ICSE ICSE Class 8 - CISCE Question Bank Solutions for Mathematics

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:

(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

Subtract the sum of 5y² + y – 3 and y² – 3y + 7 from 6y² + y – 2.

The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. Find the value of n.

What must be added to x⁴ – x³ + x² + x + 3 to obtain x⁴ + x² – 1 ?

Let M = {letters of the word REAL} and N = {letters of the word LARE}. Write sets M and N in roster form and then state whether;
M ⊆ N is true.

How much more than 2x² + 4xy + 2y² is 5x² + 10xy – y² ?

If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.

Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.

How much less 2a² + 1 is than 3a² – 6 ?

Let M = {letters of the word REAL} and N = {letters of the word LARE}. Write sets M and N in roster form and then state whether
N ⊆ M is true.

Let M = {letters of the word REAL} and N = {letters of the word LARE}. Write sets M and N in roster form and then state whether
M = N is true.

Write two sets A and B such that A ⊆ B and B ⊆ A.State the relationship between sets A and B.

The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

If x = 6a + 8b + 9c ; y = 2b – 3a – 6c and z = c – b + 3a ; find :

1. x + y + z
2. x – y + z
3. 2x – y – 3z
4. 3y – 2z – 5x

Calculate the number of sides of a regular polygon, if:  its interior angle is five times its exterior angle.

The sides of a triangle are x² – 3xy + 8, 4x² + 5xy – 3 and 6 – 3x² + 4xy. Find its perimeter.

Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.

The perimeter of a triangle is 8y² – 9y + 4 and its two sides are 3y² – 5y and 4y² + 12. Find its third side.

Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.

The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.