Differentiation and applications — Topic Review | Year 12

QUICK RECAP

Connect the ideas

A derivative is a local rate of change, with units determined by the two variables.

Choose a rule from the structure of an expression; simplify first when that reduces the work.

Stationary points solve the first-derivative equation; classification requires further evidence.

Concavity must change at an inflection point. A zero second derivative is only a candidate test.

Optimisation requires a feasible domain, all relevant candidates and an answer in context.

Practice tests

Complete each paper and show your working.

Differentiation practice test 1
10 questions · 55 marks · 75 minutes · Scientific calculator
An original progressively demanding chapter paper. Show analytical working; a scientific calculator may be used for numerical values. Diagrams and data needed for questions are supplied.
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Differentiation practice test 2
10 questions · 61 marks · 75 minutes · Scientific calculator
An original progressively demanding chapter paper. Show analytical working; a scientific calculator may be used for numerical values. Diagrams and data needed for questions are supplied.
Open test Marking guide
Differentiation practice test 3: representations and models
10 questions · 60 marks · 75 minutes · Scientific calculator
An original progressively demanding chapter paper. Show analytical working; a scientific calculator may be used for numerical values. Diagrams and data needed for questions are supplied.
Open test Marking guide
Differentiation practice test 4: connected methods
10 questions · 61 marks · 75 minutes · Scientific calculator
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
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Differentiation practice test 5: interpretation and decisions
10 questions · 64 marks · 75 minutes · Scientific calculator
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
Open test Marking guide
Differentiation practice test 6: synthesis and applications
10 questions · 76 marks · 75 minutes · Scientific calculator
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
Open test Marking guide

Back to Differentiation and applications

Connect the ideas

Practice tests

Differentiation practice test 1

Differentiation practice test 2

Differentiation practice test 3: representations and models

Differentiation practice test 4: connected methods

Differentiation practice test 5: interpretation and decisions

Differentiation practice test 6: synthesis and applications