Introduction to the concept of matrices, their properties, and basic matrix operations.

The concept of an identity matrix and inverse matrices, and determinants. Finding inverses with technology, or by hand for (2×2) matrices

Understanding how (2×2) matrices transform points and shapes on the plane. Explanations of the common IB transformations.

Solving and interpreting systems of linear equations through the lens of matrices.

Find eigenvalues & eigenvectors, and using them to diagonalize and find powers of matrices.

The concept (and basic properties) of limits and derivatives

Power rule, chain rule, product rule, quotient rule, derivatives of ex, ax, loga​(x), trigonometric, and inverse trigonometric functions

Definitions of tangent and normal, finding tangent and normal lines to a function

Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

Definition of the second derivative, concavity, inflexion points

Taking the nth derivative, inductive proofs with the nth derivative

Types of related rates, implicit differentiation