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 rhombus PQRS with diagonals PR = 8 cm and QS = 6 cm. By construction, locate point X equidistant from sides PQ and PS, and also equidistant from vertices R and S. What is the length of XR?
- A.2.5 cm
- B.3.2 cm
- C.4.0 cm
- D.5.0 cm
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2.Construct an isosceles triangle ABC with AB = 6 cm and BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Points Q and R are 5 cm from P and also 5 cm from the line AB. Where are Q and R located?
- A.On the angle bisector of ∠C, 5 cm from P.
- B.On a circle centered at P with radius 5 cm.
- C.On a line parallel to AB, 5 cm away from AB, and 5 cm from P.
- D.On the perpendicular bisector of AB, 5 cm from P.
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3.Draw an angle ABC = 75°. The locus of all the points equidistant from AB and BC is:
- A.A circle centered at B with radius equal to the length of AB
- B.The angle bisector of ∠ABC
- C.A line parallel to AB passing through point C
- D.The perpendicular bisector of segment AC
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4.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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5.Which of the following statement is correct:
- A.A point $Q$ moving in a plane about a fixed line as on are with same centre.
- B.A moving point $Q$ in a plane about another point in such a way that its distance is constant.
- C.A point equidistant from two fixed non-parallel $AB$ and $CD$ in the same plane.
- D.A point $Q$ moving in a plane about another point in such a way that its distance from a fixed line $AB$ is constant.
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