Logarithmic functions — Topic Review | Year 12

QUICK RECAP

Connect the ideas

A logarithm is an exponent; its input is positive, but its value may be negative.

Combine logs only with valid laws and retain original domain restrictions.

Use exact logarithmic answers before rounding a final numerical result.

Sketch from a domain, asymptote and exact anchor points.

Differentiate a logarithm of an input using the chain rule.

Interpret model parameters, units and limitations; log-scale changes describe ratios.

Complete each paper and show your working.

Logarithmic functions — Practice test 1
10 questions · 50 marks · 70 minutes · Scientific calculator
A balanced paper moving from inverse relationships to equations, graphs, derivatives and applications.
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Logarithmic functions — Practice test 2
10 questions · 54 marks · 70 minutes · Scientific calculator
Emphasis on domains, reflected graphs, exact solutions and logarithmic rates.
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Logarithmic functions — Practice test 3
10 questions · 56 marks · 70 minutes · Scientific calculator
A mixed paper connecting inverse functions, differentiation and supplied mathematical models.
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Logarithmic functions — Practice test 4
10 questions · 54 marks · 70 minutes · Scientific calculator
Reasoning about domains, parameters, inverse graphs and an optimisation model.
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Logarithmic functions — Practice test 5
10 questions · 57 marks · 70 minutes · Technology-assisted
Data interpretation, parameter fitting and checking claims about logarithmic models.
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Logarithmic functions — Practice test 6
10 questions · 61 marks · 70 minutes · Technology-assisted
A more demanding paper combining precise domains, parameter choices and mathematical reasoning.
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