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.
Put it together.
Choose a paper and show your working.
Differentiation practice test 1
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.
10 questions · 55 marks · 75 minutes · Scientific calculatorDifferentiation practice test 2
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.
10 questions · 61 marks · 75 minutes · Scientific calculatorDifferentiation practice test 3: representations and models
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.
10 questions · 60 marks · 75 minutes · Scientific calculatorDifferentiation practice test 4: connected methods
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
10 questions · 61 marks · 75 minutes · Scientific calculatorDifferentiation practice test 5: interpretation and decisions
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
10 questions · 64 marks · 75 minutes · Scientific calculatorDifferentiation practice test 6: synthesis and applications
Original chapter assessment with linked reasoning and applications. Show working, state relevant domains and retain exact values until a numerical answer is requested.
10 questions · 76 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Stage 2 Mathematical Methods
Further differentiation and applications from the current SACE Methods outline. Logarithmic derivatives have their own chapter; integration follows later. Trigonometric calculus uses radians.
Official curriculum source ↗