📋 Prerequisites: 🔣 Algebra — Functions & Graphs 📐 Trigonometry ➕ Arithmetic — Powers & Logs Grade 11+
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Advanced

Introduction to Limits

What happens to a function as x approaches a value?

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Advanced

Rates of Change

The concept of a derivative — instantaneous rate of change.

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d/dx
Advanced

Differentiation Rules

Power rule, product rule, quotient rule and chain rule.

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Advanced

Curve Sketching

Use derivatives to find turning points, maxima and minima.

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Advanced

Introduction to Integration

The reverse of differentiation — anti-derivatives.

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Advanced

Area Under a Curve

Use definite integrals to calculate areas.

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🎮 Practice Games — Advanced

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Pre-University

Integration Techniques

Substitution, integration by parts, partial fractions.

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Pre-University

Trig Differentiation

Derivatives of sin, cos, tan and their inverses.

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Pre-University

Exponential & Log Calculus

Differentiating and integrating eˣ and ln(x).

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Pre-University

Optimisation

Use calculus to solve real-world maximum and minimum problems.

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Pre-University

Fundamental Theorem of Calculus

The deep connection between differentiation and integration.

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Pre-University

Volumes of Revolution

Rotate a curve around an axis to create a 3D solid.

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🎮 Practice Games — Pre-University

University

Multivariable Calculus

Partial derivatives and multiple integrals in 3D.

University

Vector Calculus

Gradient, divergence, curl — calculus in vector fields.

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dy/dx
University

Differential Equations

Modelling the world with derivatives — ODEs and PDEs.

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University

Series & Convergence

Taylor series, Maclaurin series and tests for convergence.

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University

Real Analysis

Rigorous foundations of calculus — epsilon-delta proofs.

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University

Complex Analysis

Calculus extended to complex numbers — contour integration.

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🎮 Practice Games — University

Master the Mathematics of Change! ∫

Practice Calculus with all 4 game types.

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