Trigonometry Foundations

IB Mathematics

Factorials, product and sum principles, permutations and combinations, and the binomial theorem

Basic understanding of limits as tool for analyzing behavior of functions at points where they are undefined.

Evaluating limits & differentiability, l'Hôpital's rule, limit definition of the derivative

Rules for differentiating polynomials with integer exponents

Rules for differentiating polynomials with rational exponents

Rules for differentiating some of the most common functions: exponentials in base e, the natural logarithm as well as sin & cos functions.

Rule for differentiating compositions of functions (f∘g)(x)

First introduction to finding derivatives using differential calculus. Gradients & rates of change, basic limits

Using the derivative to predict if a function is increasing, decreasing, or stationary at a point.

Lines tangent & normal to the curve of a function

Increasing / decreasing functions, optimisation, tangents and more!

Integration as a process for undoing differentiation

Integrating a function between 2 points, calculating the area under a curve

Anti-differentiation, definite integrals and their applications