ICSE Board Practice

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ICSE Grade X - Problems on Quadratic Equations
Question 1
1.
The sum of the squares of two consecutive odd numbers is 650. Find the numbers
      • 17
      • ,
      • 19
      • or
      • (-17)
      • ,
      • (-19)
        		•
      • 16
      • ,
      • 18
      • or
      • (-16)
      • ,
      • (-18)
      • 19
      • ,
      • 22
      • or
      • (-19)
      • ,
      • (-22)
      • 14
      • ,
      • 16
      • or
      • (-14)
      • ,
      • (-16)
      • 18
      • ,
      • 20
      • or
      • (-18)
      • ,
      • (-20)
Question 2
2.
Twice the square of a number exceeds 3 times the number by 9. Find the number
  • 0
  • 3
  • 2
  • 4
  • 6
Question 3
3.
In a two digit number, the unit's digit exceeds it ten's digit by 5 and the product of the given number and the sum of its digits is equal to 637 . Find the number
  • 49
  • 38
  • 27
  • 71
  • 60
Question 4
4.
If the difference of two numbers is 8 and their product is -12, find the numbers
      • 3
      • ,
      • (-5)
      • or
      • (-3)
      • ,
      • 5
      • 7
      • ,
      • (-1)
      • or
      • (-7)
      • ,
      • 1
      • 8
      • ,
      • 1
      • or
      • (-8)
      • ,
      • (-1)
      • 5
      • ,
      • (-3)
      • or
      • (-5)
      • ,
      • 3
      • 6
      • ,
      • (-2)
      • or
      • (-6)
      • ,
      • 2
Question 5
5.
    • A play field is
    • 40.00 m
    • by
    • 30.00 m
    • .
    • It has a road all around it on the outside.
    • Find the width of the road if its area is
    • 5
      2
    • of the area of the play field
  • 13.00 m
  • 17.00 m
  • 16.00 m
  • 14.00 m
  • 15.00 m
Question 6
6.
The sum of the ages of a father and his son is 72 years whereas five years ago, the product of their ages was 637. Find the current ages of the son and the father.
  • 20 years , 52 years
  • 19 years , 53 years
  • 17 years , 55 years
  • 18 years , 54 years
  • 16 years , 56 years
Question 7
7.
Find two natural numbers which differ by 11 and the sum of whose squares is 2581
  • (
    29
    ,
    40
    )
  • (
    31
    ,
    42
    )
  • (
    27
    ,
    38
    )
  • (
    30
    ,
    41
    )
  • (
    33
    ,
    44
    )
Question 8
8.
Find the number which is less than its square by 420
  • 24
  • 18
  • 21
  • 20
  • 22
Question 9
9.
A stream flows from A to B, a distance of 6.00 km. A man who can row in still water at 7.00 kmph, can row up and down in 6.46 hr . What is the speed of the stream?
  • 5.00 kmph
  • 8.00 kmph
  • 7.00 kmph
  • 4.00 kmph
  • 6.00 kmph
Question 10
10.
The sum of the squares of two consecutive even numbers is 884. Find the numbers
      • 22
      • ,
      • 24
      • or
      • (-22)
      • ,
      • (-24)
      • 19
      • ,
      • 21
      • or
      • (-19)
      • ,
      • (-21)
      • 17
      • ,
      • 20
      • or
      • (-17)
      • ,
      • (-20)
      • 20
      • ,
      • 22
      • or
      • (-20)
      • ,
      • (-22)
        		•
      • 21
      • ,
      • 23
      • or
      • (-21)
      • ,
      • (-23)