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.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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2.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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3.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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4.Construct a $\Delta PQR$, given $PQ = 5$ cm, $QR = 7$ cm and $\angle PQR = 60^\circ$. To inscribe a circle in the triangle, which step is required?
- A.Draw perpendicular bisectors of $PQ$ and $QR$ to find the centre.
- B.Draw angle bisectors of $\angle Q$ and $\angle R$ intersecting at $I$.
- C.Construct the circumcircle and use its centre for the incircle.
- D.Find the midpoint of $PR$ and use it as the centre of the incircle.
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5.To draw a circle of radius $4\mathrm{cm}$ and two tangents to this circle so that the angle between the tangents is $60^{\circ}$, which of the following steps is correct?
- A.Draw arcs $OT$ and $PT$ with $60^\circ$ between them.
- B.Draw rays at $S$ and $T$ making $60^\circ$ each to meet at $P$.
- C.Draw two arcs $OT$ and $PT$ with $120^\circ$ between them.
- D.Draw tangents at $45^\circ$ to the radius.
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