ICSE Question Bank

Examined in

9 of 11 papers

Appears in most years

Typically worth

4.2 marks

Average per paper it appears in · 38 marks in total

Usual form

Numerical

92% of this chapter's 12 questions

Needs a diagram

58%

7 questions carry a figure — practise drawing them

Question-type distribution

Numerical11
MCQ1

Most frequent topics

Heights and distances 12

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Showing 12 of 12 matching questions (38 marks).

12 questions

7(i)2026

NumericalHard5 marks

A flagpole is erected at the top of a building. The angle of elevation of the top and foot of the flagpole from a point 100 m away, on the same level as that of the foot of the building, are 33° and 31° respectively. Find the height of the flagpole. Give your answer correct to the nearest metre. (Use Mathematical Tables for this question.)

6(ii)

In the given diagram, AB is a vertical tower 100 m away from the foot of a 30 storied building CD. The angles of depression from the point C and E, (E being the mid-point of CD), are 35° and 14° respectively. (Use mathematical table for the required values rounded off correct to two places of decimals only.) Find the height of the:

6(ii)(a)2025

NumericalHard3 marks

tower AB

6(ii)(b)2025

NumericalModerate2 marks

building CD

5(ii)2024

NumericalHard5 marks

The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.

9(iii)2023

NumericalHard4 marks

From the top of a tower 100 m high, a man observes the angle of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of tower and the ships are in the same horizontal line, find the distance between two ships A and B to the nearest metre. (Use Mathematical Tables for this question.)

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(v)2022

MCQEasy1 mark

A lighthouse is 80 m high. The angle of elevation of its top from a point 80 m away from its foot along the same horizontal line is:

(a)60°
(b)45°
(c)30°
(d)90°

3(iii)2022

NumericalHard3 marks

Two lamp posts AB and CD each of height 100 m are on either side of the road. P is a point on the road between the two lamp posts. The angles of elevation of the top of the lamp posts from the point P are 60°and 30°. Find the distances PB and PD.

6(c)

From the top of a cliff, the angle of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. If the height of the tower is 20 m.

6(c)

Find :

6(c)(i)2020

NumericalModerate2 marks

the height of the cliff

6(c)(ii)2020

NumericalModerate2 marks

the distance between the cliff and the tower.

NumericalHard4 marks

The angle of elevation from a point P of the top of a tower QR, 50 m high is 60° and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre.