DfE statement G2 · Geometry and measures
Ruler and compass constructions and loci
Ruler and compass constructions and loci is content statement G2 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line." (statement G2). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Rubbing out the construction arcs. The arcs are the evidence that the construction was done with compasses, and marks are given for them.
- Changing the compass radius partway through a perpendicular bisector or an angle bisector.
- Bisecting an angle by measuring with a protractor and halving, when the question says 'construct'.
Sample questions (10 of 15)
Nearby statements
Questions people ask
Is ruler and compass constructions and loci on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for ruler and compass constructions and loci?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Rubbing out the construction arcs. The arcs are the evidence that the construction was done with compasses, and marks are given for them.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Geometry and measures at Foundation or at Higher.