Loci: JAMB Mathematics Questions, Answers & Notes

What Loci covers in the JAMB Mathematics syllabus

A locus is the path traced by a point moving under a fixed rule. The standard loci to know: a fixed distance from a point → a circle; equidistant from two points → the perpendicular bisector of the segment joining them; equidistant from two intersecting lines → the bisector of the angle between them; a fixed distance from a line → two parallel lines, one each side; equidistant from two parallel lines → a line midway between them. 'Less than' a distance gives a region (inside), while exactly that distance gives the boundary. These loci underpin geometric constructions done with compasses and a ruler.

For Loci, JAMB expects you to be able to:

• Identify standard loci (circle, perpendicular bisector, angle bisector, parallel lines)
• Describe the locus of a moving point under given conditions
• Relate loci to geometric constructions

Key facts & revision notes: Loci

These are the recurring points our Loci questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• A constant distance from a fixed point traces out a circle (centre = the fixed point).
• Points equidistant from two fixed points lie on the perpendicular bisector of the segment joining them.
• Points equidistant from two intersecting lines lie on the bisector of the angle between them.
• A constant distance from a line gives two lines, one on each side, parallel to it.
• The radius of the circle equals the fixed distance, 5 cm.
• The point equidistant from all three vertices is the circumcentre (centre of the circumscribed circle).
• Equal chords are equidistant from the centre, so their midpoints form a smaller concentric circle.
• Two adjacent walls meet at a corner; equidistance from both gives the angle bisector.
• A perpendicular bisector meets the segment at its midpoint at 90°.
• The rope keeps the goat within 3 m of the peg, tracing a circle of radius 3 m.
• Halfway between two parallel lines lies a third line parallel to both.
• Equal arcs from both A and B intersect above and below; joining the intersections gives the bisector.
• The bisector splits 90° into two equal parts of 45° each.
• The centre stays a fixed distance (the radius) above the line, tracing a parallel straight line.
• 'Less than 4 cm from O' is the region inside the circle of radius 4 cm (not on it).
• Angle bisectors of a triangle meet at the incentre (equidistant from the sides).
• Outside and 2 cm away means radius 5 + 2 = 7 cm (concentric).
• There are two positions (one each side) at that distance, giving two parallel lines.
• Compasses (for arcs/equal distances) and a ruler (for straight lines) are essential for loci constructions.
• Equidistance from a point (focus) and a line (directrix) defines a parabola.
• Points a fixed distance from one point form a circle.
• Equidistance from two points gives the perpendicular bisector.
• Equidistance from two intersecting lines gives the angle bisector.
• The reachable boundary is a circle of radius 5 m about the post.

Worked examples

Three Loci questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Loci is tested in JAMB Mathematics

Our Loci bank holds 40 questions (11 easy, 19 medium, 10 hard). JAMB Mathematics typically returns to Loci year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Loci questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Loci. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Loci is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Loci

The errors that cost marks on Loci are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Loci actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Loci part of the JAMB Mathematics syllabus?

Yes. Loci is a recognised topic in the JAMB Mathematics syllabus, covering identify standard loci (circle, perpendicular bisector, angle bisector, parallel lines). You should be able to recall its key facts and apply them to multiple-choice questions.

How many Loci questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Loci questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Loci?

A locus is the path traced by a point moving under a fixed rule. The standard loci to know: a fixed distance from a point → a circle; equidistant from two points → the perpendicular bisector of the segment joining them; equidistant from two intersecting lines → the bisector of the angle between them…

How do I answer Loci questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Loci. Practising timed Loci questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Loci questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Loci questions free without signing up?

Right here — tap “Start Loci practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.