ICSE Class 10 Locus — Mock Test (2027)
Free online mock test for Locus (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Locus chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.The locus of a point $P$ in space which is always at a distance of $5\mathrm{cm}$ from a fixed point will be the:
- A.Sphere
- B.Centre of circle
- C.Centre of sphere
- D.None of the above
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2.Draw a Δ PQR such that QR = 7.5 cm, ∠PQR = 60°, and altitude PN = 4 cm. Inside the triangle, a point A is equidistant from PR and QR and also equidistant from P and R. Which construction step identifies point A?
- A.Intersection of the angle bisector of ∠P and the perpendicular bisector of QR
- B.Intersection of the angle bisector of ∠R and the perpendicular bisector of PR
- C.Intersection of the medians of Δ PQR
- D.Intersection of the altitudes of Δ PQR
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3.Locus of a point whose distance from origin is always equal to is:
- A.$a^2 + b^2 = 2$
- B.$a^2 - b^2 = 4$
- C.$a^2 + b^2 = 4$
- D.$a^2 - b^2 = 2$
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4.Draw a straight line AB of length 8 cm. What is the locus of all points equidistant from A and B, and how is it proven?
- A.A circle centered at the midpoint of AB
- B.The perpendicular bisector of AB, proven by congruence of triangles
- C.A line parallel to AB at its midpoint
- D.The angle bisector of ∠AOB, where O is the midpoint of AB
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5.A point $P$ moves two units above the $x$-axis at a constant distance. The locus of point $P$ is:
- A.$x = 2$
- B.$y = -2$
- C.$y = 2$
- D.$x = -2$
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