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

Factorise the following:
(x + y)³ - x - y

Factorise the following:
y⁴ + y² + 1

Factorise the following:

(a² – b²)(c² – d²) – 4abcd

Express each of the following as the difference of two squares:
(x² - 2x + 3)(x² + 2x + 3)

Express each of the following as the difference of two squares:
(x² - 2x + 3) (x² - 2x - 3)

Express each of the following as the difference of two squares:
(x² + 2x - 3) (x² - 2x + 3)

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: QR = QT

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: RT bisects angle R

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: ∠RTS = 90°

ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.

Prove that: BP bisects ∠ABC.

ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.

Prove that: ∠APB is a right angle.

In the given figure, MP is the bisector of ∠P and RN is the bisector of ∠R of parallelogram PQRS. Prove that PMRN is a parallelogram.

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that:CE is the bisector of angle C and angle DEC is a right angle

Observe the given frequency table to answer the following:

a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.

Construct a square with each side 4.3cm

Construct a square ABCD with AC = 6.5cm

Construct a square with perimeter = 18cm.

Construct a square whose area is 25 sq. cm.

In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.