#### 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