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Time allowed

1 hr 30 mins

Class IX – Mathematics - Lesson 1 & 2

28 Jun 2018, 4.30 pm IST

MM

40

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1

State whether the following are polynomials or not

  1. 2x2+ 3x
  2. 0
  3. 2t + 3
  4. y2+3y+ 2

2

2

If 5x + 2y = 12 and xy = 10, find the value of 25x2 + 4y2.

2

3

Find the value of p, if (x – 2) is a factor of 4x3 - 3x2 – 4x - p.

2

4

Find the value of a, if

632-23=32-a3 

2

5

Express 0.123 in the form pq, where p and q are integers and q ≠ 0.

2

6

If xy+yx= -1 then find the value of x3 - y3

2

7

Without actually calculating the cubes, find the value of 483 – 303 – 183.

2

8

Simplify

i 7+57-5+7-57+5

ii 91/3×271/231/6 ×3-3/2

3

9

If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.

3

10

If x2 +1x2 = 27, find the values of each of the following

  1. x+1x
  2. x3+1x3

4

11

If a + b + c = 9 and ab + bc + ca = 26, find the value of a3 + b3 + c3 - 3abc.

4

12

Classify the following numbers as rational or irrational with justification

(i) 196 (ii) 318 (iii) 10.124124... (vi) 1.010010001...

4

13

  1. Locate 10 on the number line
  2. Represent 5.6 on the number line

4

14

Factorise

i 22x3+8y3-27z3+182xyz

ii  1 + 64x3

iii 2x3  3x2  17x + 30

6