Hints and Tips - 5 minute read
Steven Walker, OCR Maths Subject Advisor
In this blog I will look at a range of resources available for studying the FSMQ in Additional Mathematics. This qualification sits neatly between GCSE and A Level and many of the resources identified in my previous blogs for GCSE and A Level Maths are also relevant.
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 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 the ‘Planning and teaching’ tab. Past papers with mark schemes and Examiner’ reports are on the ‘Assessment’ tab.
If you don’t have access to an electronic copy of your class textbook there’s plenty of online support:
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.
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.
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.
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.
Graphing technology, such as this Desmos circle equation graph can help with visualisation.
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.
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.
Although some students may memorise the ‘suvat’ equations, this is not required, but is not prohibited when answering questions in the FSMQ exam.
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.
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.
There are a lot of puzzles on the @OCR_Maths Twitter account - search the #OCRMathsPuzzle hashtag. Students can use these to review the fundamentals or general exploration.
@OCRMaths puzzle 8/12/2017
This puzzle could be solved numerically by trial and improvement, but the enrichment challenge would be to prove algebraically that the biggest total has been found.
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.
We regularly post links to a variety of online resources, so do follow us on Twitter @OCR_Maths.
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 email@example.com, call us on 01223 553998 or Tweet us @OCR_Maths. You can also sign up to subject updates and receive information about resources and support.
Steven joined OCR in 2014 and has worked on the redevelopment of OCR’s Entry Level, GCSE (9-1), FSMQ and A Level Mathematics qualifications. He now focuses mainly on supporting the Level 3 qualifications. Steven originally studied engineering before completing a PGCE in secondary mathematics. He is currently balancing his ‘work from home’ commitments with supporting his young daughter with reception year activities.