ICSE Class 10 Heights and Distances — Mock Test (2027)
Free online mock test for Heights and Distances (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 Heights and Distances 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.Owing away from a light house 150 m high, it takes 1·5 minutes to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
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2.The shadow of a vertical tower on a level ground increases by 10 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower correct to two decimal places.
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3.The angle of elevation of the top of a tower is observed to be $60^{\circ}$. At a point, 30 m vertically above the first point of observation, the elevation is found to be $45^{\circ}$. Find: (i) the height of the tower, (ii) its horizontal distance from the points of observation.
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4.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m high, find the height of the building.
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5.In the given diagram, the angle of elevation of the top of a pole (AB) from a point P on the level ground, 15 m away from the foot of the pole (B), is 30°. Which labelled part represents the height of the pole?
[Take √3 = 1.732]- A.PB (the distance from point P to the foot of the pole)
- B.AB (the vertical line from the ground to the top of the pole)
- C.∠APB (the angle of elevation at point P)
- D.PA (the line from point P to the top of the pole)
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