AQA Level 2 Further Maths (8365) Past Papers & Mark Schemes
Prepare for the AQA Certificate Level 2 Further Mathematics (8365) exams with past papers and official mark schemes for Paper 1 and Paper 2, organised by exam year. Often searched for as AQA GCSE Further Maths, this qualification covers number, algebra, coordinate geometry, calculus, matrix transformations and geometry. Use these resources to practise multi-step problems, understand how AQA awards marks and improve your exam technique. You can also jump to our examiner tips or read the frequently asked questions for more guidance.
2025 AQA Certificate Level 2 Further Mathematics (8365) Past Papers & Mark Schemes
2025 AQA Level 2 Further Mathematics | Downloads | |
Paper 1 Non-calculator (8365/1) – June 2025 | ||
Paper 2 Calculator (8365/2) – June 2025 |
2024 AQA Certificate Level 2 Further Mathematics (8365) Past Papers & Mark Schemes
2024 AQA Level 2 Further Mathematics | Downloads | |
Paper 1 Non-calculator (8365/1) – June 2024 | ||
Paper 2 Calculator (8365/2) – June 2024 |
2023 AQA Certificate Level 2 Further Mathematics (8365) Past Papers & Mark Schemes
2023 AQA Level 2 Further Mathematics | Downloads | |
Paper 1 Non-calculator (8365/1) – June 2023 | ||
Paper 2 Calculator (8365/2) – June 2023 |
2022 AQA Certificate Level 2 Further Mathematics (8365) Past Papers & Mark Schemes
2022 AQA Level 2 Further Mathematics | Downloads | |
Paper 1 Non-calculator (8365/1) – June 2022 | ||
Paper 2 Calculator (8365/2) – June 2022 |
2021 AQA Certificate Level 2 Further Mathematics (8365) Past Papers & Mark Schemes
2021 AQA Level 2 Further Mathematics | Downloads | |
Paper 1 Non-calculator (8365/1) – November 2021 | ||
Paper 2 Calculator (8365/2) – November 2021 |
Sample Assessment Materials
AQA Level 2 Further Mathematics Sample Papers | Downloads | |
Paper 1 Non-calculator (8365/1) – Sample Set 1 | ||
Paper 2 Calculator (8365/2) – Sample Set 1 |
AQA Level 2 Certificate in Further Mathematics (8365) FAQs for 2027
1. Is AQA Level 2 Further Mathematics the same as a GCSE?
No. AQA Level 2 Certificate in Further Mathematics (8365) is a Level 2 qualification rather than a GCSE, although it is commonly called “AQA GCSE Further Maths” by students and schools. It is designed for students who are already confident with higher-tier GCSE Mathematics and want to study more advanced topics. Available grades range from 5 to 9, with grade 9 being the highest.
2. How is AQA Level 2 Further Mathematics assessed in 2027?
AQA Level 2 Further Mathematics is assessed through two written examination papers:
Paper 1 (8365/1): Non-calculator, 1 hour 45 minutes, 80 marks
Paper 2 (8365/2): Calculator allowed, 1 hour 45 minutes, 80 marks
Each paper contributes 50% of the final qualification. There is no coursework or Non-Exam Assessment. Students should check the final 2027 examination dates with their school and the official AQA timetable.
3. What topics are included in AQA Level 2 Further Mathematics?
The AQA 8365 specification covers six principal areas:
Number
Algebra
Coordinate geometry
Calculus
Matrix transformations
Geometry
Algebra forms a particularly important part of the course. Students should be confident with functions, factorisation, equations, inequalities, algebraic fractions, sequences and unfamiliar multi-step problems.
4. Can I use a calculator in the AQA Further Maths exams?
A calculator is permitted only in Paper 2. Paper 1 is entirely non-calculator, so students need strong skills in exact arithmetic, fractions, surds, algebraic manipulation and trigonometric values. For Paper 2, make sure your calculator is in the correct angle mode and that you know how to use brackets, powers, trigonometric functions and stored answers accurately.
5. Do both papers assess the same topics?
Any part of the specification can be assessed across the two papers, so students should not divide their revision into supposed “Paper 1 topics” and “Paper 2 topics.” The main difference is that Paper 1 tests whether you can work accurately without a calculator, while Paper 2 may involve calculations for which a scientific calculator is helpful. Revise the complete specification for both examinations.
6. Which AQA Further Maths topics usually require the most revision?
Many students find calculus, matrices, functions, algebraic proofs, coordinate geometry and advanced trigonometry the most unfamiliar areas. However, difficult questions often combine several topics. For example, one problem might require algebraic manipulation, differentiation and coordinate geometry. Revision should therefore include mixed-topic questions rather than only practising each topic separately.
7. How much working should I show in the AQA 8365 exams?
Show every important stage of your method. Write the equation or formula being used, substitute the relevant values and complete the manipulation line by line. If the final answer is incorrect, clear working may still earn method marks. Avoid completing complicated algebra entirely in your head, and do not erase a valid method simply because you are uncertain about the final answer.
