Level 3 FSMQ: Additional Maths – from indices to logarithms
03 July 2024
Steven Walker, Maths Subject Advisor
To finish my series of seven FSMQ blogs, I will look at the exponentials and logarithms section of the FSMQ, the rationale for its inclusion and discuss teaching ideas.
Introducing logarithms within KS4 is a clear acceleration into A Level Maths. However, it will support students’ understanding of the application of logarithmic scales across the KS4 curriculum, especially for those looking at post-16 qualifications in subjects such as biology, chemistry, geography or economics.
Laws of logarithms
Students will be familiar with the laws of indices from the GCSE (9–1) Maths course. The FSMQ builds upon this to cover the laws of logarithms. Students may like to read up on John Napier (Napier’s bones) and the development of logarithms to support the industrial, exploration and scientific developments of the early 17th century.
The exponential function
GCSE Maths includes plotting and sketching exponential functions. The FSMQ introduces students to the use of logarithms to reduce a function to a linear form to investigate, for example, experimental data. Students may find it interesting to learn more about the use of logarithms across their academic curriculum, including the Richter scale, decibels, and the pH scale (for an example maths resource: Mathematical Modelling).
Solving equations
The GCSE Maths course covers solving linear and quadratic equations analytically and solving other equations with less formal trial and improvement methods. The inclusion of logarithms allows students that have studied the FSMQ to solve more complex equations, especially those involving exponential growth or decay (for some example calculations: Exponential Growth).
Teaching ideas
Graphing technology is useful to highlight the link between an exponential function and its linear form using logarithms (for example Reduction to linear).
There is a suitable selection of free resources on the TES platform, for example Logarithms Codebreakers.
AS/A Level resources are generally appropriate for FSMQ, for example the Log worksheets and revision pack by Susan Whitehouse. The FSMQ will focus on base 10 but covers any positive integer base. There would be no harm in letting students work with the natural logarithm, but this will not be required for the exam.
The Topical Applications of Mathematics section on the Centre for Innovation in Mathematics Teaching (CIMT) resource pages includes an interesting look at real world uses of logarithms, including the Earthquakes material.
Risp 31 Building log equations by Jonny Griffiths could be used in the FSMQ classroom and returned to during A Level Maths and Further Maths lessons to support progression though the courses.
To log or not to log on the Underground Mathematics platform is a useful interactive diagnostic check that students fully understand the types of equations that can and cannot be solved using logarithms.
Nrich also have a collection of resources that can be found searching by logarithms.
OCR support
In addition to the past papers, you will also find two practice papers on Teach Cambridge.
The Exponentials and logarithms delivery guide outlines some of the common misconceptions and has some teaching ideas with links to third party resources.
The Exponentials and logarithms check in test has been updated, providing a 15-question worksheet, with fully worked solutions.
OCR sponsorship allows your centre free subscription to FSMQ resources hosted on the MEI learning platform for teachers and students.
Don’t forget to join us for the termly FSMQ teacher network and look out for professional development events throughout the academic year.
Stay connected
Share your ideas and links in the comment box below.
If you have any queries, you can email us at maths@ocr.org.uk, call us on 01223 553998 or message us on X @OCR_Maths. You can also sign up to subject updates and receive information about resources and support.
About the author
Steven originally studied engineering before completing a PGCE in secondary mathematics. He has taught secondary maths in England and overseas. Steven joined OCR in 2014 and worked on the redevelopment of OCR’s FSMQ and the A Level Mathematics suite of qualifications. Away from the office he enjoys cooking and to travel.
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