AQA Level 2 Certificate in Further Mathematics
8365 · Level 2 · 1.4, November 2020
Both papers may assess any content. Matrix calculations are restricted to 2 × 2 and 2 × 1; matrix inversion is not specified. Formula provision is exam-year dependent.
Current official specification · Checked 2026-10-07
Select this course
Your learning checklist
Find lessons and practice questions for your course
Topics in the specification
Every specification clause is represented below. A clause may share an objective with other clauses. Questions cover selected parts of each topic.
| Topic | Strand and clause | Practice |
|---|---|---|
| Number foundations | core · 1.1 | No questions yet |
| Product rule for counting | core · 1.2 | No questions yet |
| Surds and rationalising denominators | core · 1.3 | No questions yet |
| Algebraic manipulation | core · 2.1 | No questions yet |
| Function notation | core · 2.2 | No questions yet |
| Domain and range | core · 2.3 | No questions yet |
| Composite functions | core · 2.4 | Practice questions |
| Inverse functions | core · 2.5 | No questions yet |
| Expanding and simplifying | core · 2.6 | No questions yet |
| Positive integer binomial expansions | core · 2.7 | No questions yet |
| Factorising expressions | core · 2.8 | No questions yet |
| Algebraic fractions | core · 2.9 | No questions yet |
| Rearranging formulae | core · 2.10 | No questions yet |
| Factor theorem | core · 2.11 | Practice questions |
| Completing the square | core · 2.12 | No questions yet |
| Graphs and piecewise functions | core · 2.13 | No questions yet |
| Linear and quadratic equations | core · 2.14 | Practice questions |
| Two simultaneous equations | core · 2.15 | No questions yet |
| Three simultaneous linear equations | core · 2.16 | No questions yet |
| Linear and quadratic inequalities | core · 2.17 | No questions yet |
| Fractional and negative indices | core · 2.18 | No questions yet |
| Algebraic proof | core · 2.19 | No questions yet |
| Sequence terms and limiting values | core · 2.20 | No questions yet |
| Linear sequence nth terms | core · 2.21 | Practice questions |
| Quadratic sequence nth terms | core · 2.22 | No questions yet |
| Gradient | core · 3.1 | No questions yet |
| Parallel and perpendicular lines | core · 3.2 | No questions yet |
| Distance between points | core · 3.3 | No questions yet |
| Midpoints and section ratios | core · 3.4 | No questions yet |
| Straight line equations | core · 3.5 | No questions yet |
| Drawing straight lines | core · 3.6 | No questions yet |
| Circles centred at the origin | core · 3.7 | No questions yet |
| General circle equations | core · 3.8 | No questions yet |
| Tangents to circles | core · 3.9 | No questions yet |
| Gradient functions and rate of change | core · 4.1 | No questions yet |
| Tangent gradients | core · 4.2 | No questions yet |
| Differentiating integer powers | core · 4.3 | Practice questions |
| Tangents and normals | core · 4.4 | No questions yet |
| Increasing and decreasing functions | core · 4.5 | No questions yet |
| Second derivatives | core · 4.6 | Practice questions |
| Classifying stationary points | core · 4.7 | No questions yet |
| Optimisation | core · 4.8 | Practice questions |
| Curve sketches from stationary points | core · 4.9 | No questions yet |
| Matrix multiplication | core · 5.1 | Practice questions |
| Identity matrices | core · 5.2 | No questions yet |
| Transforming the unit square | core · 5.3 | Practice questions |
| Combining transformations | core · 5.4 | No questions yet |
| Area, volume, angles and circle theorems | core · 6.1 | No questions yet |
| Geometric proof | core · 6.2 | No questions yet |
| Sine rule, cosine rule and triangle area | core · 6.3 | No questions yet |
| Pythagoras in two and three dimensions | core · 6.4 | No questions yet |
| Trigonometry in three dimensions | core · 6.5 | No questions yet |
| Trigonometric graphs | core · 6.6 | No questions yet |
| Trigonometric ratios around the circle | core · 6.7 | No questions yet |
| Exact trigonometric values | core · 6.8 | No questions yet |
| Trigonometric identities | core · 6.9 | No questions yet |
| Trigonometric equations in intervals | core · 6.10 | Practice questions |
| Solving linear equations | core · 2.14 | Practice questions |
| Two simultaneous linear equations | core · 2.15 | Practice questions |
| Binomial coefficients for integer powers | core · 2.7 | Practice questions |
