Integration techniques and applications — Topic Review | Year 12

QUICK RECAP

Connect the ideas

Check every proposed antiderivative by differentiation.

Identify the structure before choosing a technique.

Keep substitution variables and limits consistent.

Use absolute-value logarithms and check singularities.

Split geometric regions where boundaries change order.

For washers subtract squared radii; report cubic units.

Complete each paper and show your working.

Integration techniques and applications — practice test 1
10 questions · 44 marks · 75 minutes · Scientific calculator
Select methods and establish reliable exact working.
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Integration techniques and applications — practice test 2
10 questions · 46 marks · 75 minutes · Scientific calculator
Combine techniques and interpret geometric and practical results.
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Integration techniques and applications — practice test 3
10 questions · 44 marks · 75 minutes · Scientific calculator
Diagnose reasoning and connect integration to models.
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Integration techniques and applications — practice test 4
10 questions · 54 marks · 75 minutes · Scientific calculator
Mixed techniques with translated inverse functions, repeated parts, horizontal regions and accumulated rates.
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Integration techniques and applications — practice test 5
10 questions · 58 marks · 75 minutes · Scientific calculator
Reasoning and applications across exact integrals, numerical approximation, changing regions and motion.
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Integration techniques and applications — practice test 6
10 questions · 64 marks · 75 minutes · Scientific calculator
Challenging combined-method problems, parameter reasoning, singularities and geometric models.
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