50 self-marking GCSE practice questions on Loci, written specifically for AQA, Pearson, OCR across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 50 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 11 markGrade 4-5
A guard dog is tied to a post at A and can reach 3 metres in any direction. It must also stay within 2 metres of the wall BC (marked on the diagram, with A 2 metres from BC). Which of the four options, A, B, C or D, correctly shows everywhere that the dog can go - the region that is inside both shapes at once?
What are the common mistakes in Loci?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Draws a locus region with flat square ends instead of rounding them into semicircular arcs
Draws a plain rectangle strip 2.5m wide with flat square ends instead of rounding the ends into semicircular arcs of radius 2.5m, selecting option A instead of option D.
Shades the union of two loci regions instead of their intersection
Shades everywhere within 2m of A OR within 1m of wall BC (the union of the two regions), selecting option B instead of the overlap shown in option A.
Uses the radius directly in a volume or area formula instead of squaring it
Computes π × 3 = 3π instead of π × 3² = 9π, using the radius 3 directly instead of squaring it in the circle-area formula.
Quick answers about Loci
How many Loci practice questions are there?
There are 50 self-marking GCSE Maths questions on Loci, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Loci?
No. You can start practising Loci straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Show the worked solution
"Within 3 metres of A" is the inside of a circle of radius 3 centred at A; "within 2 metres of BC" is a strip 2m wide alongside BC. The region inside BOTH shapes at once is their OVERLAP, shaded in option B. Option A wrongly shades the UNION (either region on its own, not both), option C shows only the wall-strip constraint, and option D shows only the circle constraint.
Question 21 markGrade 4-5
A CCTV camera is mounted at point P(3,−2) on the plan. Its motion sensor can detect movement up to 2 units away. Using the circle tool, draw the locus of points exactly 2 units from P - the points the sensor could detect movement.
On the practice page you draw or plot the answer on screen.
Show the worked solution
Every point exactly 2 units from P forms a circle centred at P with radius 2 - this is the definition of a locus a fixed distance from a point. Draw a circle centred at P(3,−2) with radius 2.
Question 32 marksGrade 4-5
Two wind turbines are at A(−2,1) and B(2,−1). A weather sensor must be installed equidistant from both wind turbines. Using only the circle and line tools, construct the locus of points that are the same distance from A and B.
On the practice page you draw or plot the answer on screen.
Question 41 markGrade 5-6
PQ is a straight footpath. Which of the four options, A, B, C or D, shows the locus of points exactly 2.5 metres from the footpath PQ?
Question 51 markGrade 6-7
A sprinkler is fixed at point A and waters everywhere within 2 metres. It must also stay within 1 metre of the boundary fence BC (marked on the diagram, with A 2 metres from BC). Which of the four options, A, B, C or D, correctly shows everywhere that gets watered - satisfying both conditions at once?
Question 63 marksGrade 6-7
XY is a straight runway. Which of the four options, A, B, C or D, shows the locus of points exactly 2 metres from the runway XY? Then state the radius of the two semicircular end-caps in your chosen locus.