ICSE Class 10 Constructions — Mock Test (2027)
Free online mock test for Constructions (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 Constructions 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.Draw an isosceles $\Delta ABC$ in which base $BC = 6\mathrm{cm}$ and the altitude from vertex to the base is 4 cm. To draw its inscribed circle, which step is required?
- A.Draw perpendicular bisectors of $AB$ and $AC$ to find the centre.
- B.Draw angle bisectors of $\angle B$ and $\angle C$ intersecting at $I$.
- C.Construct the circumcircle and use its centre for the incircle.
- D.Find the midpoint of $BC$ and use it as the centre of the incircle.
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2.Construct a ΔPMN, given that MN = 5 cm, PN = 7 cm, and ∠PMN = 90°. After constructing the triangle, an incircle is drawn. What is the radius of this incircle?
- A.1.0 cm
- B.1.5 cm
- C.2.0 cm
- D.2.5 cm
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3.In the given diagram
, a circle of radius 4.5 cm is drawn, and two tangents are drawn to this circle such that the angle between the tangents is 60°. Which of the following correctly describes the angle between the two radii at the centre of the circle?- A.60°
- B.120°
- C.90°
- D.180°
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4.Using ruler and compasses only, an equilateral triangle of height 6 cm is drawn, and its inscribed circle is constructed. What is the radius of this inscribed circle?
- A.1.5 cm
- B.2.0 cm
- C.2.5 cm
- D.3.0 cm
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5.In the diagram showing the construction of an inscribing circle for a given regular hexagon with each side 4.6 cm, which labelled point represents the incentre of the hexagon?
- A.The point where two adjacent sides meet (a vertex).
- B.The point where the perpendicular from the centre meets a side.
- C.The intersection point of the angle bisectors of two adjacent vertices.
- D.The midpoint of any side of the hexagon.
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