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.In the given diagram
, a circle of radius 5 cm is drawn, and two tangents are drawn to this circle such that the angle between the tangents is 45°. Which of the following correctly describes the angle between the two radii drawn to the points of tangency?- A.45°
- B.90°
- C.135°
- D.180°
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2.Using ruler and compass only, draw a circle of radius 4 cm with centre O. Mark a point P outside the circle at a distance of 7 cm from O. Construct two tangents to the circle from P and measure the length of any one tangent. What is the length of one tangent?
- A.4.9 cm
- B.5.7 cm
- C.6.3 cm
- D.7.0 cm
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3.Using ruler and compasses only, the diagram below shows an equilateral triangle of side 4.5 cm with its circumscribed circle drawn. Which labelled part in the diagram represents the radius of the circumscribed circle?
- A.The line from a vertex to the midpoint of the opposite side
- B.The perpendicular bisector of a side of the triangle
- C.The line from the centre of the circle to any vertex of the triangle
- D.The line joining the midpoints of two sides of the triangle
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4.Construct $\Delta ABC, BC = 6\mathrm{cm}, \angle ABC = 45^{\circ}$ and perpendicular from $A$ to $BC$ is $3.5\mathrm{cm}$. To construct its circumcircle, which step is necessary?
- A.Draw the angle bisector of $\angle BAC$ to locate the centre.
- B.Draw perpendicular bisectors of $BC$ and $CA$ intersecting at $O$.
- C.Construct the incircle and use its radius for the circumcircle.
- D.Find the midpoint of $AB$ and use it as the centre of the circumcircle.
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5.Construct a triangle with sides 5 cm, 4 cm, and 3 cm. Draw its circumcircle and measure its radius. What is the radius of the circumcircle?
- A.2.0 cm
- B.2.5 cm
- C.3.0 cm
- D.3.5 cm
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