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 triangle with sides 5 cm, 4 cm, and 3 cm. Draw its circumcircle and measure its radius. What is the radius of the circumcircle?
   • A.2.0 cm
   • B.2.5 cm
   • C.3.0 cm
   • D.3.5 cm
2. 2.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
3. 3.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
4. 4.Draw a circle of radius 4 cm. To construct two tangents to the circle inclined at an angle of 60° to each other, what should be the angle between the two radii at the points of contact?
   • A.30°
   • B.60°
   • C.120°
   • D.180°
5. 5.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.