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 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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2.Construct a triangle ABC in which angle ABC = 75°, AB = 5 cm and BC = 6·4 cm. Draw the perpendicular bisector of side BC and also the bisector of angle ACB. If these bisectors intersect each other at point P, which of the following statements correctly describes the position of point P?
- A.P is equidistant from B and C but not necessarily from AC and BC.
- B.P is equidistant from AC and BC but not necessarily from B and C.
- C.P is equidistant from B and C, and also from AC and BC.
- D.P lies on the perpendicular bisector of AB and the angle bisector of ∠ABC.
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3.A point $P$ moves 3 units below the $x$-axis at a constant distance. The locus of point $P$ is:
- A.$y = 3$
- B.$x = -3$
- C.$x = 3$
- D.$y = -3$
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4.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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5.Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. After measuring ∠ABC and finding the point R on AD such that RB = RC, what is the length of AR?
- A.1.0 cm
- B.1.2 cm
- C.1.5 cm
- D.2.0 cm
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