# Calculus

This collection of Nuffield Maths resources explores Calculus. The demand is roughly equivalent to that in GCE A level.

They include slide shows to introduce the topics, student sheets and teacher notes, as well as other relevant resources.

The teachers' notes start with a short overview of the activity, who and what it is designed for, and lists the necessary resources. The student sheets have background information where needed, and tasks for the students to work and reflect on. Extensions and solutions are included in the teachers' notes.

The collection contains the following resources:

Exponential rates of change This activity introduces the differentiation of exponential functions. Students find gradients by drawing tangents and by using small incremental changes in a spreadsheet.

What's it worth?   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.

Stationary points   This activity shows students how to use differentiation to find stationary points on the curves of polynomial functions. It includes the use of the second derivative 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.

Maxima and minima  Students use differentiation to find maximum and minimum points in polynomial functions in order to solve a variety of real-life problems.

Coastal erosion A Estimating area  Students approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.

Coastal erosion B Integrating area  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.

Maximising and minimising  Students consider some maximisation/ minimisation problems and then devise some of their own. There are no student sheets.

Drug clearance  This activity explores the rate of drug clearance from the body, both for common analgesic compounds and for caffeine.

Derivative matching  Matching activities to check whether students can identify the derivatives of quadratic and cubic functions and their graphs.

Mean values  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.

Gradients     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.

## Resources

### Maximising and minimising

This resource is part of a collection of Nuffield Maths resources exploring Calculus. The demand is roughly equivalent to that in GCE A level.

Here, students are asked to use differentiation to find maximum and minimum points in polynomial functions in order to solve a variety of real-life problems.

### Mean values

This resource is part of a collection of Nuffield Maths resources exploring Calculus. The demand is roughly equivalent to that in GCE A level.

In this resource students learn how to find the mean values of quantities varying with time. This involves finding the area under graphs, initially by using...

### Stationary points

This resource is part of a collection of Nuffield Maths resources exploring Calculus. The demand is roughly equivalent to that in GCE A level.

This stationary points activity shows students how to use differentiation to find stationary points on the curves of polynomial functions. It includes the use of the...

### What's it worth?

This resource is part of a collection of Nuffield Maths resources exploring Calculus. The demand is roughly equivalent to that in GCE A level.

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.