Quadratic equations: factorisation, completing the square, formula, and discriminant · Polynomials: division, remainder theorem, and factor theorem · Functions: domain, range, inverse, composite, and modulus functions · Exponential and logarithmic functions, equations, and graphs · Arithmetic and geometric sequences and series including sum to infinity

Equation of a circle, tangent and normal to a circle · Sketching and transforming graphs of all function types · Modelling with functions: fitting curves to real-world data · Inequalities: linear and quadratic — algebraic and graphical methods · Parametric equations: definition, sketching, and conversion to Cartesian form

Trigonometric functions: definitions, graphs, and transformations · Exact values and the unit circle in degrees and radians · Trigonometric identities: Pythagorean, double angle, and addition formulae · Solving trigonometric equations in given domains · Sine rule, cosine rule, area formula, and 3D trigonometry problems

Limits and continuity: definition and evaluation · Differentiation from first principles · Rules of differentiation: chain, product, quotient, and implicit · Applications: tangents, normals, rates of change, increasing/decreasing functions · Optimisation: finding maximum and minimum values in real-world contexts

Indefinite and definite integrals using standard results · Integration techniques: substitution and integration by parts · Area under and between curves using definite integrals · Volumes of revolution (A-Level/IB Higher Level) · Introduction to differential equations: separable variables

Probability distributions: binomial and normal distribution · Hypothesis testing: one-tail and two-tail significance tests · Correlation and linear regression: PMCC and least-squares line · Vectors in 2D and 3D: operations, scalar product, and angle calculation · Kinematics and Newton’s laws: constant acceleration, forces, connected particles

Cambridge A-Level, IGCSE, IB, SAT, WAEC past paper practice · Exam technique: time management, mark allocation, and checking strategies · Rigorous mathematical proof: direct, contradiction, and induction · IB-style mathematical exploration: topic selection, research, and write-up · Full timed mock examination with detailed written feedback

Master pure mathematics from algebra and functions through to calculus · Apply statistics, probability, vectors, and mechanics with precision · Prepare comprehensively for Cambridge, IB, SAT, and WAEC examinations · Construct rigorous mathematical proofs and extended investigations · Achieve full readiness for university-level STEM degree programmes

Complete all 7 modules, pass a proctored examination (minimum 75%), and submit a mathematical investigation meeting IB or Cambridge extended project standards.

University mathematics, engineering, economics, medicine, data science, computer science, and all STEM degree programmes worldwide.