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.

Sample questions

1. 1.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.
2. 2.In the diagram below, a regular hexagon with side 5 cm is shown. Which labelled part represents the radius of the circumscribed circle around the hexagon?
   • A.The perpendicular bisector of a side of the hexagon
   • B.The line segment from the center to a vertex of the hexagon
   • C.The side length of the hexagon (5 cm)
   • D.The line joining the midpoints of two opposite sides
3. 3.In the diagram showing the construction of an inscribing circle for a given regular hexagon with each side 4.6 cm, which labelled point represents the incentre of the hexagon?
   • A.The point where two adjacent sides meet (a vertex).
   • B.The point where the perpendicular from the centre meets a side.
   • C.The intersection point of the angle bisectors of two adjacent vertices.
   • D.The midpoint of any side of the hexagon.
4. 4.Using a ruler, construct a ΔABC with BC = 6.4 cm, CA = 5.8 cm, and ∠ABC = 60°. Draw its incircle. What is the radius of this incircle?
   • A.1.0 cm
   • B.1.5 cm
   • C.2.0 cm
   • D.2.5 cm
5. 5.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