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.Construct a triangle ABC, given that AB = 4 cm, BC = 6 cm, and median AM = 3 cm. After constructing the triangle, a circle is circumscribed about it. Where is the centre of this circumcircle located?
- A.At the intersection of the perpendicular bisectors of AB and BC
- B.At the intersection of the perpendicular bisectors of AB and AC
- C.At the intersection of the medians of the triangle
- D.At the intersection of the angle bisectors of the triangle
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2.Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the circle. What is the length of one tangent?
- A.4.0 cm
- B.4.7 cm
- C.5.0 cm
- D.5.5 cm
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3.In the diagram below, a regular hexagon of side 5.8 cm is shown with its inscribing circle. Which labelled part represents the radius of the inscribed circle?
- A.The line joining the centre to any vertex of the hexagon
- B.The perpendicular distance from the centre to any side of the hexagon
- C.The line segment connecting two adjacent vertices of the hexagon
- D.The angle bisector of any internal angle of the hexagon
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4.Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle as shown in the diagram. Which labelled part in the diagram represents the radius of the inscribed circle?
- A.The perpendicular distance from the incentre to any side of the triangle
- B.The distance from the incentre to any vertex of the triangle
- C.The length of the angle bisector from a vertex to the opposite side
- D.The distance between two sides of the triangle along a median
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5.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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