AQA 8365 coverage by clause

All 57 clauses are mapped. 42 have selected generated forms and 42 have selected assessment items. No clause has a full set of questions calibrated to exam demand.

The last column shows what is missing from each clause. The available questions test particular methods, so this list cannot be used as evidence that a whole clause is covered. Proofs, graph construction and geometry still need more questions before complete mock papers can be offered.

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Clause	Teaching	Selected practice	Remaining work
1.1 Number foundations	Fractional and negative indices	No generated forms No test questions yet	Fractions, percentages, ratio and proportion contexts Minimum task breadth Fractions and mixed arithmetic Ratio, proportion and percentages Interpret a numerical result in context
1.2 Product rule for counting	Counting with restrictions	Product rule with no repetition Some test questions available	Dependent restrictions and disjoint counting cases Minimum task breadth Independent stage choices Dependent restrictions Disjoint cases without double counting
1.3 Surds and rationalising denominators	Surds and exact answers	Rationalise a binomial denominator Combine and simplify surds Rationalise a binomial surd denominator Some test questions available	Mixed surd operations and non-conjugate structures Minimum task breadth Simplify and combine surds Multiply surds and conjugates Rationalise and retain denominator restrictions
2.1 Algebraic manipulation	Expanding and factorising Algebraic fractions	No generated forms No test questions yet	General manipulation in unfamiliar expressions Minimum task breadth Manipulate expressions using the algebraic laws Check an unfamiliar rearrangement
2.2 Function notation	Function notation and evaluation	Evaluate a rational function Some test questions available	Function evaluation and notation diagnostics Minimum task breadth Evaluate at a numerical input Evaluate at an algebraic input Distinguish function notation from multiplication
2.3 Domain and range	Domain and range Piecewise graphs and endpoints	Range on a restricted quadratic domain Some test questions available	Ranges beyond the bounded quadratic structures and review of endpoint reasoning Minimum task breadth Find a range on a restricted domain Account for a turning point inside the domain Handle open and closed endpoints
2.4 Composite functions	Composite functions	Composite functions Some test questions available	Composition with domain restrictions and more than two functions Minimum task breadth Compose functions in the stated order Compose three functions Preserve input restrictions through composition
2.5 Inverse functions	Inverse functions Choosing an inverse branch	Inverse functions Restrict a quadratic inverse Evaluate an inverse on its permitted branch Find a quadratic inverse with its domain Some test questions available	Breadth review of branch selection and two-sided inverse verification Minimum task breadth Find and verify a linear inverse Select a nonlinear inverse branch Exchange domain and range correctly
2.6 Expanding and simplifying	Expanding and factorising	No generated forms No test questions yet	Nested multi-variable products and cancellation Minimum task breadth Expand two or more factors Simplify nested and multivariable products
2.7 Positive integer binomial expansions	Expanding and factorising	Binomial coefficients Some test questions available	Complete expansions beyond coefficient extraction Minimum task breadth Expand a positive integer binomial completely Extract a requested coefficient with Pascal resources
2.8 Factorising expressions	Expanding and factorising	No generated forms No test questions yet	Full factorisation with several variables and repeated expressions Minimum task breadth Factor out a common factor Factor a quadratic including two variables Factor repeated expressions and higher powers completely
2.9 Algebraic fractions	Algebraic fractions	Add rational expressions Subtract rational expressions Multiply rational expressions Divide rational expressions Some test questions available	Breadth review across factor structures and original excluded values Minimum task breadth Add and subtract algebraic fractions Multiply and divide algebraic fractions State original excluded values including a zero divisor
2.10 Rearranging formulae	Rearranging formulae	Rearrange a reciprocal formula Some test questions available	Symbolic rearrangement evidence, repeated-subject and varied formula structures Minimum task breadth Rearrange a formula with one occurrence of the subject Rearrange repeated and reciprocal occurrences State restrictions after division
