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 $\Delta PQR$, 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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2.Construct a triangle $DEF$, with $DE = 6$ cm, $\angle FDE = 60^\circ$ and $\angle FED = 45^\circ$. To circumscribe a circle about the triangle, which of the following steps is essential?
- A.Draw the angle bisector of $\angle DFE$ to find the centre.
- B.Draw perpendicular bisectors of $DE$ and $EF$ intersecting at $O$.
- C.Construct the incircle with centre at the intersection of medians.
- D.Join $F$ to the midpoint of $DE$ and use that point as the centre.
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3.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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4.In $\Delta ABC, AB = 5\mathrm{cm}, BC = 6.5\mathrm{cm}$ and $CA = 4.8$ cm. To draw the circumcircle of $\Delta ABC$, which step is necessary?
- A.Draw the angle bisector of $\angle BAC$ to locate the centre.
- B.Draw perpendicular bisectors of $AC$ and $BC$ 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 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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