A complete companion for Grade 9–12 Advanced Mathematics — chapters, lessons, and fully worked exercises with every step explained.
Chapters
Preliminaries of Calculus
Polynomials & rational functions · inverse functions · trigonometric · exponential & logarithmic · transformations
Limits and Continuity
Tangent lines · concept of limit · computation · continuity · asymptotes · formal definition · loss-of-significance
Differentiation
The derivative · power rule · product & quotient rules · chain rule · trig, exp, log · implicit · hyperbolic · MVT
Applications of Differentiation
Linear approximation · L'Hôpital's rule · max/min · monotonicity · concavity · curve sketching · optimisation · related rates
Integration
Antiderivatives · sigma notation · area · the definite integral · FTC · substitution · numerical integration · ln as integral
Applications of the Definite Integral
Area between curves · volumes (disks, washers, shells) · arc length · projectile motion · physics & engineering · probability
Integration Techniques & First-Order Differential Equations
Review · integration by parts · trig techniques · partial fractions · CAS · modelling · separable equations