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 ΔPQR with QR = 5 cm, ∠PQR = 60°, and the perpendicular from P to QR equal to 3 cm. Then draw its incircle. Which step correctly locates the incentre of ΔPQR?
- A.The intersection of the perpendicular bisectors of any two sides.
- B.The intersection of the angle bisectors of ∠Q and ∠R.
- C.The midpoint of the altitude from P to QR.
- D.The point where the medians of the triangle meet.
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2.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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3.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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4.Construct a triangle ABC with AB = 6 cm, BC = 8 cm, and median AM = 5 cm. Then construct the incircle of triangle ABC and measure its radius. What is the radius of the incircle?
- A.1.5 cm
- B.2.0 cm
- C.2.5 cm
- D.3.0 cm
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5.Draw a line segment OP of length 6 cm. From point O, draw a circle of radius 3.5 cm. Construct tangents PQ and PR to the circle from P. Which step ensures PQ and PR are equal in length and perpendicular to the radii at Q and R?
- A.Drawing a circle with OP as diameter and finding its intersection with the given circle.
- B.Drawing perpendiculars from P to the radii of the circle.
- C.Bisecting the angle formed at P by the tangents.
- D.Constructing the perpendicular bisector of OP and using its midpoint as centre.
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