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.

Sample questions

1. 1.Two poles AB and CD are on either side of a road BD. A ladder is placed at point L making an angle of $32^{\circ} 24'$ with the road and $57^{\circ} 24'$ with the second pole. The length of the ladder AL = CL = 30 m. In the diagram below, which labelled segment represents the width of the road BD?
   • A.The horizontal distance between points B and D
   • B.The vertical height of pole AB from point B
   • C.The length of the ladder AL or CL
   • D.The diagonal distance between points A and C
2. 2.Two lamp posts AB and CD each of heights 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 40° and 60°. Find the distance PB and PD.
3. 3.From a point A on level ground, the angle of elevation of the top of a tower is 29°. If the tower is 25 m high, find the distance of A from the foot of the tower, to the nearest metre.
4. 4.The diagram shows a vertical tower AB. When the sun’s altitude changes from 45° to 30°, the length of the shadow on level ground increases by 10 m (from BC to BD, so DC = 10 m). Which labelled segment in the diagram corresponds to the height of the tower?
   • A.AB
   • B.BC
   • C.BD
   • D.DC
5. 5.From a window A, 10 m above the ground angle of elevation of the top C of a tower is $x^{\circ}$, where $\tan x^{\circ} = \frac{5}{2}$ and the angle of depression of the foot D of the tower is $y^{\circ}$, where $\tan y^{\circ} = \frac{1}{4}$. Calculate the height CD of the tower in metres.