2.11 Factor theorem	The factor theorem	Use the factor theorem Divide polynomials Complete factorisation of a cubic Some test questions available	Rational roots and complete higher-degree factorisation Minimum task breadth Check a rational root Complete factorisation after a known factor Recover all roots and check the original polynomial
2.12 Completing the square	Completing the square	Complete the square Some test questions available	Fractional vertex coefficients and contextual extrema Minimum task breadth Complete the square with a nonunit coefficient Handle fractional vertex coordinates Interpret an extremum in context
2.13 Graphs and piecewise functions	Sketching functions Piecewise graphs and endpoints Exponential graphs and parameters	No generated forms No test questions yet	Independent assessment of exponential and piecewise construction Minimum task breadth Draw and interpret linear and quadratic graphs Draw exponential graphs and infer parameters Draw up to three pieces with endpoint conventions
2.14 Linear and quadratic equations	Solving quadratic equations	Solve a linear equation Quadratic equations Some test questions available	Contextual modelling, all methods and extraneous roots Minimum task breadth Solve linear and quadratic equations exactly Use factorisation, formula and square completion appropriately Form and solve a contextual equation
2.15 Two simultaneous equations	Simultaneous linear and quadratic equations Solving quadratic equations	Simultaneous equations Non-linear simultaneous equations Line and parabola intersections Some test questions available	Graphical solutions and varied nonlinear structures Minimum task breadth Solve a linear pair algebraically and graphically Solve a linear and second-order pair Recover and check every ordered pair
2.16 Three simultaneous linear equations	Three simultaneous linear equations	Three simultaneous linear equations Some test questions available	Dependent and inconsistent three-variable systems Minimum task breadth Eliminate in a three-variable system Check all three original equations
2.17 Linear and quadratic inequalities	Quadratic inequalities Inequalities and interval notation	Quadratic inequality interval endpoints Solve a linear inequality with a sign reversal Solve a quadratic inequality in interval notation Some test questions available	Breadth review of sign cases, endpoint inclusion and graphical solution sets Minimum task breadth Solve a linear inequality including sign reversal Solve a quadratic inequality across all sign intervals Use strict and inclusive endpoint notation
2.18 Fractional and negative indices	Fractional and negative indices	Solve an equation with a negative fractional index Some test questions available	Varied index equations, multiple roots and explicit domain reasoning Minimum task breadth Apply index laws to products and quotients Use fractional and negative powers with domains Solve an index equation without losing permitted roots
2.19 Algebraic proof	Algebraic proof and counterexamples Proving divisibility with consecutive integers	Algebraic quotient in a divisibility argument Some test questions available	Breadth and demand review across general identities, divisibility and counterexamples Minimum task breadth Prove an integer divisibility or parity statement Prove a general algebraic identity Give a counterexample to a false universal claim
2.20 Sequence terms and limiting values	Sequence terms and limiting values	Limit of a rational nth term Some test questions available	Finite-term comparisons, higher-degree ratios and limit existence Minimum task breadth Evaluate and compare specified sequence terms Find finite limiting values Explain the limiting structure
2.21 Linear sequence nth terms	Linear sequence nth terms	Arithmetic sequences Some test questions available	Symbolic linear sequences and solving for an index Minimum task breadth Infer a linear nth term Find an index from a specified term
2.22 Quadratic sequence nth terms	Quadratic sequences	Find a quadratic nth term Some test questions available	Finding all admissible indices from a specified value Minimum task breadth Infer a quadratic nth term Find all permitted positive integer indices
3.1 Gradient	Straight lines and gradients	No generated forms No test questions yet	Gradient interpretation including vertical lines Minimum task breadth Find a gradient from coordinates Interpret a horizontal or vertical line
3.2 Parallel and perpendicular lines	Straight lines and gradients	No generated forms No test questions yet	Parallel/perpendicular proofs and horizontal exceptions Minimum task breadth Construct and justify a parallel line Construct and justify a perpendicular line including axis cases
