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.A point $Q$ is at the distance of 5 units from (3, 1). Equation of locus of point $D$ is:
- A.$x^{2} + y^{2} - 6x + 4y - 15 = 0$
- B.$x^{2} + 6x + 4y - 15 = 0$
- C.$x^{2} + y^{2} - 6x - 2y - 15 = 0$
- D.$x^{2} + y^{2} + 6x - 2y - 15 = 0$
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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.Given: PQ is perpendicular bisector of side AB of the triangle ABC.
Which labelled point in the diagram is equidistant from A and B?- A.Point P
- B.Point Q
- C.Point C
- D.Point A and B themselves
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4.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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5.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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