Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Calculus

Yes, really — 4MA1 Higher Tier includes differentiation: gradients of curves, turning points, and velocity and acceleration in kinematics.

Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.

2 modules of Pearson Edexcel International GCSE Mathematics (all Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.

The modules in Calculus

Differentiation (Higher Tier)

The gradient of a curve at a single point — the power rule, and why it works. Higher Tier, and genuinely on this specification. A curve's steepness changes from point to point — differentiation gives a formula for the gradient at ANY point.

When a question is asking for it: 'Find dy/dx', 'find the gradient of the curve at x = …' (differentiate, THEN substitute), and as the engine for turning points and kinematics in the next module. Learn Differentiation →

Calculus in Motion: Kinematics (Higher Tier)

Displacement, velocity and acceleration as a chain of derivatives — the exam's favourite way to dress calculus in a story. Higher Tier. If s(t) is displacement (position) at time t, then velocity is v = ds/dt and acceleration is a = dv/dt: each is the derivative of the one before.

When a question is asking for it: Any question giving displacement or height 'as a function of t': asked for velocity → differentiate once; acceleration → twice; 'when is it at rest / at its highest?' → set v = 0 and solve for t. Learn Calculus in Motion: Kinematics →

The mistakes that cost marks in Calculus

One from each module — the error examiners see most, with the module that puts it right.

• Differentiating axⁿ as axⁿ⁻¹ (forgetting to multiply by the power): x³ → 3x², not x². (Differentiation)
• Setting s = 0 for 'at rest'. Rest is about MOTION stopping: v = 0. (s = 0 means 'back at the start' — different event.) (Calculus in Motion: Kinematics)

Where Calculus sits in the specification

Content area 3 of 4MA1, sub-topic 3.4. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.

• 3.4 — Calculus — kinematics (Higher)

How Calculus is mastered on Incandio

Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 19 authored exam-style questions across this strand, marked on Incandio.

All of Incandio Mathematics · The 4MA1 specification · Exam Ready