Connect the ideas.
- Choose an index law from the operation; do not apply product laws to sums.
- Fractional powers connect with roots. Keep even-root domains and log inputs valid.
- Simplify surds exactly and rationalise using equivalent fractions.
- Exponential change multiplies by a fixed factor over equal input intervals.
- Logarithms invert powers; logarithmic scale differences describe ratios.
- Use graphs, tables and context to choose and check a model; round at the end.
Put it together.
Choose a paper and show your working.
Exponential relationships — practice test 1
Original progressive questions on exact surds, indices, graphs and exponential/logarithmic reasoning.
16 questions · 42 marks · 60 minutes · Scientific calculatorExponential relationships — practice test 2
Original progressive questions on exact surds, indices, graphs and exponential/logarithmic reasoning.
16 questions · 47 marks · 60 minutes · Scientific calculatorExponential relationships — applications test
Apply exact arithmetic, models and logarithmic reasoning to varied contexts with all data supplied.
16 questions · 53 marks · 60 minutes · Scientific calculator
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Integer and fractional index laws; connecting fractional powers with roots; simplifying surds; operations with surds; rationalising denominators; exact and approximate values; exponential tables and graphs; growth/decay factors; comparing linear/quadratic/exponential patterns; exponential equations; logarithms as inverses; logarithm laws; interpreting logarithmic scales; graph transformations and parameter experiments; choosing and evaluating models.
Official curriculum source ↗