Further Applications of Calculus
Extension 1 calculus applications: related rates, exponential growth and decay, and simple harmonic motion.
Active lessons
9
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 8 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
9 of 9 active
Lesson 1
Related Rates of Change
Practise related rates of change with concise examples and mastery checks.
Lesson 2
Exponential Growth and Decay
Practise exponential growth and decay with concise examples and mastery checks.
Lesson 3
Simple Harmonic Motion
Practise simple harmonic motion with concise examples and mastery checks.
Lesson 4
Calculus Applications Exam Practice
Practise calculus applications exam practice with concise examples and mastery checks.
Lesson 5
Areas Between Curves and Volumes of Revolution
Calculate areas enclosed between two curves and volumes of solids formed by rotating a region about the x-axis or y-axis.
Lesson 6
Multiplicity of Zeroes of Polynomial Functions
Define the multiplicity of a zero, prove the derivative result, and sketch polynomials in factored form by reading crossing, touch, and inflection behaviour at each zero.
Lesson 7
Newton's Law of Cooling and Limited Growth
Solve dQ/dt = k(Q − A) by separation of variables to obtain Q(t) = A + Ce^(kt), apply it to Newton's Law of Cooling and population models approaching a carrying capacity, and justify long-run conclusions in context.
Lesson 8
Slope Fields and Solution Curves
Construct and read slope fields for dy/dx = f(x, y), sketch solution curves by following the direction field, identify stable and unstable equilibria, and describe long-run behaviour of solutions.
Lesson 9
Prior Knowledge Revision: Integration and Separable DEs
Activate prior knowledge for Further Applications of Calculus: standard indefinite integrals, the Fundamental Theorem of Calculus for definite integrals, and separation of variables for first-order differential equations.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.