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 ABC, given that AB = 4 cm, BC = 6 cm, and median AM = 3 cm. After constructing the triangle, a circle is circumscribed about it. Where is the centre of this circumcircle located?
- A.At the intersection of the perpendicular bisectors of AB and BC
- B.At the intersection of the perpendicular bisectors of AB and AC
- C.At the intersection of the medians of the triangle
- D.At the intersection of the angle bisectors of the triangle
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2.Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the circle. What is the length of one tangent?
- A.4.0 cm
- B.4.7 cm
- C.5.0 cm
- D.5.5 cm
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3.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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4.In the diagram
showing the construction of the circumscribing circle of triangle ABC, which labelled point represents the circumcentre of the triangle?- A.The point where two altitudes of the triangle intersect
- B.The point where the perpendicular bisectors of any two sides meet
- C.The midpoint of the longest side of the triangle
- D.The point where the angle bisectors of the triangle intersect
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5.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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