Level 3 Calculus
Students solve differential equations to find functions to model the value of a car in terms of its age. Then they compare their results with real data.
This activity introduces the differentiation of exponential functions. Students find gradients by drawing tangents and by using small incremental changes in a spreadsheet.
This activity shows students how to use differentiation to find stationary points on the curves of polynomial functions. It includes the use of to determine the nature of the stationary point. Students will learn how to use this and other information to sketch the curves, then use graphic calculators to check their answers.
Students use differentiation to find maximum and minimum points in polynomial functions in order to solve real-life problems.
Slideshow to aid class discussion about solving maximisation and minimisation problems. The slideshow then encourages students to devise and solve their own problems. There are no student sheets.
Students approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.
Students use integration to approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.
This activity explores the rate of drug clearance from the body, both for common analgesic compounds and for caffeine.
Matching activities to check whether students can identify the derivatives of quadratic and cubic functions and their graphs.
Students learn how to find the mean values of quantities varying with time. This involves finding the area under graphs, initially by using geometrical formulae for areas. It is followed by the use of integration in a variety of real life situations.
An introduction to differentiation. Students are shown how to use a spreadsheet to find the gradients of functions of the form xn. This leads to the general rule for gradients of functions of this type.