4 ways to prepare for new A Level exam questions on Logarithms
Modelling like never before
( except on legacy MEI spec)
As one of the founders of MarkIt, I compose exam style questions from scratch to make worksheets that hug the specification requirements closely. For the last two weeks I have been working on Logarithms. This is a two part worksheet because as I’m sure you are aware, modelling has been injected into this chapter in a way that is perhaps the biggest jump in expectations when comparing across all other topics.
The crux of what’s new is the process of reducing an exponential model to one that is linear in order to more simply analyse data using a line of best fit (Admittedly this has always been part of the MEI spec). Algebraically, the process is straightforward and students will need to be desensitised to seeing logs within linear equations. It is an acquired taste but they will get there!
4 scenarios to prepare for
How will the exam boards frame an exam style question around this unique way of using Logs? And where will they seek ways to add curve balls to really test students’ understanding of the models involved? Reading through all the textbooks, specifications and specimen papers for all exam boards, here’s what I found.
1. Using a plot - purely numerical basics
This is the first layer of learning that students should master. Given a straight line plotted on a set of axes, will students be able to find the gradient and y intercept and relate it back to the exponential model underlying the problem. I found many such questions in the textbooks and they tend to be set at the intermediate level of difficulty.
Beyond just algebraic stuff
Mentioned explicitly in the specification, students will need to work within real life contexts to break down an exponential equation into a linear form. Along with the routine calculations to find key parameters, the questions can often come with twists and curve balls at the end. These will involve close inspection of the equations and looking at limits as variables get indefinitely large. This is where examiners will get creative and exam questions could baffle even the brightest.
2. Population growth models
More than half of the exam style exercises in the textbooks use population growth as the underlying context. They work well because they grow with time but also need to be realistic in the long term. So students should expect to take a critical eye when a model is proposed and ask - does this population behave realistically as time goes on to infinity?
3. Compound interest models
Another interesting context, not because of the idea of investments growing but because students will be introduced to the notion of continuously compounded interest and how this can be realistically modelled. At the root of this is understanding when and why the compound interest formula fails to be realistic. I encourage you to show students what happens when interest is compounded n times in a year and then ask - what happens if interest is compounded continuously and indefinitely?
4. Radioactive and drug concentration decay
These questions provide examiners perfect fodder to test a particular learning outcome : ‘Students must know that gradient is proportional to y, means an exponential model needs to be used’ because the notion of a half life of a drug or a radioactive element perfectly fits the idea of a rate of decay being proportional to the amount of substance there is at a given time. Give students the words and ask them to form the equations to really crystallise this idea.
Preview a MarkIt exam style question I wrote
Here’s a preview of a wonderfully unpredictable question that will be part of our upcoming MarkIt worksheet on exponential models. We ask students to have a look at the logistic model for population growth. We do not expect them to be biologists but they should be able to extend their knowledge of exponential functions to answer part (b).
Have a read, share with colleagues and tell us what you think!