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.Using ruler and compass, construct a $\Delta ABC$ where $AB = 3\mathrm{cm}$, $BC = 4\mathrm{cm}$ and $\angle ABC = 90^{\circ}$. What is the radius of the circle circumscribing $\Delta ABC$?
- A.$2$ cm
- B.$2.5$ cm
- C.$3$ cm
- D.$5$ cm
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3.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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4.Using ruler and compass, a triangle ABC is constructed with AB = 6 cm, ∠BAC = 120°, and AC = 5 cm. A circle is then drawn passing through points A, B, and C. What is the approximate radius of this circle?
- A.4.2 cm
- B.5.3 cm
- C.6.0 cm
- D.7.1 cm
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5.Using a ruler and compass only, construct a ΔABC such that AB = 5 cm, ∠ABC = 75°, and the radius of the circumcircle of ΔABC is 3.5 cm. On the same diagram, construct a circle touching AB at its midpoint and also touching side AC. Where is the centre of this second circle located?
- A.At the intersection of the perpendicular bisector of AB and the angle bisector of ∠CAB
- B.At the intersection of the medians of the triangle
- C.At the midpoint of side AC
- D.At the intersection of the perpendicular bisectors of AB and BC
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