(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a² - b².

If a - b = 4 and a + b = 6; find
(i) a² + b²
(ii) ab

If a + `1/a`= 6 and  a ≠ 0 find :
(i) `a - 1/a   (ii)  a^2 - 1/a^2`

If a - `1/a`= 8 and  a ≠ 0 find :
(i) `a + 1/a   (ii)  a^2 - 1/a^2`

If a² - 3a + 1 = 0, and a ≠ 0; find: 

1. `a + 1/a`         
2. `a^2 + 1/a^2`

The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

If 3x + 4y = 16 and xy = 4, find the value of 9x² + 16y².

If a² - 5a - 1 = 0 and a ≠ 0 ; find:

1. `a - 1/a`
2. `a + 1/a`
3. `a^2 - 1/a^2`

Factorise by taking out the common factors : 
2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)

Factories by taking out common factors :
xy(3x² - 2y²) - yz(2y² - 3x²) + zx(15x² - 10y²)

Factories by taking out common factors :
ab(a² + b² - c²) - bc(c² - a² - b²) + ca(a² + b² - c²)

Factories by taking out common factors :
2x(a - b) + 3y(5a - 5b) + 4z(2b - 2a)

Factorise:

`x^2 + 1/(4x^2) + 1 - 7x - 7/(2x)`

Factorise : `(9a)^2 + 1/(9a)^2 - 2 - 12a + 4/(3a)`

Factorise : `x^2 + [a^2 + 1]/a x + 1`

Factorise:

`x^4 + y^4 - 27x^2y^2`

Factorise : 4x⁴ + 9y⁴ + 11x²y²

Factorise : `x^2 + 1/x^2 - 3`

Factorise : a - b - 4a² + 4b²