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.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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3.In the given diagram,, a circle of diameter 9 cm is drawn, and a point P is marked at a distance of 7.5 cm from the centre O of the circle. Tangents PA and PB are drawn from P to the circle. Which labelled segment correctly represents the length of each tangent?
- A.OA = 4.5 cm
- B.OP = 7.5 cm
- C.PA = 6 cm
- D.AB = 9 cm
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4.Construct a regular hexagon of side $3.5$ cm. To construct its circumcircle, which of the following is the correct method?
- A.Draw perpendicular bisectors of two adjacent sides to find the centre.
- B.Use the intersection of diagonals as the centre of the circumcircle.
- C.Construct the incircle first and use its centre for the circumcircle.
- D.Find the midpoint of one side and use it as the centre.
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5.Without calculating base angles, construct an isosceles ΔPQR with base QR = 6 cm and ∠P = 75°. To draw its circumcircle, where should the centre of the circumcircle lie?
- A.At the intersection of the medians of the triangle.
- B.On the perpendicular bisector of the base QR.
- C.At the vertex P of the triangle.
- D.At the intersection of the angle bisectors of the triangle.
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