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.On a graph paper, draw the line $x = 6$. Now, on the same graph paper, draw the locus of the point which moves in such a way that its distance from the given line is always equal to 3 units. What is the resulting locus?
- A.A single line $x = 3$ parallel to $x = 6$.
- B.The pair of lines $x = 3$ and $x = 9$, each 3 units from $x = 6$.
- C.A circle centered at $x = 6$ with radius 3 units.
- D.The lines $y = 3$ and $y = -3$ intersecting $x = 6$.
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2.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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3.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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4.A point $Q$ is always at the distance of 4 units from (3, 2). Equation of locus of a point $Q$, will be
- A.$x^{2} + y^{2} + 6x + 4y - 3 = 0$
- B.$x^{2} + y^{2} + 6x - 4y - 3 = 0$
- C.$x^{2} + y^{2} - 6x - 4y - 3 = 0$
- D.$x^{2} + y^{2} - 6x - 4y + 3 = 0$
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5.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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