps with the mark scheme. Marks are often awarded for method and structure, not just answers.

6. Revise Mistakes

Create a “mistake log” where you write down any question you got wrong. Revisit these regularly until you master them.

7. Time Yourself

Closer to the exam, time yourself while solving questions. This helps improve speed and time management.

8. Practice Full Papers After Topic Mastery

Once you’re confident with each topic, start solving full past papers. This tests your endurance and helps you manage pressure.

Are You Having Trouble with Your Studies? Get the Help You Need Today

If you’re struggling with your studies and looking for extra support, why not consider hiring a tutor or enrolling in summer school or Easter revision services? Whether you’re aiming to boost your grades or better understand complex topics, targeted revision can make a big difference. Accessing the right resources is crucial, and there are multiple options available to help you succeed.

Why Consider a Tutor for Your Studies?

A personal tutor can provide tailored support based on your individual learning needs. Tutors offer one-on-one sessions that focus on the areas where you need the most improvement. Whether it’s mathematics, science, or language arts, a tutor can provide targeted strategies and techniques to ensure that you understand key concepts and are prepared for upcoming exams.

Summer School and Easter Revision Services: A Great Opportunity

Summer and Easter revision services are an excellent way to prepare for exams while still having time to relax. These sessions are structured to help you revisit your syllabus, revise key topics, and practice with exam papers. These services offer intensive study periods, which can be highly beneficial for students aiming to refresh their knowledge and boost confidence.

Accessing the Board Syllabus for Efficient Studying

Accessing your exam board’s syllabus is one of the most effective ways to stay on track during your revision. The syllabus provides a clear outline of the topics you need to cover and allows you to prioritize areas that require more attention.

The comprehensive CIE A Level Further Maths syllabus ensures that you are following the right path and studying the correct resource material.

Where to Find the Best Educational Services

For further support, you can check out services offered by our Sister Companies Lite Regal International College and Lite Regal Education, both of which provide expert tutors and revision resources. Whether you need a tutor for personalized lessons or are looking to join a revision group, these services have a wide range of options to fit your study needs.

With the right mindset and resources, CIE A-Level Further Maths (9231) doesn’t have to be a mountain. At Exam Papers Practice, our topic-based question sets are your secret weapon to mastering the syllabus.

From matrices to mechanics, every concept is covered. You’ll study smarter, not harder — and boost your chances of achieving that A* grade.