01 / 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.
02 / PRACTICE TESTS
Put it together.
Choose a paper and show your working.
Integration — Practice test 1
A balanced first paper: rules, interpretation, area and motion.
10 questions · 41 marks · 70 minutes · Scientific calculatorIntegration — Practice test 2
A second balanced paper with flow, cost and graphical reasoning.
10 questions · 50 marks · 70 minutes · Scientific calculatorIntegration — Practice test 3
Reasoning, sign changes and model interpretation, with several linked calculations.
10 questions · 47 marks · 70 minutes · Scientific calculatorIntegration — Practice test 4
A varied fourth paper emphasising trigonometric, exponential and logarithmic accumulation.
10 questions · 44 marks · 70 minutes · Scientific calculatorIntegration — Practice test 5
A modelling paper connecting rates, marginal values, averages and particle movement.
10 questions · 45 marks · 70 minutes · Scientific calculatorIntegration — Applications and reasoning test
A harder original applications paper testing choice of method, model assumptions and mathematical explanation.
10 questions · 49 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Mathematical Methods integration and logarithmic antiderivatives; original learning and assessment material, with by-hand methods and explicitly described numerical models.
Official curriculum source ↗