Quantifying physical space. Perimeter, area, volume, and the coordinate geometry that lets you describe any shape with numbers.
Volume 3 — Shape and measure
Volume 3
Shape and Measure
You already know how to calculate and balance equations. This volume shows you how algebraic tools can describe the physical world — and how the world, in turn, can give meaning to abstract mathematics.
This is the bridge where algebra stops being just letters on a page and starts becoming a map of reality. By the end you will be able to map distances, relate angles to side lengths, deconstruct non-linear relationships, and formally describe how different parameters interact.
5 chapters
Grade 9–10
Needs Volume 2
Chapter Map
Relating angles to side lengths. Sine, cosine, and tangent as ratios — and how a right triangle connects every angle to a ratio you can calculate.
Deconstructing complex equations. Polynomials as sums of power terms, factoring as reverse multiplication, and the quadratic formula as a shortcut.
Mapping inputs to outputs. The formal definition of a function, domain and range, composition, and what it means for a function to be invertible.
The algebra of true and false. AND, OR, NOT as operations — and how the same algebraic rules that govern numbers also govern logic and digital circuits.