Year 12 Maths Advanced Module 6 15 Lessons

Further Calculus

Integration reverses differentiation, turning rates of change into total change. It finds the area under curves, the volume of solids, and the solutions to differential equations that model everything from tumour growth to cooling coffee. This module connects the abstract power of calculus to the concrete problems of science and engineering.

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Know

Key Facts

Integration rules for powers, exponentials, and logarithms
The Fundamental Theorem of Calculus
Methods for solving differential equations

Understand

Concepts

Integration as the inverse of differentiation
Definite integrals as accumulated change
Differential equations as models of change

Can Do

Skills

Integrate polynomial, exponential, and logarithmic functions
Calculate areas and volumes using integration
Set up and solve differential equations

Lessons

Introduction to Integration

~35 min · Antiderivatives, notation, reversing differentiation

Integrating Power Functions

~35 min · Power rule, special case n = -1

Integrating Exponentials and Logarithms

~35 min · e^x, a^x, 1/x

The Definite Integral

~35 min · Limits, geometric interpretation

The Fundamental Theorem of Calculus

~35 min · Connecting definite and indefinite integrals

Checkpoint 1 — Lessons 1–5

~25 min · 8 MC + 3 SA

Areas Between Curves

~35 min · Finding intersections, top/bottom functions

Volumes of Revolution

~35 min · Disk and washer methods

Integration by Substitution

~35 min · Reverse chain rule, changing limits

Integration by Parts

~35 min · LIATE rule, product rule reverse

Partial Fractions

~35 min · Decomposing rational functions

Checkpoint 2 — Lessons 6–10

~25 min · 8 MC + 3 SA

Introduction to Differential Equations

~35 min · Order, general and particular solutions

Separable Differential Equations

~35 min · Separation of variables, exponential model

Growth and Decay Models

~35 min · Half-life, doubling time, real-world applications

Motion Applications

~35 min · Position, velocity, acceleration, distance vs displacement

Module Synthesis

~35 min · Consolidation, connections, mixed problems

Checkpoint 3 — Lessons 11–15

~25 min · 8 MC + 3 SA

Module Quiz — Full Module

~40 min · 10 MC + 5 SA

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