Objectives and assessed practice
The bank has 128 question families. 128 objectives have a direct family contract. Of the 61 without one, 45 have related child structures. A prerequisite relationship suggests partial support; it does not establish complete coverage.
None of these counts is a whole-course sign-off. Read the qualification coverage limits.
| Objective | Assessment evidence | Selected structures |
|---|---|---|
| Number foundations | no direct or related child assessment evidence | Needs assessed tasks and review |
| Product rule for counting | partly supported through related child structures | Product rule with no repetition |
| Surds and rationalising denominators | partly supported through related child structures | Rationalise a binomial denominator, Combine and simplify surds, Rationalise a binomial surd denominator |
| Algebraic manipulation | no direct or related child assessment evidence | Needs assessed tasks and review |
| Function notation | partly supported through related child structures | Composite functions, Evaluate a rational function |
| Domain and range | partly supported through related child structures | Composite functions, Range on a restricted quadratic domain |
| Composite functions | direct bounded assessment | Composite functions |
| Inverse functions | partly supported through related child structures | Inverse functions, Restrict a quadratic inverse, Evaluate an inverse on its permitted branch, Find a quadratic inverse with its domain |
| Expanding and simplifying | partly supported through related child structures | Use the factor theorem |
| Positive integer binomial expansions | partly supported through related child structures | Binomial coefficients |
| Factorising expressions | partly supported through related child structures | Quadratic equations |
| Algebraic fractions | partly supported through related child structures | Add rational expressions, Subtract rational expressions, Multiply rational expressions, Divide rational expressions |
| Rearranging formulae | partly supported through related child structures | Rearrange a reciprocal formula |
| Factor theorem | direct bounded assessment | Use the factor theorem, Complete factorisation of a cubic |
| Completing the square | partly supported through related child structures | Complete the square |
| Graphs and piecewise functions | no direct or related child assessment evidence | Needs assessed tasks and review |
| Linear and quadratic equations | direct bounded assessment | Quadratic equations, Solve a linear equation |
| Two simultaneous equations | partly supported through related child structures | Simultaneous equations, Non-linear simultaneous equations, Line and parabola intersections |
| Three simultaneous linear equations | partly supported through related child structures | Three simultaneous linear equations |
| Linear and quadratic inequalities | partly supported through related child structures | Quadratic inequality interval endpoints, Solve a linear inequality with a sign reversal, Solve a quadratic inequality in interval notation |
| Fractional and negative indices | partly supported through related child structures | Differentiate a polynomial, Solve an equation with a negative fractional index |
| Algebraic proof | partly supported through related child structures | Algebraic quotient in a divisibility argument |
| Sequence terms and limiting values | partly supported through related child structures | Limit of a rational nth term |
| Linear sequence nth terms | direct bounded assessment | Arithmetic sequences |
| Quadratic sequence nth terms | partly supported through related child structures | Find a quadratic nth term |
| Gradient | no direct or related child assessment evidence | Needs assessed tasks and review |
| Parallel and perpendicular lines | no direct or related child assessment evidence | Needs assessed tasks and review |
| Distance between points | partly supported through related child structures | Distance between points, Exact distance between general coordinates |
| Midpoints and section ratios | partly supported through related child structures | Divide a line in a ratio |
| Straight line equations | partly supported through related child structures | Line through two points, Line equation in equivalent forms |
| Drawing straight lines | no direct or related child assessment evidence | Needs assessed tasks and review |
| Circles centred at the origin | partly supported through related child structures | Chord length from its distance to the centre |
| General circle equations | partly supported through related child structures | Centre and radius of a circle |
| Tangents to circles | partly supported through related child structures | Tangent to a circle |
| Gradient functions and rate of change | no direct or related child assessment evidence | Needs assessed tasks and review |
| Tangent gradients | no direct or related child assessment evidence | Needs assessed tasks and review |
| Differentiating integer powers | direct bounded assessment | Differentiate a polynomial, Maclaurin polynomials, Second derivative of a polynomial, Gradient with a negative integer power |
| Tangents and normals | partly supported through related child structures | Equation of a tangent, Equation of a normal |
| Increasing and decreasing functions | partly supported through related child structures | Interval of increase for a quadratic |
| Second derivatives | direct bounded assessment | Second derivative of a polynomial |