3.3 Distance between points	Pythagoras in three dimensions	Distance between points Exact distance between general coordinates Some test questions available	Irrational coordinate distances and geometric deductions Minimum task breadth Find an exact coordinate distance Use a distance to deduce a geometric property
3.4 Midpoints and section ratios	Midpoints and section ratios	Divide a line in a ratio Some test questions available	Reverse ratio and midpoint inference Minimum task breadth Find a midpoint and an internal section point Recover an endpoint or ratio
3.5 Straight line equations	Straight lines and gradients	Line through two points Line equation in equivalent forms Some test questions available	Equivalent line forms and vertical lines Minimum task breadth Determine and rearrange a line equation Handle horizontal and vertical lines
3.6 Drawing straight lines	Straight lines and gradients Sketching functions	No generated forms No test questions yet	Generated line drawing and graphical evidence Minimum task breadth Draw a line from its equation Read and check intercepts and gradient
3.7 Circles centred at the origin	Circles and tangents Circle theorems and angle reasoning	Chord length from its distance to the centre Some test questions available	All listed circle facts and justified applications Minimum task breadth Use the origin-centred circle equation Use radius-tangent and perpendicular-bisector facts Use equal tangents and chord facts with reasons
3.8 General circle equations	Circles and tangents	Centre and radius of a circle Some test questions available	Reverse circle construction and mixed coordinate problems Minimum task breadth Read and construct a general circle equation Link the equation to points and geometric constraints
3.9 Tangents to circles	Circles and tangents	Tangent to a circle Some test questions available	Tangents at axis endpoints and linked geometric reasoning Minimum task breadth Find a tangent at a specified circle point Handle vertical and horizontal tangents
4.1 Gradient functions and rate of change	Differentiating powers	No generated forms No test questions yet	Rates with units and derivative interpretation Minimum task breadth Interpret derivative as instantaneous rate with units Distinguish average and instantaneous rate
4.2 Tangent gradients	Tangents and normals	No generated forms No test questions yet	Distinguishing tangent gradient from secant gradient Minimum task breadth Evaluate a tangent gradient Link a gradient to the graph at a point
4.3 Differentiating integer powers	Differentiating powers	Differentiate a polynomial Gradient with a negative integer power Some test questions available	Expression-level negative-power derivatives and expressions requiring simplification Minimum task breadth Differentiate integer powers including negative powers Simplify an expression before differentiation
4.4 Tangents and normals	Tangents and normals	Equation of a tangent Equation of a normal Some test questions available	Horizontal tangents, vertical normals and inverse tasks Minimum task breadth Find tangent and normal equations Handle horizontal tangents and vertical normals Recover a point from a stated tangent gradient
4.5 Increasing and decreasing functions	Stationary points Increasing and decreasing intervals	Interval of increase for a quadratic Some test questions available	Breadth review beyond bounded polynomial sign intervals Minimum task breadth Find intervals of increase and decrease Explain derivative signs and isolated zero gradients
4.6 Second derivatives	Stationary points	Second derivative of a polynomial Some test questions available	Varied second derivatives and their rate-of-change interpretation Minimum task breadth Calculate second derivatives Interpret the change in gradient
4.7 Classifying stationary points	Stationary points	Find a stationary point Some test questions available	Multiple stationary points and zero second-derivative cases Minimum task breadth Find and classify several stationary points Use sign changes when the second derivative is zero
4.8 Optimisation	Optimisation with a stated domain	Optimise the area of a rectangle Some test questions available	Unbounded domains, reciprocal objectives and modelling choices Minimum task breadth Form a one-variable objective with its domain Find and compare stationary and boundary candidates Justify the admissible optimum
4.9 Curve sketches from stationary points	Sketching functions Stationary points Sketching a curve from its derivative	No generated forms No test questions yet	Demand review of sketch tasks using extrema, intercepts and end behaviour Minimum task breadth Sketch from stationary points and intercepts Explain behaviour between and beyond stationary points
