ICSE Board Practice

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ICSE Grade X - Problems on Quadratic Equations
Question 1
1.
    • The denominator of a fraction exceeds the numerator by
    • 8
    • .
    • The square of the fraction is equal to
    • 4
      9
    • . Find the fraction
  • 3
    4
  • 8
    11
  • 2
    3
  • 8
    13
  • 7
    12
Question 2
2.
    • 53 is divided into two parts such that the sum of their reciprocals is
    • 53
      690
    • .
    • Find the two parts
  • (
    30
    ,
    23
    )
  • (
    28
    ,
    25
    )
  • (
    29
    ,
    24
    )
  • (
    31
    ,
    22
    )
  • (
    32
    ,
    21
    )
Question 3
3.
If the difference of two numbers is 2 and their product is 323, find the numbers
      • (-18)
      • ,
      • (-20)
      • or
      • 18
      • ,
      • 20
      • (-16)
      • ,
      • (-18)
      • or
      • 16
      • ,
      • 18
      • (-20)
      • ,
      • (-21)
      • or
      • 20
      • ,
      • 21
      • (-14)
      • ,
      • (-16)
      • or
      • 14
      • ,
      • 16
      • (-17)
      • ,
      • (-19)
      • or
      • 17
      • ,
      • 19
Question 4
4.
The sum of the squares of two consecutive even numbers is 244. Find the numbers
      • 13
      • ,
      • 15
      • or
      • (-13)
      • ,
      • (-15)
      • 10
      • ,
      • 12
      • or
      • (-10)
      • ,
      • (-12)
        		•
      • 9
      • ,
      • 11
      • or
      • (-9)
      • ,
      • (-11)
      • 11
      • ,
      • 13
      • or
      • (-11)
      • ,
      • (-13)
      • 8
      • ,
      • 9
      • or
      • (-8)
      • ,
      • (-9)
Question 5
5.
The sum of the squares of two consecutive odd numbers is 290. Find the numbers
      • (-14)
      • ,
      • (-12)
      • or
      • 14
      • ,
      • 12
      • (-13)
      • ,
      • (-11)
      • or
      • 13
      • ,
      • 11
        		•
      • (-12)
      • ,
      • (-10)
      • or
      • 12
      • ,
      • 10
      • (-10)
      • ,
      • (-9)
      • or
      • 10
      • ,
      • 9
      • (-16)
      • ,
      • (-14)
      • or
      • 16
      • ,
      • 14
Question 6
6.
The product of two consecutive even numbers is 24. Find the numbers
  • 6 , 8 or -6 , -8
  • 5 , 7 or -5 , -7
  • 4 , 6 or -4,-6
  • 3 , 5 or -3 , -5
  • 1 , 4 or -1 , -4
Question 7
7.
    • A can do a work in
    • x
    • days and B can do it in
    • (
      x
      −
      9
      		)
    • days.
    • Both of them working together can do it in
    • 7
      7
      11
    • days. Calculate
    • x
  • 18
  • 22
  • 21
  • 20
  • 24
Question 8
8.
The area of a rectangular room is 20.00 sq.m. If the length and breadth are increased by 4 m, the area would become 72.00 sq.m. Find the original dimensions of the room
  • 4.00 m , 5.00 m
  • 9.00 m , 2.22 m
  • 10.00 m , 2.00 m
Question 9
9.
Find the number which is less than its square by 30
  • 8
  • 7
  • 3
  • 5
  • 6
Question 10
10.
    • The sum of the numerator and denominator of a fraction is
    • 40
    • .
    • If
    • 9
    • is added to both the numerator and denominator,
    • the fraction is increased by
    • 9
      85
    • . Find the fraction
  • 13
    25
  • 15
    25
  • 25
    15
  • 17
    25
  • 15
    23