AQA A-Level Further Mathematics (7367) Topic Questions

Achieving an A* in AQA A-Level Further Maths (7367) requires dedication, strategy, and the right resources. At Exam Papers Practice, we provide high-quality materials to help students excel in exams for 2025 and beyond.

AQA A Level Further Mathematics Specification:

  • Written exam: 2 hours
  • 100 marks
  • 33⅓ % of A-level

Below are the variety of study materials that can help you focus your revision and develop the skills necessary to perform at your best to achieve an A* rating.

A. Proof

A1: Proof by Induction

B. Complex Numbers

B1: Solve equation. Real Coefficients

B2: Add; Subtract; Multiply; Divide

B3a: Complex Conjugate

B3b: Roots Occur in Conjugate Pairs

B5: Modulus, Argument, and Cartesian Forms

B6: Multiplication and Division in Modulus Argument Form

B8: De Moivre’s Theorem

B9: Exponential Form

B10: Nth Roots

B11: Geometric Problems

C. Matrices

C1: Manipulate Matrices

C2: Zero and Identity

C3a: Matrix transformations (2D)

C3b: Matrix transformations (3D)

C4: Invariant Points and Lines

C5a: Determinants (2x2 Determinants)

C5b: Determinants (3x3 Determinants)

C5c: Geometric Interpretation of Determinants

C6a: Singular Matrices (Properties of Singular Matrices)

C6b: Singular Matrices and Inverse of a 2x2 Matrix

C6c: Singular Matrices and Inverse of a 3x3 Matrix

C7: Inverse Matrices to Solve Simultaneous Equations

C8: Geometric Interpretation of Solutions

C9: Factorise Determinants

C10: Eigenvalues and Eigenvectors

C11: Diagonalisation

D. Further Algebra and Functions

D1: Sums and Products of Roots

D2: Transform Polynomial Equation

D3: Sums of Integers, Squares, and Cubes

D4a: Method of Differences

D4b: Method of Differences - Use of Partial Fractions

D5: Find Maclaurin Series

D6: Use Standard Maclaurin Series

D7a: Evaluate Limits Using L'Hôpital's Rule

D7b: Evaluate Limits Using Maclaurin

D9: Rational Inequalities

D10: Modulus Functions and Inequalities

D11: Graphs of Modulus Functions – Graphs of Reciprocal Functions

D12a: Graphs of Rational Functions

D12b: Graphs of Rational Functions - Asymptotes

D13: Graph Rationals with Quadratics

D14: Stationary Points Without Calculus

D15: Graphs of Conics

D16a: Transformations of Graphs

D16b: Transformations of Graphs – Rotations and Enlargements

DA. Graphs

DA1: Terminology for Graphs

DA2: Graph Properties (Eulerian/Hamiltonian)

