Integration — Topic Review | Year 12

QUICK RECAP

Connect the ideas

An indefinite integral is a family: include the arbitrary constant.

Differentiate an antiderivative to check every coefficient and sign.

A definite integral is upper antiderivative value minus lower value.

Find and split at sign changes for geometric area and total distance.

For area between curves integrate upper minus lower on each interval.

An integral of a rate gives change; add the initial amount when finding a final quantity.

Use the chain rule when an accumulation function has a changing endpoint.

Numerical rules estimate integrals; state the spacing, units and assumptions.

Complete each paper and show your working.

Integration — Practice test 1
10 questions · 41 marks · 70 minutes · Scientific calculator
A balanced first paper: rules, interpretation, area and motion.
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Integration — Practice test 2
10 questions · 50 marks · 70 minutes · Scientific calculator
A second balanced paper with flow, cost and graphical reasoning.
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Integration — Practice test 3
10 questions · 47 marks · 70 minutes · Scientific calculator
Reasoning, sign changes and model interpretation, with several linked calculations.
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Integration — Practice test 4
10 questions · 44 marks · 70 minutes · Scientific calculator
A varied fourth paper emphasising trigonometric, exponential and logarithmic accumulation.
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Integration — Practice test 5
10 questions · 45 marks · 70 minutes · Scientific calculator
A modelling paper connecting rates, marginal values, averages and particle movement.
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Integration — Applications and reasoning test
10 questions · 49 marks · 75 minutes · Scientific calculator
A harder original applications paper testing choice of method, model assumptions and mathematical explanation.
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