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 cm, ∠PQR = 45°, and PQ - PR = 1.8 cm. A point O inside the triangle is equidistant from PQ, QR, and PR. Which construction step identifies point O?
- A.Intersection of the perpendicular bisectors of PQ and QR
- B.Intersection of the angle bisectors of ∠Q and ∠R
- C.Intersection of the medians of Δ PQR
- D.Intersection of the altitudes of Δ PQR
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3.Construct a triangle ABC with BC = 8 cm, AB = 7 cm, and ∠ABC = 60°. A point P inside the triangle is equidistant from BA and BC and also equidistant from B and C. What is the length of PB?
- A.3.5 cm
- B.4.0 cm
- C.4.6 cm
- D.5.0 cm
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4.A circle with centre O and radius $r$ cm is the locus of a point which moves in a plane in such a way that its distance from the fixed point O is always equal to $r$ cm. What does the concept of locus represent in this context?
- A.The locus is the fixed point O itself, as it remains stationary while the point moves.
- B.The locus is the path traced by the moving point, which forms a circle since every point on it is at a constant distance $r$ cm from O.
- C.The locus is the radius $r$ cm, as it defines the distance from O to the moving point.
- D.The locus is the set of all possible distances from O, varying continuously as the point moves.
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5.O is a fixed point. Point P moves along a fixed line AB. Q is a point on OP produced such that OP = PQ. What is the locus of point Q?
- A.A line parallel to AB and twice as far from O as AB is
- B.A circle centered at O with radius equal to the distance from O to AB
- C.A line perpendicular to AB passing through O
- D.A line identical to AB but shifted closer to O
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