8. What calculus do I need to know for AQA Level 2 Further Mathematics?
Students need to understand differentiation as a method for finding a gradient and use it with algebraic functions. You may be asked to:
Differentiate powers of x
Find the gradient of a curve at a particular point
Determine the equation of a tangent or normal
Identify stationary points
Decide whether a stationary point is a maximum or minimum
Solve optimisation problems
Do not revise differentiation as an isolated rule. Practise explaining what the derivative means within the context of a graph or problem.
9. What do I need to know about matrices?
You must understand how matrices can represent geometrical transformations. This includes identifying and using matrices for rotations, reflections, enlargements and stretches. Pay close attention to the order of matrix multiplication because changing the order can change the resulting transformation. Practise moving between a transformation description, its matrix and the transformed coordinates.
10. What is the best way to revise for AQA Level 2 Further Mathematics in 2027?
Begin by securing the underlying higher-tier GCSE Maths skills, especially algebra, graphs, trigonometry and exact values. Then complete topic-based AQA Further Maths questions before progressing to full timed papers. After marking each paper, record whether each lost mark resulted from a knowledge gap, algebraic error, misread question, weak working or time pressure. Redo incorrect questions without the mark scheme and practise Paper 1 questions without reaching for a calculator.
Six Essential Examiner Tips for AQA Level 2 Further Mathematics (8365)
Simplify Expressions Before Differentiating
Students often attempt to differentiate an expression before preparing the algebra. Common errors include differentiating the numerator and denominator of a fraction separately, failing to expand brackets and rewriting negative powers incorrectly.
Always simplify the expression before differentiating. Expand brackets and split algebraic fractions into separate terms where possible. Convert fractions involving powers into index form before applying the power rule.
For example:
3/(4x^4) = (3/4)x^(-4)
Once the expression has been simplified, differentiate each term separately. Check the coefficient, sign and index carefully at every stage.
Complete the Full Stationary-Point Test
Students often correctly solve dy/dx = 0 but fail to use the second derivative to determine whether the stationary point is a maximum or minimum. Some students incorrectly set d2y/dx2 = 0 to locate stationary points. Others find the x-coordinate but forget to calculate the required y-coordinate or maximum or minimum value.
Follow this sequence:
Find dy/dx.
Set dy/dx = 0 and solve for x.
Find d2y/dx2.
Substitute the stationary x-value into d2y/dx2.
If d2y/dx2 > 0, the point is a minimum.
If d2y/dx2 < 0, the point is a maximum.
Substitute x into the original function if the coordinates or maximum or minimum value are required.
Do not stop after finding the x-value. Re-read the question to check exactly what must be stated.
Use Brackets When Subtracting or Squaring Expressions
Students frequently make sign errors when subtracting a complete algebraic expression without placing it in brackets. Brackets are also omitted when composite expressions are squared, particularly in geometry and proof questions.
Place the complete expression in brackets before applying a negative sign or exponent.
For example:
(42 - 3n) - (8n + 6)
When using Pythagoras’ theorem, write:
(3w + 2)^2 = (2w + 5)^2 + w^2
Expand one line at a time and show every important stage in “show that” and algebraic proof questions. This reduces sign errors and allows examiners to award method marks.
Find Every Valid Trigonometric Solution
Students often find only the acute calculator angle and miss other valid solutions within the specified interval. Other common errors include using false identities or dividing an equation by sin(x) or cos(x), which can remove valid solutions.
Use a CAST diagram or sketch the appropriate trigonometric graph to identify every solution within the stated range.
Use only valid identities, including:
tan(x) = sin(x)/cos(x)
sin^2(x) + cos^2(x) = 1
If a trigonometric term is common to every part of an equation, factorise instead of dividing by that term. Dividing by sin(x) or cos(x) may remove solutions where the term equals zero.
Check the Turning Point When Finding a Quadratic’s Range
Students sometimes calculate the range by substituting only the endpoints of the domain. This can produce an incorrect answer if the quadratic’s turning point lies inside the domain. Students may also omit zero and negative integers when solving inequalities or write the range using x instead of y or f(x).
Find the turning point and check whether its x-coordinate lies within the stated domain. If it does, compare the output at the turning point with the outputs at the domain’s endpoints.
For quadratic inequalities:
Rearrange the inequality so that one side equals zero.
Factorise or solve the related quadratic equation.
Identify the critical values.
Sketch the quadratic.
Select the correct region from the sketch.
State the range using output notation. For example, write f(x) >= 5 rather than x >= 5 if the restriction applies to the function’s output.
Apply Matrix Transformations in the Correct Order
Students often reverse the order of matrix multiplication, write the identity matrix incorrectly or give incomplete descriptions of transformations. Matrix multiplication is not commutative, meaning that AB is not generally equal to BA.
Remember that in the matrix product AB, matrix B acts first and matrix A acts second. Complete matrix multiplication carefully using the row-by-column method.
The two-dimensional identity matrix is:
[[1, 0], [0, 1]]
It is not:
[[1, 1], [1, 1]]
When describing a transformation, include all the required information:
The type of transformation
The angle or scale factor
The centre of transformation, usually the origin (0, 0)
For example, do not write only “rotation”. State the angle, direction and centre of rotation.