DA3: Eulers Formula

DA4: Kuratowski’s Theorem

DA5: Complete, Bipartite, and Complement Graphs

DA6: Simple Graphs and Trees

DA7: Graph Isomorphisms

DB. Networks

DB1: Terminology for Networks

DB2: Network Optimisation/Spanning Trees

DB3: Route Inspection Problems

DB4: Travelling Salesperson

DB5: Evaluate, Modify, and Refine Models

DC. Network Flows

DC1: Interpret Directed Networks

DC2: Understand Cuts

DC3: Max Flow-Min Cut Theorem

DC4: Supersources and Supersinks

DC5: Flow Augmentation

DC6: Arcs with Minimum Capacities

DC7: Refined Network Flow Problems

DD. Linear Programming

DD1: Formulate Optimisation Problems

DD2: Find Optimal Solution Graphically

DD3: Simplex Algorithm

DD4: Interpreting Simplex Tableau

DE. Critical Path Analysis

DE1: Precedence Networks

DE2: Find Start and Finish Times

DE3: Critical activities and Paths

DE4: Refine Critical Path Models

DE5: Gantt (Cascade) Diagrams

DE6: Resource Levelling

DF. Game Theory

DF1: Payoff Matrices

DF2: Play Safe Strategies

DF3: Stable Solutions

DF4: Dominated Strategies

DF5: Optimal Mixed Strategies

DF6: Convert Games to Linear Programming Problems

DG. Binary Operations

DG1: Use Binary Operations

DG3: Use and Prove Associativity

DG5: Identity Elements

DG6: Inverse Elements

Question Paper

Mark Scheme

DG7: Terms for Groups

DG8: Group Axioms

DG9: Finite Groups

Question Paper

Mark Scheme

DG10: Lagrange's Theorem

DG11: Group Generators

DG12: Finite Group Isomorphisms

E. Further Calculus

E1: Improper Integrals

E2: Volume of Revolution

Mark Scheme

E3: Mean of a Function

E4: Integration by Partial Fractions

E5: Differentiation of Inverse Trigonometric Functions

E6: Standard Integrals

E7: Arc Length

E8: Reduction Formulae

E9: Improper Integrals Using Standard Limits

F. Further Vectors

F1: Vector Equation of a Line

F2: Vector Equation of a Plane

F3: Scalar Product

F4: Perpendicular Vectors

F5: Vector Product

F6: Intersection of Lines

G. Polar Coordinates

G1: Convert Between Polar and Cartesian

G2: Polar Curve Sketching

G3: Area Enclosed by Polar Curves

H. Hyperbolic Functions

H1: Definitions as Exponentials

H2: Hyperbolic Calculus

H3: Inverse Hyperbolic Functions

H4: Log Form of Inverse Hyperbolics

H5: Integration - Hyperbolic Substitution

H6: Hyperbolic Identities

I. Differential Equations

I1: Integrating Factors

I2: General and Particular Solutions

I3: Modeling in Context with Differential Equations

I4: Second-Order Homogeneous Equations

I5: Non-Homogeneous Second-Order Equations

I6: Auxiliary Equation Discriminant

I7: Solve Simple Harmonic Motion Equation

I8: Damped Oscillations

I9: Coupled First-Order Simultaneous Equations

I10: Form Differential Equations Using Hooke's Law

I11: Form Differential Equations; Damping Proportional to Velocity

K. Numerical methods

K1: Numerical Integration

K2: Euler's Method for Differential Equations

K3: Improved Euler Methods

MA. Dimensional Analysis

MA1: Finding Dimensions

MA2: Prediction of Formulae

MB. Momentum and Collisions

MB1: Conservation of Momentum

MB2: Coefficient of Restitution

MB3: Impulse and Momentum

MB4: Impulse - Variable Force

MC. Work, Energy and Power

MC1: Work Done by a Force

MC2: Gravitational Potential Energy

MC3: Kinetic Energy

MC4: Hooke's Law

MC5: Work Done by a Variable Force

MC6: Elastic Potential Energy

MD. Circular Motion

MD1: Circular Motion – Constant Speed

MD2: Angular Speed

MD3: Speed, Angular Speed, and Acceleration

MD4: Circular Motion with Vectors

MD5: Conical Pendulum

MD6: Vertical Circular Motion

ME. Centers of Mass and Moments

ME1: System of Particles

ME2: Composite Body

ME3: Lamina by Integration

ME4: Solid Rotating About the X-axis

ME5: Sliding and Toppling

ME6: Body in Equilibrium

SA. Discrete Random Variables

SA1: Discrete Random Variables (DRVs) as Tables or Functions

SA2: Evaluate Probabilities for DRVs

SA3: Measures of Spread and Average

SA4: Expectation and Variance of DRVs

SA5: Linear Transformations of a DRV

SB. Poisson Distribution

SB1: Conditions for Poisson Distribution

SB2: Calculate Poisson Probabilities

SB3: Mean and Variance for

SB4: Sum of Independent Poisson Distributions

SB5: Poisson Hypothesis Test

SC. Type I and Type II Errors

SC1: Interpret Errors in Context

SC2: Probability of Type II Error

SD. Continuous Random Variables

SD1: Probability Density Function

SD2: Find Probability for an Interval

SD3: Find Median and Quartiles

SD4: Mean, Variance, and Standard Deviation for Continuous Random Variables (CRV)

SD5: Linear Transformations of a CRV

SD6: Cumulative Distribution Function

SD7: Rectangular Distribution

SD8: Independent CRVs and DRVs

SE. Chi-Squared Test

SE1: Construct Contingency Tables

SE2: Calculate Chi-Squared Statistic

SE3: Expected Values Less Than 5; Pooling Data

SE4: Identify Sources of Association

SE5: Yates' Correction

SF. Exponential Distribution

SF1: Conditions for Exponential Distribution

SF2: Probability Using Exponential Distribution

SF3: Prove Mean, Variance, and Standard Deviation of Exponential Distribution

SF4: Link Poisson and Exponential Distribution

SG. Inference T-Distribution

SG1: T-Statistic Test for Mean

SH. Confidence Intervals

SH1: Confidence Interval for Normal Distribution with Known Variance

SH2: Confidence Interval for Normal Distribution with Unknown Variance

SH3: Make Inferences from Confidence Intervals

SH4: Confidence Interval for Normal Distribution and T-Distribution

Additional AQA A Level Further Mathematics Resources

Further Calculus Topic Questions

Improper Integrals

Volume of Revolution

Mean of a Function

Integrate using Partial Fractions

Differentiate Inverse Trigonometric Functions

Integrate using Trigonometric Substitutions

Standard Integrals

Area of Surface of Revolution

Reduction Formulae

Improper Integrals Using Standard Limits

Continuous Random Variables (CRVs) Topic Questions

Find Probability of Observation in Specified Interval

Finding Median and Quartiles

Functions of a CRV

Mean, Variance and Standard Deviation for CRV

Rectangular Distribution

Understanding the Structure of AQA A-Level Further Maths

Before diving into resources, it’s important to understand the structure of the AQA A-Level Further Maths exam. The AQA A-Level Further Maths consists of several topics across both pure mathematics and applied mathematics. These topics include algebra, calculus, vectors, mechanics, and statistics, each with varying levels of difficulty. The aim is not only to solve individual problems but also to understand the underlying concepts and methods behind each question type.

