#### 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