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 $AB = 4$ cm, $BC = 6$ cm and $\angle ABC = 90^\circ$. What is the key step to construct the circle passing through points $A$, $B$, and $C$?
- A.Draw perpendicular bisectors of $AB$ and $BC$ intersecting at $O$.
- B.Draw angle bisectors of $\angle ABC$.
- C.Join $A$ to $C$ and measure $AC$.
- D.Draw a circle with radius $AB$.
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2.In the given diagram,
a circle of radius 3 cm is drawn with centre O. A point P is marked at a distance of 5 cm from O. Two tangents PA and PB are drawn to the circle. Which labelled segment correctly represents the length of each tangent from P to the circle?- A.OA = 3 cm
- B.OP = 5 cm
- C.PA = 4 cm
- D.AB = 6 cm
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3.Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle as shown in the diagram. Which labelled part in the diagram represents the radius of the inscribed circle?
- A.The perpendicular distance from the incentre to any side of the triangle
- B.The distance from the incentre to any vertex of the triangle
- C.The length of the angle bisector from a vertex to the opposite side
- D.The distance between two sides of the triangle along a median
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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°
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5.Construct a regular hexagon of side 5 cm and inscribe a circle in it. Which of the following steps correctly identifies the centre of the incircle?
- A.The intersection of the perpendicular bisectors of any two sides.
- B.The intersection of the angle bisectors of any two interior angles.
- C.The midpoint of any side of the hexagon.
- D.The point where the diagonals of the hexagon meet.
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