Algebra Model Question Paper

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
    7 x 1 = 7
  1. If p(a)= 0 then (x-a) is a ___________ of p(x)

    (a)

    divisor

    (b)

    quotient

    (c)

    remainder

    (d)

    factor

  2. Zeros of (2-3x) is ___________

    (a)

    3

    (b)

    2

    (c)

    2/3

    (d)

    3/2

  3. If x - 3 is a factor of p(x), then the remainder is

    (a)

    3

    (b)

    -3

    (c)

    p(3)

    (d)

    p(-3)

  4. In an expression ax2+bx c the sum and product of the factors respectively,

    (a)

    a, bc

    (b)

    b, ac

    (c)

    ac, b

    (d)

    bc, a

  5. Cubic polynomial may have maximum of ___________ linear factors

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  6. The remainder when (x2-2x+7) is divided by (x + 4) is

    (a)

    28

    (b)

    31

    (c)

    30

    (d)

    20

  7. The GCD of x4-y4 and x2-y2 is

    (a)

    x4-y4

    (b)

    x2-y2

    (c)

    (x+y)2

    (d)

    (x+y)4

  8. 8 x 2 = 16
  9. Show that (x+2) is a factor of x3-4x2-2x+20

  10. If (x -1) divides the polynomial kx3-2x2+25x-26 without remainder, then find the value of k.

  11. Expand (2x+3y)3

  12. Expand the following: (2a-3b+4c)2

  13. Factorise the following: 36m2-49n2

  14. Find: x3-y3, if x-y=4, xy=5

  15. Factorise the following: m3+512

  16. Factorise the following: x3+8y3+6xy-1

  17. 4 x 3 = 12
  18. Is (2x -3) a factor of p(x)=2x3-9x2+x+12?

  19. If 2x −3y −4z = 0 , then find 8x3-27y3-64z3

  20. If the quotient obtained on dividing (8x4-2x2+6x-7) is (4x3+px2-qx+3), then find p, q and also the remainder

  21. Factorise x3+13x2+32x+20 into linear factors.

  22. 3 x 5 = 15
  23. Expand the following:
    (i) (x+5)(x+6)(x+4)
    (ii) (b+3)(b+4)(b-5)
    (iii) (2x+3)(2x+4)(2x+5)
    (iv) (3x-1)(3x+2)(3x-4)

  24. Verify x3+y3+z3-3xyz=\(\frac{1}{2}\)[x+y+z][(x-y)2+(y-z)2+(z-x)2]

  25. Find the GCD of the following:
    (i) (2x+5), (5x+2)
    (ii) am+1, am+2, am+3
    (iii) 2a2+a, 4a2-1
    (iv) 3a2, 5b3, 7c4
    (v) x4-1, x2-1
    (vi) a3-9ax2, (a-3x)2

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