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.In $\Delta ABC, AB = 5\mathrm{cm}, BC = 6.5\mathrm{cm}$ and $CA = 4.8$ cm. To draw the circumcircle of $\Delta ABC$, which step is necessary?
- A.Draw the angle bisector of $\angle BAC$ to locate the centre.
- B.Draw perpendicular bisectors of $AC$ and $BC$ intersecting at $O$.
- C.Construct the incircle and use its radius for the circumcircle.
- D.Find the midpoint of $AB$ and use it as the centre of the circumcircle.
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2.In the given diagram
, the point labelled H represents the orthocentre of triangle ABC. Which of the following correctly describes how this point is determined?- A.It is the point where the perpendicular bisectors of the sides of the triangle meet.
- B.It is the point where the altitudes of the triangle, drawn from each vertex to the opposite side, intersect.
- C.It is the point where the angle bisectors of the triangle meet.
- D.It is the point where the medians of the triangle intersect.
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3.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.
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4.Draw a line segment OP of length 6 cm. From point O, draw a circle of radius 3.5 cm. Construct tangents PQ and PR to the circle from P. Which step ensures PQ and PR are equal in length and perpendicular to the radii at Q and R?
- A.Drawing a circle with OP as diameter and finding its intersection with the given circle.
- B.Drawing perpendiculars from P to the radii of the circle.
- C.Bisecting the angle formed at P by the tangents.
- D.Constructing the perpendicular bisector of OP and using its midpoint as centre.
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5.(i) Using a ruler and compass, construct a ΔABC with AB = 6 cm, AC = 4.5 cm, and ∠BAC = 120°. After constructing the triangle, measure and determine the radius of the circumscribed circle around ΔABC.
- A.3 cm
- B.4.5 cm
- C.6 cm
- D.7.5 cm
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