5.1 Matrix multiplication	Matrix multiplication	Multiply two matrices Some test questions available	Scalar products and both permitted matrix dimensions Minimum task breadth Multiply permitted 2 by 2 and 2 by 1 matrices Multiply by a scalar Check dimensions and multiplication order
5.2 Identity matrices	The identity matrix Combining matrix transformations	No generated forms No test questions yet	Identity matrix recognition and its action Minimum task breadth Recognise the identity matrix Demonstrate its action on matrices and column vectors
5.3 Transforming the unit square	Matrix transformations	Transform a point Fixed points of a reflection Some test questions available	All specified rotations, reflections, enlargements and unit-square images Minimum task breadth Draw the transformed unit square Use specified rotations, reflections and enlargements Recover a matrix from unit-vector images
5.4 Combining transformations	Combining matrix transformations	Combine a reflection and a rotation Some test questions available	Reverse constructions and all permitted transformation combinations Minimum task breadth Compose transformations in the correct order Describe the combined transformation Compare reversed compositions
6.1 Area, volume, angles and circle theorems	Area, volume and angle facts Circle theorems and angle reasoning Pythagoras in three dimensions	Angles in a cyclic quadrilateral Exact circle area with pi Some test questions available	Areas, surface areas, volumes, polygons and the remaining circle facts Minimum task breadth Calculate areas, surface areas and volumes Use polygon and angle facts Use all stated circle theorems with reasons
6.2 Geometric proof	Writing a geometric proof Proving equal tangent lengths	No generated forms No test questions yet	Breadth review across circle-theorem proofs and formal argument chains Minimum task breadth Construct a general circle-theorem proof Link a chain of justified geometric statements
6.3 Sine rule, cosine rule and triangle area	Sine rule, cosine rule and triangle area The two possible sine-rule angles	Triangle area from an included angle Cosine rule with an exact side Sine rule with an exact squared side Some test questions available	Generated ambiguous cases and breadth of angle-solving structures Minimum task breadth Use sine and cosine rules for sides and angles Find triangle area Consider both admissible sine-rule angles
6.4 Pythagoras in two and three dimensions	Pythagoras in three dimensions	Space diagonal of a cuboid Some test questions available	Pyramids, non-cuboid solids and reverse lengths Minimum task breadth Use Pythagoras in a plane Use Pythagoras in cuboids and other solids Recover an unknown length
6.5 Trigonometry in three dimensions	Angles between lines and planes Angles between two planes	Angle between a line and a plane Some test questions available	Generated plane-plane angle tasks and non-right triangles in solids Minimum task breadth Find a line-plane angle from a projection Find a plane-plane angle using perpendicular sections
6.6 Trigonometric graphs	Sketching sine, cosine and tangent	No generated forms No test questions yet	Graph construction, negative angles and tangent asymptote reasoning Minimum task breadth Draw and interpret sine and cosine over negative and positive angles Draw tangent with its asymptotes Use periodicity and intercepts
6.7 Trigonometric ratios around the circle	Trigonometric ratios in each quadrant	No generated forms No test questions yet	All quadrants, axis values and positive angles through 360° Minimum task breadth Use quadrant signs and axis values Relate an angle to its reference angle
6.8 Exact trigonometric values	Exact trigonometric values	Exact squared trigonometric values Exact trigonometric values in all quadrants Some test questions available	Breadth review of exact values and triangle derivations Minimum task breadth Derive special-angle values from triangles Use all specified exact sine, cosine and tangent values
6.9 Trigonometric identities	Trigonometric identities Identity proofs and permitted angles	Use trigonometric identities and the quadrant Some test questions available	Breadth review of identity proofs and rational-expression domains Minimum task breadth Apply both stated identities with quadrant conditions Prove an identity with its domain restrictions
6.10 Trigonometric equations in intervals	Trigonometric equations in intervals	Trigonometric equations in an interval A trigonometric equation using an identity Some test questions available	Broader interval equations and identity-based reductions Minimum task breadth Solve sine, cosine and tangent equations over the stated interval Reduce an equation using an identity Check endpoints and recover every solution