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.In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and $\angle B = 60^{\circ}$. Calculate the length of the board AB.
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2.In the given diagram,
the top of a church spire is 96 m high. The angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it, are labelled x° and y°, where $\tan x° = \frac{1}{4}$ and $\tan y° = \frac{1}{7}$. Which labelled segment represents the distance between the two vehicles?- A.The horizontal distance from the spire to the nearer vehicle
- B.The horizontal distance from the spire to the farther vehicle
- C.The difference between the two horizontal distances from the spire
- D.The vertical height of the spire above the road level
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3.The ratio of the length of a rod and its shadow is $1:\sqrt{3}$ then the angle of elevation of the sun is
- a.$90^{\circ}$
- b.$45^{\circ}$
- c.$30^{\circ}$
- d.$75^{\circ}$
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4.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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5.A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. What is the speed of the boat in km/hr?
- A.(3/2)(3 - √3) km/hr
- B.3(3 - √3) km/hr
- C.(3 - √3) km/hr
- D.2(3 - √3) km/hr
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