01 / QUICK RECAP
Connect the ideas.
- Use the chain rule when differentiating y with respect to x.
- Write related-rates relations before inserting instantaneous measurements.
- Check the differential equation and the initial data independently.
- Keep equilibrium solutions when separating variables.
- Interpret derivative signs, units and model limits.
- For SHM, acceleration is proportional to displacement toward equilibrium.
02 / PRACTICE TESTS
Put it together.
Choose a paper and show your working.
Rates of change and differential equations — Test 1
Build fluency across implicit rates, initial conditions and models.
10 questions · 60 marks · 75 minutes · Scientific calculatorRates of change and differential equations — Test 2
Use different equation forms and interpret their solutions.
10 questions · 60 marks · 75 minutes · Scientific calculatorRates of change and differential equations — Test 3
Connect geometry, separation and rate models.
10 questions · 60 marks · 75 minutes · Scientific calculatorRates of change and differential equations — Test 4
Reason from functions and slope information.
10 questions · 60 marks · 75 minutes · Scientific calculatorRates of change and differential equations — Test 5
Apply calculus while checking signs, distances and assumptions.
10 questions · 60 marks · 75 minutes · Scientific calculatorRates of change and differential equations — Test 6
Combine methods and critique common modelling errors.
10 questions · 63 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Specialist Mathematics topic 6.1–6.2, with the approved school-level rates, differential-equation and motion applications.
Official curriculum source ↗