ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Factor Theorem
Question 1
1.
    • The remainder when
    • (
      3
      d
      3
       
      +
      2
      d
      2
       
      −
      2
      		)
    • is divided by
    • (
      d
      2
       
      +
      9
      d
      +
      8
      		)
    • is
  • (
    202
    d
    +
    198
    		)
  • (
    199
    d
    +
    198
    		)
  • (
    203
    d
    +
    198
    		)
  • (
    200
    d
    +
    198
    		)
  • (
    201
    d
    +
    198
    		)
Question 2
2.
    • In which of the cases,
    •  
    • g
      (
      x
      )
    •  
    • is a factor of
    •  
    • f
      (
      x
      )
    • ?
  • f
    (
    x
    )
    =
    (
    −
    x
    3
     
    +
    4
    x
    2
     
    +
    29
    x
    +
    24
    		)
    ,
    g
    (
    x
    )
    =
    (
    2
    x
    +
    3
    		)
  • f
    (
    x
    )
    =
    (
    x
    3
     
    −
    7
    x
    2
     
    −
    14
    x
    +
    48
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    8
    		)
  • f
    (
    x
    )
    =
    (
    −
    2
    x
    3
     
    +
    x
    2
     
    +
    12
    x
    +
    9
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    2
    		)
  • f
    (
    x
    )
    =
    (
    −
    2
    x
    3
     
    −
    x
    2
     
    +
    7
    x
    +
    6
    		)
    ,
    g
    (
    x
    )
    =
    (
    x
    +
    3
    		)
  • f
    (
    x
    )
    =
    (
    2
    x
    3
     
    +
    11
    x
    2
     
    +
    18
    x
    +
    9
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    3
    		)
Question 3
3.
    • Given
    • f
      (
      t
      )
    • =
    • (
      7
      t
      +
      4
      		)
    • ,
    • find
    •  
    • f
      (
      0
      )
  • 5
  • 2
  • 7
  • 3
  • 4
Question 4
4.
    • Find the quadratic polynomial which when divided by
    • (
      2
      x
      −
      7
      		)
    • ,
    • (
      x
      −
      4
      		)
    • ,
    • (
      x
      +
      8
      		)
    • leaves remainders of
    •  
    • 693
      4
    • ,
    • 198
    • ,
    • 18
    • respectively.
  • (
    x
    2
     
    +
    4
    x
    −
    32
    		)
  • (
    2
    x
    2
     
    −
    15
    x
    +
    28
    		)
  • (
    x
    2
     
    +
    15
    x
    +
    56
    		)
  • (
    3
    x
    2
     
    +
    27
    x
    +
    42
    		)
  • (
    6
    x
    2
     
    −
    9
    x
    −
    42
    		)
Question 5
5.
    • If
    • (
      x
      −
      a
      		)
    • is a factor of
    • x
      3
      		  −  
      a
      x
      2
      		  −  
      x
      		  −  
      2
    • ,
    • find the value of
    • a
  • 1
  • (-4)
  • (-2)
  • (-1)
  • (-3)
Question 6
6.
Which of the following are true?
a)
    • π
    • r
      2
    • is a monomial
b)
A binomial has two and only two terms
c)
Degree of zero polynomial is zero
d)
Every polynomial is a binomial
e)
A binomial may have degree 3
  • {c,d,e}
  • {c,a}
  • {d,b}
  • {c,a,b}
  • {a,b,e}
Question 7
7.
    • The value of the polynomial
    • (
      −
      3
      q
      4
       
      −
      3
      q
      3
       
      −
      5
      q
      2
       
      +
      9
      q
      +
      9
      		)
    • at
    •  
    • q
    • =
    • 2
    • is
  • -68
  • -65
  • -64
  • -63
  • -66
Question 8
8.
    • (
      60
      x
      3
       
      y
      2
       
      z
      3
       
      +
      12
      x
      2
       
      y
      3
       
      z
      3
       
      +
      4
      x
      2
       
      y
      2
       
      z
      3
       
      		)
    • ÷
    		•
      2
      x
      y
      z
    • =
  • (
    30
    x
    3
     
    y
    3
     
    z
    2
     
    +
    6
    x
    y
    2
     
    z
    2
     
    +
    2
    x
    y
    z
    2
     
    		)
  • (
    30
    x
    3
     
    y
    2
     
    z
    2
     
    +
    6
    x
    y
    2
     
    z
    2
     
    +
    2
    x
    y
    z
    2
     
    		)
  • (
    30
    x
    2
     
    y
    z
    2
     
    +
    6
    x
    y
    3
     
    z
    3
     
    +
    2
    x
    y
    z
    2
     
    		)
  • (
    30
    x
    2
     
    y
    z
    2
     
    +
    2
    x
    y
    z
    2
     
    +
    6
    y
    3
     
    z
    2
     
    		)
  • (
    30
    x
    2
     
    y
    z
    2
     
    +
    6
    x
    y
    2
     
    z
    2
     
    +
    2
    x
    y
    z
    2
     
    		)
Question 9
9.
    • Given
    • f
      (
      h
      )
    • =
    • (
      3
      h
      2
       
      +
      2
      h
      +
      4
      		)
    • ,
    • find
    •  
    • f
      (
      1
      )
  • 9
  • 8
  • 11
  • 10
  • 7
Question 10
10.
    • The degree of the polynomial
    • (
      8
      u
      2
       
      −
      5
      u
      +
      1
      		)
    • is
  • 3
  • 2
  • 1
  • 5
  • (-1)