Coordinate Geometry — A-Level Mathematics Revision

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What is Coordinate Geometry?

Coordinate geometry at A-Level involves the study of geometric shapes and figures using coordinates. It builds on GCSE concepts by introducing more complex ideas such as the equations of circles, the properties of tangents and normals, and the use of parametric equations to describe curves.

Board notes: All major A-Level Maths boards (AQA, Edexcel, OCR) cover coordinate geometry in depth, including circles and parametric equations. The level of complexity of the problems can vary slightly between boards.

Worked example

Common mistakes

• 1Confusing the formulae for the gradient and the length of a line segment. The gradient is the change in y divided by the change in x, while the length is found using Pythagoras' theorem.
• 2Making errors when finding the equation of a line, particularly with the use of the formula y - y1 = m(x - x1).
• 3Incorrectly identifying the centre and radius of a circle from its equation, especially when the equation is not in the standard (x-a)² + (y-b)² = r² form.

Coordinate Geometry exam questions

Exam-style questions for Coordinate Geometry with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.

Frequently asked questions

• How do I find the point of intersection of two lines?

  To find the point of intersection of two lines, you need to solve their equations simultaneously. This can be done by substitution or elimination.

• What is a normal to a curve?

  A normal to a curve at a particular point is a line that is perpendicular to the tangent at that same point. The gradient of the normal is the negative reciprocal of the gradient of the tangent.