Modelling with calculus

Skill Activities

We welcome feedback and contributions. If you have any comments, ideas or resources to offer please contact June Haighton.

Please note that resources added most recently are at the bottom of the page.

Coastal Erosion A
This activity uses the context of coastal erosion to introduce the trapezium rule for estimating the area under a curve. Can be combined with Coastal Erosion B. Teacher notes included.

Student Information (application/msword, 314 KB) (application/pdf, 139 KB)

Coastal Erosion B
Students use integration to estimate loss of land due to coastal erosion. Can be combined with Coastal Erosion A. Teacher Notes included.

Student Information (application/msword, 446 KB) (application/pdf, 143 KB)

Drug Clearance
Data Sheet shows how drug clearance after taking a painkiller can be modelled by exponential decay. Students investigate further (including the clearance of caffeine after a variety of drinks). Teacher notes included.

Activity (application/msword, 167 KB) (application/pdf, 49 KB)

Maxima and Minima
Powerpoint presentation and practice questions using differentiation to solve maxima and minima problems. Teacher notes included.

Student Information (application/msword, 129 KB) (application/pdf, 51 KB)
Powerpoint (application/vnd.ms-powerpoint, 91 KB)

Stationary Points
Powerpoint presentation, examples and practice questions on sketching graphs. Teacher notes included.

Student Information (application/msword, 107 KB) (application/pdf, 49 KB)
Powerpoint (application/vnd.ms-powerpoint, 108 KB)

What's it worth?
Investigate a variety of suggested models for the depreciation of a car. Involves solving differential equations, drawing sketch graphs and comparison with real data. Teacher notes included.

Student Information: (application/msword, 129 KB) (application/pdf, 53 KB)
Spreadsheet: (application/vnd.ms-excel, 17 KB)

Polynomial graphs and gradients
12 sets of cards, each consisting of a polynomial function, its graph, its gradient function and the graph of the gradient function – for students to match. Teacher Notes included.

Student Information and Teacher notes: (application/msword, 122 KB) (application/pdf, 54 KB)

Mean Values
Students use area formulae and integration to find mean values of speed, share prices and water depth. Supported by Powerpoint presentation. Teacher Notes included.

Student information and teacher notes (application/msword, 1.0 MB) (application/pdf, 72 KB)
PowerPoint presentation (application/vnd.ms-powerpoint, 217 KB)