Term 2 Algebra Five Marks Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    10 x 5 = 50
  1. Evaluate the following by using identities:
    (i) 983
    (ii) 1033
    (iii) 993
    (iv) 10013

  2. Simplify: \(\left[ \frac { ({ x }^{ 2 }-{ y }^{ 2 })^{ 3 }+({ y }^{ 2 }-{ z }^{ 2 })^{ 3 }+({ z }^{ 2 }-{ x }^{ 2 })^{ 3 } }{ (x-y)^{ 3 }+(y-z)^{ 3 }+(z-x)^{ 3 } } \right] \) by using identity

  3. If a = 4, b = 5 and c = 6 , then find the value of \(\left[ \frac { (ab+bc+ca-{ a }^{ 2 }-{ b }^{ 2 }-{ c }^{ 2 }) }{ (3abc-{ a }^{ 3 }-{ b }^{ 3 }-{ c }^{ 3 }) } \right] \).

  4. Factorise 2x2-15x+27

  5. Factorise 2x2 + 15x - 27

  6. Factorise (x + y)2 + 9(x+y) + 20

  7. Factorise the following:
    (i) 2a2+9a+10
    (ii) 11+5m-6m2
    (iii) 4x2-20x+25
    (iv) 3268x-60x2
    (v) 5x2-29xy-42y2
    (vi) 9-189x+8x2
    (vii) 6x2+16xy+8y2
    (viii) 9+3x-12x2
    (ix)10-7a-3a2
    (x) 12x2+36x2y+27y2x2
    (xi) (a+b)+ (a+b)+18

  8. Find the quotient and remainder for the following using synthetic division:
    (i) (x3+x2-7x-3) ÷ (x-3)
    (ii) (x3+2x2-x-4) ÷ (x+2)
    (iii) (x3+4x2+16x+61) ÷ (x-4)
    (iv) (3x3-2x2+7x-5) ÷ (x+3)
    (v) (3x3-4x2-10x+8) ÷ (3x-2)
    (vi) (8x4-2x2+6x+5) ÷ (4x+1)

  9. Factorise x3−5x2−2x +24

  10. Factorise each of the following polynomials using synthetic division:
    (i) x3-3x210x +24
    (ii) 2x3-3x2-3x+2
    (iii) 4x3+5x2+7x-6
    (iv) −7x+3+ 4x3
    (v) x3+x214x-24
    (vi) x3-7x+6
    (vii) x3-10x2-x+10
    (viii) x3-5x+4

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