| Classifying stationary points | partly supported through related child structures | Find a stationary point |
| Optimisation | direct bounded assessment | Optimise the area of a rectangle |
| Curve sketches from stationary points | no direct or related child assessment evidence | Needs assessed tasks and review |
| Matrix multiplication | direct bounded assessment | Multiply two matrices, Determinants |
| Identity matrices | no direct or related child assessment evidence | Needs assessed tasks and review |
| Transforming the unit square | partly supported through related child structures | Transform a point, Fixed points of a reflection |
| Combining transformations | partly supported through related child structures | Combine a reflection and a rotation |
| Area, volume, angles and circle theorems | partly supported through related child structures | Angles in a cyclic quadrilateral, Exact circle area with pi |
| Geometric proof | no direct or related child assessment evidence | Needs assessed tasks and review |
| Sine rule, cosine rule and triangle area | partly supported through related child structures | Triangle area from an included angle, Cosine rule with an exact side, Sine rule with an exact squared side |
| Pythagoras in two and three dimensions | partly supported through related child structures | Space diagonal of a cuboid |
| Trigonometry in three dimensions | partly supported through related child structures | Angle between a line and a plane |
| Trigonometric graphs | partly supported through related child structures | Range and period of a sine graph |
| Trigonometric ratios around the circle | no direct or related child assessment evidence | Needs assessed tasks and review |
| Exact trigonometric values | partly supported through related child structures | Exact squared trigonometric values, Exact trigonometric values in all quadrants |
| Trigonometric identities | partly supported through related child structures | Use trigonometric identities and the quadrant |
| Trigonometric equations in intervals | partly supported through related child structures | Trigonometric equations in an interval, A trigonometric equation using an identity |
| Complex number arithmetic | direct bounded assessment | Multiply complex numbers, Divide complex numbers, Recover a real quadratic |
| Modulus and argument | no direct or related child assessment evidence | Needs assessed tasks and review |
| De Moivre and roots | partly supported through related child structures | Powers of a complex number, All arguments of complex roots |
| Complex loci | partly supported through related child structures | An Argand perpendicular bisector, Intersecting an Argand circle and line |
| Determinants | direct bounded assessment | Determinants, Inverse of a matrix, A parameter that makes a matrix singular |
| Inverse matrices | direct bounded assessment | Inverse of a matrix |
| Proof by induction | partly supported through related child structures | An induction step, The algebra in a telescoping induction step |
| Sums of powers | no direct or related child assessment evidence | Needs assessed tasks and review |
| Integration methods | partly supported through related child structures | Definite polynomial integrals, An exact integral of an even sine power |
| Areas in polar coordinates | partly supported through related child structures | Area of a polar circle, Area of a limaçon, Area of one polar rose petal, Area swept by a polar spiral |
| Hyperbolic functions | partly supported through related child structures | Exact hyperbolic values, Recovering e^x from a hyperbolic value, Hyperbolic double angles |
| First order differential equations | partly supported through related child structures | Exponential differential equations, A first-order equation with a forcing term, A coefficient in a resonant particular integral |
| Scalar products and vector geometry | partly supported through related child structures | Scalar products, Find a point on a line, Intersecting a line and a plane, The closest point on a line, Resolve every line-plane intersection case |
| Arithmetic series sums | direct bounded assessment | Arithmetic series |
| Geometric series sums | direct bounded assessment | Finite geometric series |
| Binomial probabilities | direct bounded assessment | Binomial probability, A geometric waiting-time probability |
| Shortest paths | direct bounded assessment | Shortest paths, A minimum spanning tree |
| Momentum and impulse | direct bounded assessment | Conservation of momentum, A one-dimensional collision with restitution |
| Solving linear equations | direct bounded assessment | Solve a linear equation |
| Two simultaneous linear equations | direct bounded assessment | Simultaneous equations |
| Binomial coefficients for integer powers | direct bounded assessment | Binomial coefficients |
| Inverting a linear function | direct bounded assessment | Inverse functions |
| Inverting a restricted quadratic | direct bounded assessment | Restrict a quadratic inverse |
| Equation of a tangent | direct bounded assessment | Equation of a tangent |
| Equation of a normal | direct bounded assessment | Equation of a normal |
| A polynomial stationary point | direct bounded assessment | Find a stationary point |
| Exact polynomial definite integrals | direct bounded assessment | Definite polynomial integrals |
| A plane matrix transformation | direct bounded assessment | Transform a point |
| Dividing complex numbers | direct bounded assessment | Divide complex numbers |
