Level 3 FSMQ: Additional Maths – enriching GCSE trigonometry
28 May 2024
Steven Walker, Maths Subject Advisor
Continuing my series of FSMQ blogs, I turn my attention to the Pythagoras’ theorem and trigonometry section of the FSMQ, the depth of study and teaching ideas.
The FSMQ is designed as both an GCSE enrichment course and an acceleration programme to introduce students to aspects of post-16 maths study.
Any angle
GCSE focuses only on the angles 0 ≤ θ < 90, with only a small section on obtuse angle triangles and a brief look at the graphs of trigonometric functions. The FSMQ extends this to look at the full 360 rotation. The content covers the ambiguous sine rule case which allows students to understand the criteria for identifying congruent triangles (especially why the angle must be included between two given sides) more fully (see this example drawn on Geogebra).
Trig identities
GCSE (9–1) Maths briefly covers the idea of finding, for example, sin x given the value of cos x, and this link between Pythagoras and trigonometry can be explored in more depth by looking explicitly at the relationship between tan x, sin x and cos x and the relationship between sin2 x and cos2 x. A brief guide is available on BBC Bitesize and there are extra questions on trigonometry equations on mathcentre. Questions on this topic also encourage students’ development of algebraic manipulation and the use of surds.
Modelling the real world
The GCSE (9–1) work on bearings is assumed knowledge and the new knowledge of angles in a full rotation allow Ferris wheel and tidal type problems to name but two that go beyond GCSE. In fact, many of the problems seen in the FSMQ (and AS Maths) would make great extension problems for GCSE: too long for a GCSE exam question, but perfect for a homework task.
Teaching ideas
Constructing triangles and checking that the measurements match the calculated values is a good starting point. This could be turned into a quiz, with students challenging each other with different triangles.
Graphing functions using software is a good way to investigate a large variety of equations. You may find it easier to plot graphs using radians since relationships are easy to spot, although radians as a topic is beyond the FSMQ specification requirements.
The opportunity to make a clinometer and investigate the heights of trees and building around the school is always popular with students. The use of magnetic compasses allows students to use bearings for real and combining the two activities allows students to create their own 3D trigonometry questions.
There are a number of great websites with ideas on teaching trigonometry.
OCR support
In addition to the past papers, you will also find two practice papers on our secure teacher site, Teach Cambridge (login required, talk to your exams officer about access).
The Pythagoras’ theorem and trigonometry delivery guide has some teaching ideas and links to third party resources.
The Pythagoras’ theorem and trigonometry Check In test has been updated with extra questions, with fully worked solutions.
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 resource 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 (formerly Twitter) @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 travel.
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