Studying Level 3 FSMQ: Additional Maths at home
19 August 2024
Steven Walker, Maths Subject Advisor
This blog was originally published in June 2020 and has been updated to include the latest information and links to additional support material.
In this blog I will look at a range of resources available for studying the FSMQ in Additional Mathematics.
What is Level 3 FSMQ: Additional Mathematics?
This course is designed to be studied alongside the GCSE as an enrichment course. It is not a prerequisite for studying A Level Maths or Further Maths, although it might offer a head start as the content is explored further at A Level. We recommend it for students with a love of the subject who are seeking a challenge but aren’t under time pressures with their other studies.
The qualification may also be appropriate for post-16 students that need an introduction to topics such as calculus and logarithms but do not have space in their timetable for AS Maths or Core Maths.
There is a deliberate focus on modelling across the course, linking the abstract mathematical techniques to real world contexts that upper secondary students will recognise.
Our maths support
The specification is a good starting point and the GCSE mapping document highlights where the course supports and reinforces GCSE study.
We have a set of delivery guides, with links to free resources, and check in tests for each section of the specification. You’ll find these on Teach Cambridge, our secure platform for teachers, along with past papers, practice papers and the specimen paper.
Learning without a textbook
OCR sponsorship means that centres offering the FSMQ can register to set up teacher and students’ accounts on the Integral platform.
For more information and to sign up for access see the MEI website.
You may find the following websites useful:
It is worth mentioning here that candidates are never penalised for using alternative, or more advanced, techniques unless the question explicitly asks for a specific technique to be used.
This means that any of the efficient techniques that you pick up from A Level resources can be used to answer questions in the FSMQ, and, perhaps more importantly, the additional techniques learnt for the FSMQ can be used to answer GCSE questions.
If you find you are struggling with a particular topic, it may be worth referring back to the content covered at GCSE. See my previous blog on studying GCSE (9 – 1) Maths at home.
The OCR-endorsed textbook is published by Hodder, who also publish a range of revision and practice material.
Use of technology
Online graphing calculators, such as Desmos and GeoGebra offer an interactive resource for investigating curves. For a few ideas on Desmos, see this activity list, which is reviewed and updated regularly.
Algebra section
The video Dividing polynomials using the box method shows a nice alternative method for polynomial division. The factor theorem can be used to determine how the denominator was identified as the factor in the first place.
See my blog on developing confidence with algebra for more information on this section.
Enumeration section
The counting and probability introduction section on the Interactive Mathematics website nicely bridges content from GCSE to FSMQ and continues into the statistics content of A Level Maths.
See my introducing the enumeration section blog for more information.
Coordinate geometry section
Graphing technology, such as this Desmos circle equation graph can help with visualisation.
See my blog on introducing coordinate geometry for more information.
Pythagoras’ theorem and trigonometry section
Graphing technology, such as this Geogebra sine example, cleverly illustrates transformations of graphs. Modelling problems may involve more challenging geometrical contexts and could use bearings or be set in 3 dimensions.
See my enriching GCSE trigonometry blog for more information.
Calculus section
This section expands on the GCSE requirement to estimate gradients and areas under a curve with an initial introduction to the more formal analytical techniques. Graphing technology, such as this Desmos integration example, can animate these new concepts.
Kinematics has been included in this section to provide a concrete example of these calculus techniques and to allow students to investigate the difference between constant acceleration and variable acceleration models.
The ‘suvat’ equations have been given on the formulae sheet, but the intention was for students to investigate these situations in terms of the algebraic functions and graphs.
See my blog on introducing calculus alongside GCSE Maths blog for more information.
Numerical methods section
For GCSE mathematics, students only need an informal understanding of estimating solutions to equations, gradients and areas under a graph. The FSMQ introduces more formal approaches for calculating these approximations. Spreadsheets are useful tools for numerical method investigations.
See my using numerical methods to solve complex problems blog for more information.
Exponential and logarithms section
This section builds on the laws of indices and includes more abstract equation solving problems where the exponent is the unknown. For an introduction to this topic see the notes on purplemath.
See my from indices to logarithms blog for more information.
Short activities and puzzles
There are a lot of puzzles on the @OCR_Maths X (formerly Twitter) account: search the #OCRMathsPuzzle hashtag. Students can use these to review the fundamentals or general exploration.
Other sites with great short puzzles and activities include NRICH, Underground Maths and TES. The Intermediate Mathematical Challenge from the UKMT provides a range of thought provoking problems.
Stay connected
There are so many great online resources available, so join the conversation by sharing your ideas and links in the comment box below.
If you have any queries or questions, you can email us at maths@ocr.org.uk, call us on 01223 553998 or message us @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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