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.An equilateral triangle of side 4 cm is drawn. Which step is NOT part of constructing its circumcircle?
   • A.Draw perpendicular bisectors of two sides
   • B.Find the intersection of the bisectors as centre
   • C.Draw arcs of radius 4 cm from all vertices
   • D.Draw circle with radius equal to distance from centre to vertex
2. 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
3. 3.Draw a circle of radius 3 cm. Construct tangents to the circle so that the angle between them is 45°. What is the measure of the angle subtended by the two points of tangency at the centre of the circle?
   • A.45°
   • B.90°
   • C.135°
   • D.180°
4. 4.Construct a regular hexagon of side 4 cm. To construct a circle circumscribing the hexagon, which step is correct?
   • A.Draw perpendicular bisectors of two adjacent sides to find the centre.
   • B.Use the intersection of the diagonals as the centre of the circle.
   • 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.
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