Exponential relationships.
Exponential relationships: integer and fractional index laws, connecting fractional powers with roots, simplifying surds.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Integer and fractional index laws
Use index laws to simplify products, quotients and powers, including negative and fractional indices.
- 02
Connecting fractional powers with roots
Read fractional indices as roots and move between the two notations.
- 03
Simplifying surds
Extract square factors to write surds in their simplest exact form.
- 04
Operations with surds
Add like surds and multiply or divide surd expressions exactly.
- 05
Rationalising denominators
Remove a square-root surd from a denominator using an equivalent fraction.
- 06
Exact and approximate values
Keep exact expressions through a calculation, then round only when a decimal is required.
- 07
Exponential tables and graphs
Build tables of exponential values and connect them to the shape of a graph.
- 08
Growth/decay factors
Turn percentage increases and decreases into repeated multiplicative factors.
- 09
Comparing linear/quadratic/exponential patterns
Use differences and ratios to distinguish common patterns, without assuming a short table proves a unique rule.
- 10
Exponential equations
Solve exponential equations by matching bases or using logarithms when a matching base is unavailable.
- 11
Logarithms as inverses
Understand a logarithm as the exponent needed to produce a positive number.
- 12
Logarithm laws
Use logarithm laws to combine or separate products, quotients and powers with valid positive inputs.
- 13
Interpreting logarithmic scales
Interpret equal steps on logarithmic scales as equal multiplicative changes.
- 14
Graph transformations and parameter experiments
Describe how parameters shift, stretch or reflect an exponential graph.
- 15
Choosing and evaluating models
Choose a model from context and evidence, test its fit, and state its limitations.
Topic review
Revisit the key ideas, then choose a practice paper.