ICSE Board Practice

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ICSE Grade X - Problems on Quadratic Equations
Question 1
1.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 165 . Find the three numbers.
  • 11, 12, 13
  • 14, 15, 16
  • 16, 17, 18
  • 15, 16, 17
  • 13, 14, 15
Question 2
2.
The product of two consecutive even numbers is 0. Find the numbers
  • -3 , -1 or 3 , 1
  • 0 , 2 or 0 , -2
  • -5 , -2 or 5 , 2
  • -1 , 1 or 1 , -1
  • -2 , 0 or 2,0
Question 3
3.
    • A play field is
    • 30.00 m
    • by
    • 10.00 m
    • .
    • It has a road all around it on the outside.
    • Find the width of the road if its area is
    • 5
      3
    • of the area of the play field
  • 4.00 m
  • 5.00 m
  • 7.00 m
  • 6.00 m
  • 3.00 m
Question 4
4.
The area of a rectangular room is 136.00 sq.m. If the length and breadth are increased by 7 m, the area would become 451.00 sq.m. Find the original dimensions of the room
  • 16.00 m , 8.50 m
  • 17.00 m , 8.00 m
  • 7.00 m , 19.43 m
  • 4.00 m , 34.00 m
  • 8.00 m , 17.00 m
Question 5
5.
The perimeter of a rectangular room is 82.00 m and the length of its diagonal is 30.41 m . Find the dimensions of the room
  • 29.00 m , 12.00 m
  • 25.00 m , 16.00 m
  • 28.00 m , 13.00 m
  • 27.00 m , 14.00 m
  • 26.00 m , 15.00 m
Question 6
6.
The sum of the squares of two consecutive odd numbers is 10. Find the numbers
      • (-4)
      • ,
      • (-2)
      • or
      • 4
      • ,
      • 2
      • (-3)
      • ,
      • (-1)
      • or
      • 3
      • ,
      • 1
        		•
      • (-2)
      • ,
      • 0
      • or
      • 2
      • ,
      • 0
      • 0
      • ,
      • 2
      • or
      • 0
      • ,
      • (-2)
      • (-5)
      • ,
      • (-4)
      • or
      • 5
      • ,
      • 4
Question 7
7.
A two digit number is such that the product of the digits is 12. When 36 is added to the number, the digits are reversed. Find the number
  • 24
  • 26
  • 25
  • 27
  • 29
Question 8
8.
    • 30 is divided into two parts such that the sum of their reciprocals is
    • 30
      29
    • .
    • Find the two parts
  • (
    29
    ,
    1
    )
  • (
    27
    ,
    3
    )
  • (
    28
    ,
    2
    )
  • (
    30
    ,
    0
    )
  • (
    31
    ,
    -1
    )
Question 9
9.
The sum of the squares of two consecutive even numbers is 884. Find the numbers
      • 20
      • ,
      • 22
      • or
      • (-20)
      • ,
      • (-22)
        		•
      • 23
      • ,
      • 25
      • or
      • (-23)
      • ,
      • (-25)
      • 18
      • ,
      • 19
      • or
      • (-18)
      • ,
      • (-19)
      • 21
      • ,
      • 23
      • or
      • (-21)
      • ,
      • (-23)
      • 19
      • ,
      • 21
      • or
      • (-19)
      • ,
      • (-21)
Question 10
10.
The sum of the ages of a father and his son is 58 years whereas seven years ago, the product of their ages was 123. Find the current ages of the son and the father.
  • 12 years , 46 years
  • 8 years , 50 years
  • 10 years , 48 years
  • 9 years , 49 years
  • 11 years , 47 years