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.In the given diagram
, an equilateral triangle with side 5.6 cm is shown. Which labelled point represents the centre of the circle that can be inscribed within this triangle?- A.The point where two medians intersect
- B.The point where two angle bisectors intersect
- C.The point where two altitudes intersect
- D.The midpoint of any side of the triangle
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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 $\Delta PQR$, 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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4.Construct ΔABC with BC = 6.5 cm, AB = 5.5 cm, and AC = 5 cm. After constructing its incircle, what determines the radius of the incircle?
- A.The length of the longest side of the triangle.
- B.The area and semi-perimeter of the triangle.
- C.The sum of the angles of the triangle.
- D.The altitude from vertex A to side BC.
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5.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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