ICSE Board Practice

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ICSE Grade X - Similarity (As a Size Transformation)
Question 1
1.
Which of the following are true?
a)
Similar and congruent are not synonymous.
b)
Similar figures have same area.
c)
Congruent figures have same area.
d)
If two figures are similar, then they are congruent too.
e)
If two figures are congruent, then they are similar too.
  • {a,c,e}
  • {b,d,e}
  • {d,c}
  • {b,a,c}
  • {b,a}
Question 2
2.
A model of building is made with a scale factor of 1 : 30. Find the volume of the tank on the top of the model if its actual volume is 91125 cu.cm.
  • 3.38 cu.cm
  • 2.38 cu.cm
  • 1.38 cu.cm
  • 5.38 cu.cm
  • 4.38 cu.cm
Question 3
3.
    • The ratio of the bases of two triangles ABC and DEF is
    • 9
      		:
      3
    • .
    • If the triangles are equal in area, then the ratio of their heights is
  • 9
    		:
    6
  • 10
    		:
    3
  • 9
    		:
    1
  • 3
    		:
    9
  • 8
    		:
    3
Question 4
4.
△ABC is a triangle with sides BC = 12 cm, CA = 14 cm and AB = 10 cm.  △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 13.33 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.
  • 18 cm, 20.67 cm, 15.33 cm
  • 16 cm, 18.67 cm, 13.33 cm
  • 14 cm, 16.67 cm, 11.33 cm
  • 17 cm, 19.67 cm, 14.33 cm
  • 15 cm, 17.67 cm, 12.33 cm
Question 5
5.
Which of the following are true?
a)
Area of the union of two polygonal region is not equal to the sum of the individual area.
b)
Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.
c)
Area of the union of two polygonal region is the sum of the individual area.
d)
A polygonal region can be divided into a finite number of triangles in a unique way.
  • {d,b}
  • {c,a}
  • {c,d,a}
  • {c,b,a}
  • {a,b}
Question 6
6.
Which of the following are necessary conditions for similarity of two polygons ?
a)
The corresponding angles are proportional.
b)
The corresponding sides are equal.
c)
The corresponding sides are proportional.
d)
The corresponding angles are equal.
  • {c,d}
  • {a,c}
  • {a,b,c}
  • {b,d}
  • {a,d,c}
Question 7
7.
A model of a ship is made to a scale of 1 : 185. If length of the model ship is 16 m, calculate the length of the ship.
  • 2820.00 m
  • 3010.00 m
  • 2960.00 m
  • 2680.00 m
  • 3230.00 m
Question 8
8.
Which of the following are true?
a)
A square is a polygonal region.
b)
A triangle is a polygonal region.
c)
A circle is a polygonal region.
d)
A sector is a polygonal region.
e)
A semi-circle is a polygonal region.
  • {a,b}
  • {c,a}
  • {e,c,a}
  • {d,b}
  • {d,b,a}
Question 9
9.
The measurements of a triangular field △ABC are BC = 14 cm, AB = 12 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 18000. Calculate the actual area of the plot in sq.km.
  • 0.72 sq.km
  • 4.72 sq.km
  • 2.72 sq.km
  • 3.72 sq.km
  • 1.72 sq.km
Question 10
10.
A model of a ship is made to a scale of 1 : 190. If the area of the deck of the ship is 144400 sq.m, calculate the area of the deck of the model ship.
  • 4.00 sq.m
  • 6.00 sq.m
  • 3.00 sq.m
  • 2.00 sq.m
  • 5.00 sq.m