ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade VIII - Simplification of Algebraic Fractions
Question 1
1.
Which of the following gives the L.C.M. of two or more polynomials?
  • ( Product of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
  • ( L.C.M. of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
  • ( Product of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
  • ( L.C.M. of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
Question 2
2.
    • Simplify
    • (
      9
      x
      2
       
      −
      49
      		)
      (
      4
      x
      2
       
      −
      4
      		)
    • ✕
    • (
      2
      x
      +
      2
      		)
      (
      3
      x
      −
      7
      		)
  • (
    3
    x
    +
    7
    		)
    (
    2
    x
    −
    2
    		)
  • (
    3
    x
    +
    7
    		)
    (
    2
    x
    +
    2
    		)
  • (
    4
    x
    +
    7
    		)
    (
    2
    x
    +
    2
    		)
  • (
    3
    x
    −
    7
    		)
    (
    2
    x
    +
    2
    		)
  • (
    6
    x
    +
    7
    		)
    (
    −
    x
    −
    2
    		)
Question 3
3.
    • Find the L.C.M. of
    • 4
      x
      3
       
      y
      2
       
      z
      2
       
    • and
    • 32
      x
      2
       
      y
      2
       
      z
  • 32
    x
    4
     
    y
    2
     
    z
    2
     
  • 32
    x
    3
     
    y
    4
     
    z
    2
     
  • 128
    x
    5
     
    y
    4
     
    z
    3
     
  • 32
    x
    3
     
    y
    2
     
    z
    2
     
  • 4
    x
    2
     
    y
    2
     
    z
Question 4
4.
    • Simplify
    • (
      3
      x
      +
      9
      		)
      (
      15
      x
      2
       
      +
      48
      x
      +
      9
      		)
  • 1
    (
    5
    x
    −
    1
    		)
  • 1
    (
    5
    x
    +
    1
    		)
  • 3
    (
    3
    x
    +
    1
    		)
  • 3
    (
    5
    x
    −
    1
    		)
  • 2
    (
    5
    x
    −
    1
    		)
Question 5
5.
    • Simplify
    • (
      x
      −
      3
      		)
      (
      x
      2
       
      −
      9
      x
      +
      18
      		)
    • +
    • (
      2
      x
      +
      4
      		)
      (
      2
      x
      2
       
      −
      2
      x
      −
      12
      		)
    • −
    • (
      5
      x
      −
      1
      		)
      (
      x
      2
       
      −
      9
      x
      +
      18
      		)
  • (
    −
    8
    		)
    (
    −
    x
    2
     
    −
    9
    x
    +
    18
    		)
  • (
    −
    2
    x
    −
    8
    		)
    (
    x
    2
     
    −
    9
    x
    −
    18
    		)
  • (
    −
    3
    x
    −
    8
    		)
    (
    x
    2
     
    −
    9
    x
    +
    18
    		)
  • (
    −
    3
    x
    +
    8
    		)
    (
    x
    2
     
    −
    9
    x
    −
    18
    		)
  • (
    −
    3
    x
    −
    8
    		)
    (
    x
    2
     
    −
    9
    x
    −
    18
    		)
Question 6
6.
    • Simplify
    • (
      16
      x
      2
       
      −
      36
      		)
      (
      25
      x
      2
       
      −
      9
      		)
    • ÷
    • (
      4
      x
      −
      6
      		)
      (
      5
      x
      −
      3
      		)
  • (
    4
    x
    +
    6
    		)
    (
    5
    x
    −
    3
    		)
  • (
    2
    x
    +
    2
    		)
    (
    x
    +
    1
    		)
  • (
    4
    x
    +
    6
    		)
    (
    5
    x
    +
    3
    		)
  • (
    5
    x
    +
    6
    		)
    (
    5
    x
    −
    3
    		)
  • (
    4
    x
    −
    6
    		)
    (
    5
    x
    −
    3
    		)
Question 7
7.
    • Simplify
    • (
      10
      x
      2
       
      −
      19
      x
      +
      7
      		)
      (
      10
      x
      2
       
      −
      9
      x
      −
      7
      		)
  • (
    2
    x
    −
    1
    		)
    (
    2
    x
    +
    1
    		)
  • (
    2
    x
    +
    1
    		)
    (
    2
    x
    −
    1
    		)
  • (
    3
    x
    −
    1
    		)
    (
    2
    x
    −
    1
    		)
  • (
    5
    x
    −
    1
    		)
    1
  • (
    2
    x
    −
    1
    		)
    (
    2
    x
    −
    1
    		)
Question 8
8.
    • Find the H.C.F. of
    • 42
      x
      2
       
    • and
    • 12
      x
      2
       
  • 6
    x
    4
     
  • 84
    x
    2
     
  • 6
    x
    2
     
  • 6
    x
    5
     
  • 6
    x
    3
     
Question 9
9.
    • Find the H.C.F. of
    • 42
      x
      y
      2
       
      z
      3
       
    • and
    • 66
      x
      3
       
      y
      3
       
      z
      2
       
  • 462
    x
    3
     
    y
    3
     
    z
    3
     
  • 6
    x
    2
     
    y
    2
     
    z
    2
     
  • 6
    x
    y
    4
     
    z
    2
     
  • 6
    x
    y
    2
     
    z
    4
     
  • 6
    x
    y
    2
     
    z
    2
     
Question 10
10.
    • Simplify
    • (
      81
      x
      5
       
      −
      81
      x
      		)
      (
      27
      x
      3
       
      +
      27
      x
      2
       
      +
      27
      x
      +
      27
      		)
  • (
    3
    x
    		) (
    x
    +
    1
    		)
  • (
    3
    x
    		) (
    x
    −
    1
    		)
  • (
    6
    x
    		) (
    x
    +
    1
    		)
  • (
    −
    6
    x
    		) (
    x
    +
    1
    		)