Course: Year 12 Mathematics Advanced

Differential Calculus

A structured pathway through the key Year 12 differential calculus skills, built around explicit teaching, worked examples, guided practice, independent practice, and mastery checks.

Active lessons

12

Planned lessons

12

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Start with the first active lesson if you are new to differential calculus.
  • You may try the mastery quiz early.
  • If you do not pass, the app will guide you through the full lesson sequence.
  • Work through lessons in order for best results.

What this unit covers

Differentiation rules
Tangents and normals
Stationary points
Increasing and decreasing functions
First and second derivative tests
Curve sketching
Optimisation
Rates of change applications

Unit pathway

Lesson pathway

12 of 12 active

1

Lesson 1

The derivative as rate of change

Understand average rate of change, instantaneous rate of change, tangent gradients, and derivative notation.

Active
2

Lesson 2

Differentiating polynomial terms

Use the power rule to differentiate individual polynomial terms accurately.

Active
3

Lesson 3

Differentiating polynomial functions

Differentiate full polynomial expressions term-by-term and simplify the derivative.

Active
4

Lesson 4

Tangents and normals

Use derivatives to find gradients and equations of tangents and normals.

Active
5

Lesson 5

Stationary points

Solve derivative equations and find the coordinates of stationary points.

Active
6

Lesson 6

Increasing and decreasing functions

Use the sign of the derivative to determine where a function is increasing or decreasing.

Active
7

Lesson 7

First derivative test

Classify stationary points using sign changes in the first derivative.

Active
8

Lesson 8

Second derivative test

Use the second derivative to classify local maxima and minima.

Active
9

Lesson 9

Curve sketching with derivatives

Combine intercepts, stationary points, derivative signs, and concavity to sketch curves.

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10

Lesson 10

Optimisation problems

Form objective functions and use derivatives to solve maximum and minimum problems.

Active
11

Lesson 11

Rates of change applications

Interpret derivatives as rates of change in applied contexts.

Active
12

Part of the Online Learning Package

This unit is part of the Nova Maths online learning package. The lesson pathway is available for preview, and full access requires an active online learning subscription.

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