The Mathematical
Foundation

"Physics is the language of nature written in mathematics. Sharpen your tools before you speak."

Before diving into motion and forces, we build the mathematical vocabulary fluent physicists use every day — algebra, trigonometry, vectors, dimensional analysis, and the first ideas of calculus. This chapter lays the ground for everything that follows.

📋 Prerequisites

Basic high school algebra — solving equations, working with fractions and powers. No prior physics knowledge required.

🎯 By the End of This Chapter

Units · Dimensional Analysis · Algebra · Trigonometry · Graphs · Calculus Basics · Scientific Notation & Significant Figures

Learning Outcomes

What you will be able to do after this chapter

Convert between units confidently and apply dimensional analysis to check and derive equations

Solve physics equations using algebra techniques — rearranging, substituting, and simplifying with ease

Use trigonometry — sine, cosine, tangent, and the Pythagorean theorem — to solve triangle problems in any physics context

Read, interpret, and create physics graphs — and recognise linear, quadratic, and inverse relationships at a glance

Understand derivatives and integrals as tools for motion — and work comfortably with scientific notation and significant figures

The Lessons

Six lessons. One complete toolkit.

1.1

Foundation Concept Easy

Numbers, Units & Dimensional Analysis

Master the language of physics: learn to speak in numbers, units, and dimensions with confidence. Why 9.8 m/s² and not just 9.8 — and how dimensional analysis lets you derive, check, and remember formulas without memorising them.

Read Lesson →

1.2

Foundation Concept Easy

Algebra Essentials for Physics

Sharpen your algebra toolkit: solve equations, manipulate formulas, and rearrange relationships like a pro. Every physics problem is ultimately an algebra problem — this lesson makes algebra feel effortless so the physics can take centre stage.

Read Lesson →

1.3

GCSE Concept Medium

Trigonometry Basics

Triangles are everywhere in physics — in force diagrams, in wave descriptions, in projectile motion. Master sine, cosine, tangent, the Pythagorean theorem, and the unit circle. You will never look at an angle the same way again.

Coming Soon

1.4

Foundation Concept Easy

Graphs and Functions

Learn to read, interpret, and create physics graphs. Understand linear, quadratic, and inverse relationships — and why the shape of a graph tells you more than any equation alone. Gradient as rate of change. Area under curve as accumulation.

Coming Soon

1.5

AP-Physics Concept Medium

Introduction to Calculus

Understand derivatives as rates of change and integrals as accumulation — the mathematical foundation of all motion analysis. Built from first principles: why calculus exists, what it describes, and how to use it before you have formally studied it.

Coming Soon

1.6

Foundation Concept Easy

Scientific Notation & Significant Figures

Express very large and very small numbers efficiently, and understand precision in measurements. From the mass of a proton (1.67 × 10⁻²⁷ kg) to the distance to the sun (1.5 × 10¹¹ m) — scientific notation is the physicists' shorthand for speaking about the universe at any scale.

Coming Soon

← Back

Mechanics Hub

Return to the Mechanics overview — all chapters, all lessons, in order.

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Next Chapter →

Kinematics — 1D Motion

With your mathematical tools sharpened, begin the physics: position, velocity, acceleration, and the equations of motion in one dimension.

Begin Chapter 2 →