**Steven Walker, Maths Subject Advisor**

Continuing my series of FSMQ focused blogs I take a closer look at the coordinate geometry section, share the rationale for its inclusion and offer some links to examples and ideas to support your teaching.

The FSMQ is designed as both a GCSE enrichment course and an acceleration programme to introduce students to A Level study. The section on coordinate geometry is all about going into a bit more depth with the graphing content of the GCSE (9–1) Maths specification.

### Investigating a line segment

Finding the distance and mid-point between two points defined on a coordinate grid allows students to apply standard GCSE skills in a new context. It also allows students to start linking the work they have previously done on paper to a more screen based environment. For example, try out this Line segment challenge on Desmos.

### General equation of a circle

The GCSE (9–1) Maths only covers the equation of a circle about the origin, so this enrichment item generalises that work for any centre point on the cartesian grid. In class this should allow students to make links between their compasses and ruler constructions and defined equations on graph paper. For example, try out this Equation of a circle demonstration on Geogebra.

### Tangents and normals

The GCSE (9–1) Maths covers gradients and equations of parallel and perpendicular lines, and the estimation of tangents to curves. The introduction to calculus in the FSMQ course allows students to investigate features of a wider range of graphs. Linked to the general equation of a circle, students can investigate some of their circle theorems in more depth as well. You’ll find a selection of general circle theorem resources from Geogebra to try out.

### Linear programming

The GCSE (9–1) Maths introduces the idea of inequalities but the progression to inequalities with two variables allows more problem solving that links algebra and graphs to word problems in a way that is less abstract. Always important to discuss “Shading in” or “Shading out”, especially when using graphing technology. Use the shading in or shading out demonstration, and discuss the benefits of each approach with your students.

### Teaching ideas

Constructing circles with tangents and normals on graph paper can help students link their work on equations with circle theorems. Introducing the use of graphing software may make this an interesting flipped learning activity, especially for those students with an interest in art and technology. Resources such as this Circle patterns activity on Desmos and Soddy circles on Geogebra are useful.

Students could use their new calculus skills (or use calculator technology) to calculate exact values for GCSE (9-1) Maths questions (make use of ExamBuilder, searching for Gradients and Areas in the Interpreting graphs from the J560 GCSE section) that request an estimation of the gradient of a defined curve, and then calculate the exact equation for the tangent and exact coordinates for points on that line.

Linear programming is not included in the current GCSE (9–1) Maths, but it has been assessed at this level many times in the past. It was also included in many D1 (AS unit for GCE Maths) courses prior to reform so there are quite a few old textbooks with good notes and exercises available. For a good introduction, the Discrete Maths Unit 3 Linear programming resources, by CIMT and produced for Core Maths, looks useful, although the final chapter on the simplex method does go beyond the FSMQ course.

### OCR support

In addition to the past papers, you will find two practice papers on Teach Cambridge (login required, talk with your Exams Officer).

Also available are the following teaching resources:

- The Coordinate geometry delivery guide has some teaching ideas, and links to third party resources.
- The Coordinate geometry ‘check In test’ has been updated, there are 15 questions with fully worked solutions.

Don’t forget to join us for the termly FSMQ Teacher Network and look out for our professional development events throughout the academic year.

### Stay connected

Share your ideas and links in the comment box below. For some interesting maths puzzles, see our weekly #OCRMathspuzzle each Friday.

If you have any queries or questions, 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.

#### Related blogs by the same author

- Level 3 FSMQ: Additional Maths – introducing the enumeration section
- FSMQ: developing confidence with algebra
- Level 3 FSMQ: Additional Maths (6993) - an enrichment of the GCSE curriculum
- Level 3 FSMQ: Additional Mathematics – formulae sheets and support for the summer exam
- Studying Level 3 FSMQ: Additional Maths at home