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.Construct a triangle ABC, in which AB = 4·2 cm, BC = 6·3 cm and AC = 5 cm. Draw the perpendicular bisector of BC which meets AC at point D. Why is D equidistant from B and C?
- A.D lies on the perpendicular bisector of BC, so it is equidistant from B and C.
- B.D divides AC into two equal parts, making it equidistant from B and C.
- C.D is the midpoint of BC, so it must be equidistant from B and C.
- D.D is closer to C because AC is shorter than AB, making distances unequal.
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2.The locus of vertices of all isosceles triangles having a common base will be the ... of the common base of the triangles:
- A.Perpendicular
- B.Perpendicular Bisector
- C.Bisector
- D.None of the above
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3.Given: CP is the bisector of angle C of Δ ABC.
Which property explains why point P is equidistant from sides AC and BC?- A.P lies on the angle bisector of ∠C, so it is equidistant from AC and BC.
- B.P is the midpoint of side AB, making it equidistant from AC and BC.
- C.P divides CP in the ratio of the adjacent sides, so distances are equal.
- D.P lies on the perpendicular bisector of AB, ensuring equal distances.
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4.In the figure given below, which labelled point on CD is equidistant from points A and B?
- A.The point where CD intersects the line joining A and B
- B.The midpoint of CD
- C.The intersection of CD with the perpendicular bisector of AB
- D.The point on CD closest to the midpoint of AB
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5.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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