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 compass only, draw a circle of radius 4 cm with centre O. Mark a point P outside the circle at a distance of 7 cm from O. Construct two tangents to the circle from P and measure the length of any one tangent. What is the length of one tangent?
- A.4.9 cm
- B.5.7 cm
- C.6.3 cm
- D.7.0 cm
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2.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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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
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4.Draw an isosceles $\Delta ABC$ in which base $BC = 6\mathrm{cm}$ and the altitude from vertex to the base is 4 cm. To draw its inscribed circle, which step is required?
- A.Draw perpendicular bisectors of $AB$ and $AC$ to find the centre.
- B.Draw angle bisectors of $\angle B$ and $\angle C$ intersecting at $I$.
- C.Construct the circumcircle and use its centre for the incircle.
- D.Find the midpoint of $BC$ and use it as the centre of the incircle.
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5.Using a ruler, construct a ΔABC with BC = 6.4 cm, CA = 5.8 cm, and ∠ABC = 60°. Draw its incircle. What is the radius of this incircle?
- A.1.0 cm
- B.1.5 cm
- C.2.0 cm
- D.2.5 cm
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