In order to succeed in AQA A-Level Further Maths, you must have a deep understanding of the concepts and the ability to apply these concepts to solve problems under exam conditions. This is where Exam Papers Practice comes into play. Our website offers a wide range of past papers, topic questions, and detailed solutions that will help you become familiar with the exam format and improve your problem-solving skills.

How Exam Papers Practice Can Help You Succeed

At Exam Papers Practice, we offer a variety of tools designed to help you excel in your AQA A-Level Further Maths exams:

  1. AQA A-Level Further Maths Past Papers: Past papers are one of the best ways to prepare for exams. They give you a clear picture of the types of questions that may appear and the exam’s structure. By practicing past papers, you will learn how to manage your time effectively, which questions to tackle first, and the format of the problems you’ll encounter.

  2. Topic Questions for AQA A-Level Further Maths: Our website provides a vast collection of topic-specific questions that cover all the key areas of AQA A-Level Further Maths. These questions are designed to test your understanding of individual topics and to give you the practice you need to reinforce each concept. The more you practice, the more confident you will become with solving a wide variety of questions.

  3. Detailed Solutions: Simply practicing past papers and topic questions isn’t enough—you need to understand how to solve the problems correctly. Our platform provides detailed step-by-step solutions to help you understand how to approach each question and why certain methods are used. This is crucial for improving your problem-solving techniques and for helping you learn from your mistakes.

  4. Customizable Study Plans: At Exam Papers Practice, you can create customized study plans that are tailored to your strengths and weaknesses. Focus more time on areas that you find difficult, and strengthen your knowledge of areas where you are already strong.

  5. Real Exam Simulations: We offer the option to take mock exams, simulating real exam conditions. This can help you build your confidence and get used to working under pressure. By practicing in a timed setting, you will learn how to pace yourself and avoid spending too much time on one question.

Tips for Effective Studying for AQA A-Level Further Maths

Now that you know how Exam Papers Practice can help you succeed, here are some additional tips to make your study sessions more effective:

Focus on Understanding, Not Just Memorization

It’s easy to think that memorizing formulas and procedures will guarantee success, but AQA A-Level Further Maths is more about understanding concepts and applying them. When you study, focus on understanding how and why methods work rather than just memorizing them. Understanding the logic behind each formula or method will help you apply it to different problems in the exam.

Work Through Topic Questions Regularly

Consistent practice is key. Make it a habit to work through topic-specific questions regularly, using the resources available on Exam Papers Practice. This will help you identify areas where you need to improve and reinforce your understanding of core concepts. Start with easier questions and gradually move on to more challenging ones as you gain confidence.

Review Mistakes and Learn from Them

When you make mistakes, take the time to understand why you got the answer wrong. Review your solutions and compare them to the step-by-step explanations provided on Exam Papers Practice. Learning from mistakes is an essential part of the learning process.

Break Down Complex Problems

Some questions in AQA A-Level Further Maths can seem daunting at first. However, breaking them down into smaller, more manageable steps can make them easier to solve. Practice simplifying complex problems and isolating the core parts of the question. This will help you avoid feeling overwhelmed and help you stay focused during the exam.

Use Study Groups

Sometimes studying with peers can help you gain a deeper understanding of topics. Join a study group or discuss challenging questions with classmates. Explaining concepts to others can strengthen your understanding, and your peers might have insights that you missed.

Set Realistic Goals

Set small, achievable goals for each study session. For example, you could aim to complete a set number of topic questions or review a specific topic thoroughly. Breaking down your revision into manageable chunks will make it feel less overwhelming and will help you stay on track.

Practice Time Management

AQA A-Level Further Maths exams are time-limited, so practicing time management is crucial. When working on past papers, try to stick to the time limits. This will help you develop the skills necessary to complete each section within the allotted time during the real exam.

Use Your Resources Wisely

At Exam Papers Practice, we offer a wide range of resources that can enhance your revision. In addition to topic questions and past papers, make sure to take full advantage of any video tutorials, revision notes, or guides that can explain difficult topics in a more accessible way.

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 AQA A-Level Further Maths (7367) Specification 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.

Achieving an A* in AQA A-Level Further Maths (7367) is definitely possible, and using the right resources is key to making that a reality. By utilizing Exam Papers Practice for past papers, mark schemes, and exam-style questions, along with following effective study techniques like active recall and spaced repetition, you’ll be setting yourself up for success.

Stay consistent with your revision, focus on understanding key concepts, and practice regularly to boost your chances of achieving an A*. With the right tools and strategies, an A* in AQA Further Maths could be yours!