Managing multiplicative growth. Exponential functions and their inverses — logarithms as the answer to "what power gives me this result?"
Volume 4 — Functions and change
Volume 4
Functions and Change
In previous volumes, you studied relationships where scaling happens in simple or periodic ways. This volume is about what happens when growth accelerates, when dimensions expand, and when you need to handle many different, changing variables all at once.
By the end you will be comfortable navigating exponential growth and decay, working within the complex plane, organising large sets of linear constraints using matrices, and making sense of infinite step-by-step accumulations.
6 chapters
Grade 10–11
Needs Volume 3
Chapter Map
Expanding the number plane. The imaginary unit as a rotation, Argand diagrams, polar form, and why complex numbers solve problems real numbers cannot.
Handling multiple relationships at once. Matrix notation, row reduction, determinants, and the geometric meaning of a system of linear equations.
Identifying and summing discrete patterns. Convergence, geometric series, and the surprising fact that infinitely many terms can have a finite sum.
Breaking a complicated fraction into simpler pieces. A technique that appears in integration and in Laplace transforms — decomposing to compute.
A rotating complex number traces a sine wave. Phasors let you do AC circuit analysis with algebra instead of trigonometric identities.