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
-
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
-
2.Construct a ΔPMN, given that MN = 5 cm, PN = 7 cm, and ∠PMN = 90°. After constructing the triangle, an incircle is drawn. What is the radius of this incircle?
- A.1.0 cm
- B.1.5 cm
- C.2.0 cm
- D.2.5 cm
-
3.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.
-
4.Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle. Which construction step ensures the tangents are correctly drawn?
- A.Drawing a circle with the radius of the outer circle as diameter.
- B.Drawing a circle with the line joining the centre and the external point as diameter.
- C.Drawing perpendiculars from the external point to the radii of the inner circle.
- D.Bisecting the angle formed by the two radii of the inner circle.
-
5.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°
Ready? Take the full 20-question test free — instant marking, no sign-up needed.
▶ Start free mock test