| Inverting a linear function | core · 2.5 | Practice questions |
| Inverting a restricted quadratic | core · 2.5 | Practice questions |
| Equation of a tangent | core · 4.4 | Practice questions |
| Equation of a normal | core · 4.4 | Practice questions |
| A polynomial stationary point | core · 4.7 | Practice questions |
| A plane matrix transformation | core · 5.3 | Practice questions |
| Polynomial division | core · 2.11 | Practice questions |
| A linear and nonlinear simultaneous pair | core · 2.15 | Practice questions |
| Trigonometric solutions in an interval | core · 6.10 | Practice questions |
| Exact distance between two points | core · 3.3 | Practice questions |
| Internal division of a line segment | core · 3.4 | Practice questions |
| A line through two points | core · 3.5 | Practice questions |
| Centre and radius from a circle equation | core · 3.8 | Practice questions |
| A tangent at a specified circle point | core · 3.9 | Practice questions |
| Chord length from its distance to the centre | core · 3.7 | Practice questions |
| An angle in a cyclic quadrilateral | core · 6.1 | Practice questions |
| A cuboid space diagonal | core · 6.4 | Practice questions |
| Triangle area from two sides and the included angle | core · 6.3 | Practice questions |
| An exact cosine-rule side calculation | core · 6.3 | Practice questions |
| An exact sine-rule side calculation | core · 6.3 | Practice questions |
| Use an identity with a quadrant restriction | core · 6.9 | Practice questions |
| A trigonometric ratio for a line and plane | core · 6.5 | Practice questions |
| Coefficients in completed square form | core · 2.12 | Practice questions |
| Coefficients of a quadratic sequence | core · 2.22 | Practice questions |
| Counting arrangements under a restriction | core · 1.2 | Practice questions |
| Rationalise a conjugate denominator | core · 1.3 | Practice questions |
| A linear and quadratic pair with all solutions | core · 2.15 | Practice questions |
| Compose two permitted plane transformations | core · 5.4 | Practice questions |
| Exact three-variable linear elimination | core · 2.16 | Practice questions |
| A fractional or negative index equation | core · 2.18 | Practice questions |
| A repeated subject in a formula | core · 2.10 | Practice questions |
| A rational sequence limiting value | core · 2.20 | Practice questions |
| Squared exact trigonometric values | core · 6.8 | Practice questions |
| Endpoints of an explicitly stated quadratic inequality interval | core · 2.17 | Practice questions |
| Gradient from a negative integer power | core · 4.3 | Practice questions |
| A polynomial quotient supporting a divisibility argument | core · 2.19 | Practice questions |
| Evaluate a rational function at a permitted input | core · 2.2 | Practice questions |
| Range of a quadratic on a restricted interval | core · 2.3 | Practice questions |
| Evaluate a quadratic inverse on one stated branch | core · 2.5 | Practice questions |
| A symbolic quadratic inverse formula on a stated branch | core · 2.5 | Practice questions |
| Exact operations on surds | core · 1.3 | Practice questions |
| Exact rationalisation with denominator restrictions | core · 1.3 | Practice questions |
| Add rational expressions with original exclusions | core · 2.9 | Practice questions |
| Subtract rational expressions with original exclusions | core · 2.9 | Practice questions |
| Multiply rational expressions with original exclusions | core · 2.9 | Practice questions |
| Divide rational expressions and exclude a zero divisor | core · 2.9 | Practice questions |
| Solve a linear inequality as an interval | core · 2.17 | Practice questions |
| Solve a quadratic inequality as a union of intervals | core · 2.17 | Practice questions |
| An exact coordinate distance with an irrational result | core · 3.3 | Practice questions |
| Equivalent equations including horizontal and vertical lines | core · 3.5 | Practice questions |
| Exact special-angle values with quadrant signs | core · 6.8 | Practice questions |
| Exact circle area retaining pi | core · 6.1 | Practice questions |
| Intervals determined by the sign of a derivative | core · 4.5 | Practice questions |
| A cubic with a rational root and complete equivalent product | core · 2.11 | Practice questions |
| Fixed points of a reflection | core · 5.3 | Practice questions |
| A trigonometric equation using an identity | core · 6.10 | Practice questions |