ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Similarity (As a Size Transformation)
Question 1
1.
△ABC is a triangle with sides BC = 13 cm, CA = 15 cm and AB = 11 cm.  △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 2.75 cm. Find the corresponding lengths of the reduced triangle △A'B'C'.
  • 4.25 cm, 4.75 cm, 3.75 cm
  • 5.25 cm, 5.75 cm, 4.75 cm
  • 3.25 cm, 3.75 cm, 2.75 cm
  • 1.25 cm, 1.75 cm, 0.75 cm
  • 2.25 cm, 2.75 cm, 1.75 cm
Question 2
2.
A model of a ship is made to a scale of 1 : 180. If length of the model ship is 13 m, calculate the length of the ship.
  • 2340.00 m
  • 2190.00 m
  • 2460.00 m
  • 2320.00 m
  • 2570.00 m
Question 3
3.
The measurements of a triangular field △ABC are BC = 9 cm, AB = 13 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 19000. Calculate the actual area of the plot in sq.km.
  • 3.11 sq.km
  • 2.11 sq.km
  • 4.11 sq.km
  • 0.11 sq.km
  • 1.11 sq.km
Question 4
4.
The dimensions of the model of a multi-storey building are 1.5 cm ✕ 6.5 cm ✕ 4 cm. If the model is drawn to a scale of 1 : 80, find the floor area of a room of the building whose area in the model is 36 sq.cm.
  • 20.04 sq.m
  • 23.04 sq.m
  • 26.04 sq.m
  • 18.04 sq.m
  • 28.04 sq.m
Question 5
5.
The measurements of a triangular field △ABC are BC = 7 cm, AB = 11 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 21000. Calculate the actual length of CA in km.
  • 4.74 km
  • 0.74 km
  • 3.74 km
  • 1.74 km
  • 2.74 km
Question 6
6.
The dimensions of the model of a multi-storey building are 5.5 cm ✕ 2.5 cm ✕ 8 cm. If the model is drawn to a scale of 1 : 80, find the actual dimensions of the building.
  • 440 cm ✕ 201 cm ✕ 640 cm
  • 440 cm ✕ 200 cm ✕ 640 cm
  • 441 cm ✕ 201 cm ✕ 640 cm
  • 440 cm ✕ 200 cm ✕ 641 cm
  • 441 cm ✕ 200 cm ✕ 640 cm
Question 7
7.
Which of the following are true?
a)
Any two triangles are similar.
b)
Any two triangles are congruent.
c)
Any two squares are similar.
d)
Any two squares are congruent.
e)
Any two circles are similar.
f)
Any two circles are congruent.
  • {b,e}
  • {a,e,c}
  • {d,f,c}
  • {c,e}
  • {a,c}
Question 8
8.
The dimensions of the model of a multi-storey building are 4.5 cm ✕ 2.5 cm ✕ 8 cm. If the model is drawn to a scale of 1 : 150, find the volume of the room in the model whose actual volume is 4492.125 cu.m.
  • 1511.00 cu.cm
  • 1331.00 cu.cm
  • 1391.00 cu.cm
  • 1181.00 cu.cm
  • 1071.00 cu.cm
Question 9
9.
A model of a ship is made to a scale of 1 : 150. If the volume of the ship is 216000000 cu.m, calculate the volume of the model ship.
  • 59.00 cu.m
  • 64.00 cu.m
  • 69.00 cu.m
  • 61.00 cu.m
  • 67.00 cu.m
Question 10
10.
Which of the following are true?
a)
Any two quadrilaterals are similar if the corresponding angles are equal.
b)
Any two triangles are similar if the corresponding angles are equal.
c)
Any two quadrilaterals are similar if the corresponding sides are proportional.
d)
Any two triangles are similar if the corresponding sides are proportional.
  • {a,b,c}
  • {a,c}
  • {a,b}
  • {b,c,d}
  • {a,d}