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 PQR, given PQ = 5 cm, QR = 6.5 cm, and ∠PQR = 120°. After constructing the triangle, a circumcircle is drawn. Where is the centre of this circumcircle located?
- A.At the intersection of the perpendicular bisectors of PQ and PR
- B.At the intersection of the perpendicular bisectors of PQ and QR
- C.At the intersection of the angle bisectors of the triangle
- D.At the midpoint of side PR
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2.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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3.Draw a circle of radius 2.5 cm. Mark a point P at a distance of 6.5 cm from the centre O of the circle. Using ruler and compass, draw two tangents to the circle from P and measure the length of each tangent. What is the length of each tangent?
- A.4.0 cm
- B.5.0 cm
- C.6.0 cm
- D.7.0 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.Construct a $\Delta PQR$, given $PQ = 5$ cm, $QR = 7$ cm and $\angle PQR = 60^\circ$. To inscribe a circle in the triangle, which step is required?
- A.Draw perpendicular bisectors of $PQ$ and $QR$ to find the centre.
- B.Draw angle bisectors of $\angle Q$ and $\angle R$ intersecting at $I$.
- C.Construct the circumcircle and use its centre for the incircle.
- D.Find the midpoint of $PR$ and use it as the centre of the incircle.
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