AA HL · Revision Pack
Higher Level, with the reasoning left in.
For 2027 examinations
The Higher Level pack covers the full course. Topic sets sit beside the Test Series. Questions marked free stay open. Paid questions open with the pack.
8 questions are open. A dashed card means that set is still being written.
Topic 1
Number and algebra
Sequences, exponents, and the binomial expansion.
Sequences and series
Arithmetic and geometric progressions, sigma notation, and the sum of the first n terms.
Exponents and logarithms
Index laws, log laws, and equations that need a change of base.
The binomial theorem
Expand a power, find a single term, and read a coefficient.
Proof
Direct proof, proof by contradiction, and writing a claim so the logic is visible.
Complex numbers
Cartesian and polar form, modulus, argument, and products as a stretch and a turn.
Systems of equations
Linear systems, and how many solutions a pair of equations can have.
Topic 2
Functions
Quadratics, inverses, graph moves, and the exponential and log models.
Quadratics
Roots, the vertex, and the axis of symmetry of a quadratic graph.
Composite and inverse functions
Build a composite, then undo a function on a stated domain.
Transformations of graphs
Translations, stretches, and reflections, written as changes to the equation.
Exponential and log models
Growth and decay, and the log graph that straightens an exponential model.
Rational functions
Asymptotes, the domain, and the shape of a rational graph.
Polynomials
Factors, the remainder, and how the degree controls the ends of the graph.
Topic 3
Geometry and trigonometry
Triangle trigonometry, radians, and the circular functions.
Trigonometry
Right and non-right triangles, radians, the circular functions, and trig equations.
Vectors
Components, magnitude, and position vectors in two and three dimensions.
Scalar and vector products
The angle between two vectors, and the product that returns a perpendicular.
Lines and planes
Vector equations, intersections, and when two lines never meet.
Topic 4
Statistics and probability
Data, probability, and the binomial and normal models used on the papers.
Working with data
Averages, spread, and a regression line read from a scatter graph.
Probability
Combined events, conditional probability, and a tree or a table.
Discrete distributions
A probability table, the expected value, and the binomial model.
The normal distribution
Standardising a value and reading a probability from the bell curve.
Continuous random variables
A density function, and probability as an area.
Topic 5
Calculus
Derivatives, stationary points, and the area under a curve.
Differentiation
The derivative, the rules, and stationary points on a curve.
Integration and area
Antiderivatives, definite integrals, and the area between curves.
Kinematics
Displacement, velocity, and acceleration linked by derivatives and integrals.
Differential equations
Separable equations, the constant, and a particular solution from a point.