Rates of change and differential equations — Topic Review | Year 12

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.

Complete each paper and show your working.

Rates of change and differential equations — Test 1
10 questions · 60 marks · 75 minutes · Scientific calculator
Build fluency across implicit rates, initial conditions and models.
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Rates of change and differential equations — Test 2
10 questions · 60 marks · 75 minutes · Scientific calculator
Use different equation forms and interpret their solutions.
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Rates of change and differential equations — Test 3
10 questions · 60 marks · 75 minutes · Scientific calculator
Connect geometry, separation and rate models.
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Rates of change and differential equations — Test 4
10 questions · 60 marks · 75 minutes · Scientific calculator
Reason from functions and slope information.
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Rates of change and differential equations — Test 5
10 questions · 60 marks · 75 minutes · Scientific calculator
Apply calculus while checking signs, distances and assumptions.
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Rates of change and differential equations — Test 6
10 questions · 63 marks · 75 minutes · Scientific calculator
Combine methods and critique common modelling errors.
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