| Conjugate roots of a real quadratic | direct bounded assessment | Recover a real quadratic |
| Vector scalar product | direct bounded assessment | Scalar products |
| A point on a vector line | direct bounded assessment | Find a point on a line |
| Hyperbolic functions at logarithmic arguments | direct bounded assessment | Exact hyperbolic values |
| An exponential growth differential equation | direct bounded assessment | Exponential differential equations |
| Area swept by constant polar radius | direct bounded assessment | Area of a polar circle |
| The algebra in an induction step | direct bounded assessment | An induction step |
| Expected value of a discrete variable | direct bounded assessment | Expected value |
| Constant acceleration | direct bounded assessment | Constant acceleration |
| Partial fractions | direct bounded assessment | Partial fractions |
| Linear recurrence calculation | direct bounded assessment | Linear recurrence |
| One Newton-Raphson iteration | direct bounded assessment | One Newton–Raphson step |
| Polynomial division | direct bounded assessment | Divide polynomials |
| A linear and nonlinear simultaneous pair | direct bounded assessment | Non-linear simultaneous equations |
| Trigonometric solutions in an interval | direct bounded assessment | Trigonometric equations in an interval |
| Second order differential equations | direct bounded assessment | Second-order differential equations, A differential equation with a repeated root, A polynomial particular integral |
| Maclaurin expansions | direct bounded assessment | Maclaurin polynomials, A logarithm Maclaurin expansion, A negative-power binomial expansion, Keep the binomial convergence interval |
| Eigenvalues of a 2 × 2 matrix | direct bounded assessment | Eigenvalues of a matrix, An eigenvector component, Eigenvalues of a non-triangular matrix, A matrix power acting on a vector, Powers without diagonalisation |
| An eigenvector of a 2 × 2 matrix | direct bounded assessment | An eigenvector component, An eigenvector of a non-triangular matrix |
| An area swept by a limaçon | direct bounded assessment | Area of a limaçon |
| A one-sided binomial critical region | direct bounded assessment | A binomial critical region |
| Conditional probability | direct bounded assessment | Conditional probability |
| Critical path in an activity network | direct bounded assessment | Critical path duration |
| Modular inverses | direct bounded assessment | Multiplicative inverses modulo a prime |
| Bisection interval refinement | direct bounded assessment | One bisection step |
| Exact distance between two points | direct bounded assessment | Distance between points |
| Internal division of a line segment | direct bounded assessment | Divide a line in a ratio |
| A line through two points | direct bounded assessment | Line through two points |
| Centre and radius from a circle equation | direct bounded assessment | Centre and radius of a circle |
| A tangent at a specified circle point | direct bounded assessment | Tangent to a circle |
| Chord length from its distance to the centre | direct bounded assessment | Chord length from its distance to the centre |
| An angle in a cyclic quadrilateral | direct bounded assessment | Angles in a cyclic quadrilateral |
| A cuboid space diagonal | direct bounded assessment | Space diagonal of a cuboid |
| Triangle area from two sides and the included angle | direct bounded assessment | Triangle area from an included angle |
| An exact cosine-rule side calculation | direct bounded assessment | Cosine rule with an exact side |
| An exact sine-rule side calculation | direct bounded assessment | Sine rule with an exact squared side |
| Use an identity with a quadrant restriction | direct bounded assessment | Use trigonometric identities and the quadrant |
| A trigonometric ratio for a line and plane | direct bounded assessment | Angle between a line and a plane |
| Coefficients in completed square form | direct bounded assessment | Complete the square |
| Coefficients of a quadratic sequence | direct bounded assessment | Find a quadratic nth term |
| Counting arrangements under a restriction | direct bounded assessment | Product rule with no repetition |
| Rationalise a conjugate denominator | direct bounded assessment | Rationalise a binomial denominator |
| A linear and quadratic pair with all solutions | direct bounded assessment | Line and parabola intersections |
| Compose two permitted plane transformations | direct bounded assessment | Combine a reflection and a rotation |
| Estimate an area using the trapezium rule | no direct or related child assessment evidence | Needs assessed tasks and review |
| Optimise over a feasible region | no direct or related child assessment evidence | Needs assessed tasks and review |
| Exact three-variable linear elimination | direct bounded assessment | Three simultaneous linear equations |
| A fractional or negative index equation | direct bounded assessment | Solve an equation with a negative fractional index |
| A repeated subject in a formula | direct bounded assessment | Rearrange a reciprocal formula |
| A rational sequence limiting value | direct bounded assessment | Limit of a rational nth term |
| Range of a shifted trigonometric graph | direct bounded assessment | Range and period of a sine graph |
| Squared exact trigonometric values | direct bounded assessment | Exact squared trigonometric values |
| Endpoints of an explicitly stated quadratic inequality interval | direct bounded assessment | Quadratic inequality interval endpoints |
