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UK A Level Mathematics · independent study · myAudience
Independent myAudience subject study using references for England. Published readings cover selected topics; full curriculum, assessment and practical coverage are not verified. No awarding-body affiliation, endorsement, qualification or grade guarantee is offered. Check the source specification and your centre for the requirements of your chosen course.
Say exactly what an algebraic argument proves
Extend index laws to roots and reciprocals
Keep irrational quantities exact
Choose the quadratic form that reveals the feature
Use the discriminant to reason about parameters
Recognise a quadratic hidden inside another equation
Solve intersections while keeping paired coordinates
Solve inequalities as sets of permitted inputs
Use division and the factor theorem to expose roots
Simplify rational expressions without losing restrictions
Build a graph sketch from algebraic evidence
Specify a function before composing its rules
Restrict a domain so that a rule can be reversed
Track coordinates through graph transformations
Read modulus graphs as piecewise rules
Use a function model and test its limitations
Radians and a constrained sector
Recover every angle from a hidden quadratic
A derivative is a limiting slope, not a fraction at zero
Rational powers: keep the domain when finding a tangent
Exponentials, logarithms and trigonometry: the input changes the gradient
From gradients to decisions: stationary points and a box with limits
Differentiating a construction: product, quotient and chain rules
Reciprocal and inverse trigonometry: notation, branches and slopes
Connected rates: identify what changes before cancelling symbols
Implicit curves: a relation can contain more than one local branch
Parametric curves: one point can be reached by different branches
Reading a curve as a graph of gradients
Why sine differentiates to cosine — and why radians matter
Recover a changing quantity from its rate
Find area by deciding which boundary is above
A substitution must preserve the domain and limits