Exponential and logarithmic graphs (new A level maths)

This resource is designed to introduce the key properties of exponential and logarithmic graphs that students need to understand for the topic of exponential models. Explaining the key properties of exponential graphs to students who haven’t learned chain rule is tricky so this printable/projectable resource may be a good way to help improve your students’ understanding and save you time as it has examples and exercises already prepared.

It begins with learning the shape of exponential graphs by plotting points, drawing the curves and then summarising the properties of each graph (first y=a^x and then y=a x b^x). There is then a short exercise (23 questions) where they practice sketching exponential graphs and determining the equation of a given graph.

The next section involves sketching the gradient function for different types of graph (linear, quadratic, cubic and reciprocal) and this work leads towards the idea that the gradient function of an exponential graph is itself exponential.

To build on this the students are then given the result for the gradient of y=a^x. The exercise that follows allows them to establish by themselves that for dy/dx=y we require that a = e.

Students can then prove (without use of chain rule) that the gradient of y=e^(kx) is y=ke^(kx), a key property of exponential models. There are then some examples and an exercise for students to practise using this result.

The final section gets students to plot the graph of y=ln(x) and summarise its properties. Some examples and an exercise of questions connected the graph of y=ln(x) then follow.

Answers to all the exercises are included.

Here is an example of one of my A level resources that is freely available:

https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186