| Gradient from a negative integer power | direct bounded assessment | Gradient with a negative integer power |
| A polynomial quotient supporting a divisibility argument | direct bounded assessment | Algebraic quotient in a divisibility argument |
| Evaluate a rational function at a permitted input | direct bounded assessment | Evaluate a rational function |
| Range of a quadratic on a restricted interval | direct bounded assessment | Range on a restricted quadratic domain |
| Evaluate a quadratic inverse on one stated branch | direct bounded assessment | Evaluate an inverse on its permitted branch |
| A symbolic quadratic inverse formula on a stated branch | direct bounded assessment | Find a quadratic inverse with its domain |
| Exact operations on surds | direct bounded assessment | Combine and simplify surds |
| Exact rationalisation with denominator restrictions | direct bounded assessment | Rationalise a binomial surd denominator |
| Add rational expressions with original exclusions | direct bounded assessment | Add rational expressions |
| Subtract rational expressions with original exclusions | direct bounded assessment | Subtract rational expressions |
| Multiply rational expressions with original exclusions | direct bounded assessment | Multiply rational expressions |
| Divide rational expressions and exclude a zero divisor | direct bounded assessment | Divide rational expressions |
| Solve a linear inequality as an interval | direct bounded assessment | Solve a linear inequality with a sign reversal |
| Solve a quadratic inequality as a union of intervals | direct bounded assessment | Solve a quadratic inequality in interval notation |
| An exact coordinate distance with an irrational result | direct bounded assessment | Exact distance between general coordinates |
| Equivalent equations including horizontal and vertical lines | direct bounded assessment | Line equation in equivalent forms |
| Exact special-angle values with quadrant signs | direct bounded assessment | Exact trigonometric values in all quadrants |
| Exact circle area retaining pi | direct bounded assessment | Exact circle area with pi |
| Intervals determined by the sign of a derivative | direct bounded assessment | Interval of increase for a quadratic |
| A cubic with a rational root and complete equivalent product | direct bounded assessment | Complete factorisation of a cubic |
| Powers of a complex number | direct bounded assessment | Powers of a complex number |
| All arguments of complex roots | direct bounded assessment | All arguments of complex roots |
| An Argand perpendicular bisector | direct bounded assessment | An Argand perpendicular bisector |
| Intersecting an Argand circle and line | direct bounded assessment | Intersecting an Argand circle and line |
| Eigenvalues of a non-triangular matrix | direct bounded assessment | Eigenvalues of a non-triangular matrix |
| An eigenvector of a non-triangular matrix | direct bounded assessment | An eigenvector of a non-triangular matrix |
| A matrix power acting on a vector | direct bounded assessment | A matrix power acting on a vector |
| A parameter that makes a matrix singular | direct bounded assessment | A parameter that makes a matrix singular |
| The algebra in a telescoping induction step | direct bounded assessment | The algebra in a telescoping induction step |
| A logarithm Maclaurin expansion | direct bounded assessment | A logarithm Maclaurin expansion |
| A negative-power binomial expansion | direct bounded assessment | A negative-power binomial expansion |
| A differential equation with a repeated root | direct bounded assessment | A differential equation with a repeated root |
| A polynomial particular integral | direct bounded assessment | A polynomial particular integral |
| A first-order equation with a forcing term | direct bounded assessment | A first-order equation with a forcing term |
| Recovering e^x from a hyperbolic value | direct bounded assessment | Recovering e^x from a hyperbolic value |
| Hyperbolic double angles | direct bounded assessment | Hyperbolic double angles |
| Area of one polar rose petal | direct bounded assessment | Area of one polar rose petal |
| Area swept by a polar spiral | direct bounded assessment | Area swept by a polar spiral |
| An exact integral of an even sine power | direct bounded assessment | An exact integral of an even sine power |
| Intersecting a line and a plane | direct bounded assessment | Intersecting a line and a plane |
| The closest point on a line | direct bounded assessment | The closest point on a line |
| A one-dimensional collision with restitution | direct bounded assessment | A one-dimensional collision with restitution |
| A geometric waiting-time probability | direct bounded assessment | A geometric waiting-time probability |
| A minimum spanning tree | direct bounded assessment | A minimum spanning tree |
| Fixed points of a reflection | direct bounded assessment | Fixed points of a reflection |
| A trigonometric equation using an identity | direct bounded assessment | A trigonometric equation using an identity |
| Resolve every line-plane intersection case | direct bounded assessment | Resolve every line-plane intersection case |
| Powers without diagonalisation | direct bounded assessment | Powers without diagonalisation |
| A coefficient in a resonant particular integral | direct bounded assessment | A coefficient in a resonant particular integral |
| Keep the binomial convergence interval | direct bounded assessment | Keep the binomial convergence interval |