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 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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2.Draw a straight line AB of length 8 cm. What is the locus of all points equidistant from A and B, and how is it proven?
- A.A circle centered at the midpoint of AB
- B.The perpendicular bisector of AB, proven by congruence of triangles
- C.A line parallel to AB at its midpoint
- D.The angle bisector of ∠AOB, where O is the midpoint of AB
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3.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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4.Statement 1: The point which is equidistant from three non-collinear points $D, E$ and $F$ is the circumcentre of the $\Delta DEF$. Statement 2: The incentre of a triangle is the point where the bisector of the angles intersects. (a) Both the statements are true (b) Both the statements are false (c) Statement 1 is true and Statement 2 is false (d) Statement 1 is false and Statement 2 is true
- a.Both the statements are true
- b.Both the statements are false
- c.Statement 1 is true and Statement 2 is false
- d.Statement 1 is false and Statement 2 is true
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5.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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