Linear and exponential models.
Build, use and evaluate practical linear, piecewise and exponential models.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Linear equations and formulas
Solve linear equations by balancing both sides, then rearrange and use practical formulas.
- 02
Gradient/intercepts
Find a straight line’s gradient and intercepts and interpret their units.
- 03
Constructing and interpreting straight-line models
Build a straight-line model from observations and give it a sensible domain.
- 04
Simultaneous equations and break-even situations
Solve simultaneous rules and distinguish break-even from making a profit.
- 05
Piecewise practical models where relevant
Choose the correct branch of a practical piecewise rule and handle threshold values consistently.
- 06
Exponential graphs and constant percentage change
Recognise an exponential pattern from equal ratios and interpret its multiplier.
- 07
Growth/decay models
Choose a percentage multiplier and use growth or decay models forwards and backwards.
- 08
Comparing linear with exponential change
Compare additive and multiplicative models over a stated time horizon.
- 09
Fitting, predicting and interpreting models
Fit a simple model to observations and use residuals to check its predictions.
- 10
Limitations of extrapolation
Judge a prediction against its data range, physical limits and modelling assumptions.
Topic review
Revisit the key ideas, then choose a practice paper.