Exponentials and logarithms.
Exponentials and logarithms: integer and fractional index laws, rational/irrational numbers and surd operations, exponential growth and decay.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Integer and fractional index laws
Understand roots and reciprocals, then apply index laws with appropriate restrictions.
- 02
Rational/irrational numbers and surd operations
Recognise rational and irrational quantities, calculate exactly with surds and rationalise denominators.
- 03
Exponential growth and decay
Identify a constant multiplier and build exponential growth or decay models with meaningful time units.
- 04
Transformations and asymptotes of exponential graphs
Connect an exponential rule with its graph, transformations, intercepts, domain, range and horizontal asymptote.
- 05
Fitting/interpreting exponential models
Build an exponential rule from data, interpret its factor and test whether a fixed-ratio model is justified.
- 06
Compound growth, depreciation and half-life
Match a model to its compounding period, depreciation rate or half-life, and compare rates fairly.
- 07
Meaning of a logarithm
Read a logarithm as an exponent and move confidently between exponential and logarithmic statements.
- 08
Logarithm laws
Use logarithm laws to expand, combine and solve expressions while checking positive arguments.
- 09
Solving exponential equations with base-10 logs
Use common logarithms to solve exponential equations and translate continuous times into practical thresholds.
- 10
Checking domains and the reasonableness of model predictions
Check algebraic domains and evaluate whether a model prediction is meaningful in its original context.
Topic review
Revisit the key ideas, then choose a practice paper.