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

Construct a quadrilateral ABCD, when:
AB = 7.2 cm, BC = 5.8 cm, CD = 6.3 cm, AD = 4.3 cm and angle A = 75°.

Construct a quadrilateral ABCD, when:
∠ A = 90^o, AB = 4.6 cm, BD = 6.4 cm, AC = 6.0 cm and CD = 4.2 cm.

Construct a quadrilateral ABCD, when:
AB = 3.8 cm, AC = 4.8 cm, AD = 2.8 cm, angle A = 105° and angle B = 60°.

Construct a quadrilateral ABCD, when:
BC = 7.5 cm AC = 5.8 cm, AD = 3.6 cm, CD = 4.2 cm and angle A = 120°.

Construct a quadrilateral ABCD, when:
AD = AB = 4 cm, BC = 2.8 cm, CD = 2.5 cm and angle BAD = 45°.

Construct a quadrilateral ABCD, when:
AB = 6.3 cm, BC = CD = 4.2 cm and ∠ABC = ∠BCD = 90°.

Using ruler and compasses only, construct the quadrilateral ABCD, having given AB = 5 cm, BC = 2.5 cm CD = 6 cm, ∠BAD = 90^o and diagonal BD = 5.5 cm.

Using ruler and compasses only, construct the quadrilateral ABCD, having given AB = 5 cm, BC = 2.5 cm, CD = 6 cm. angle BAD = 90^o and the diagonal AC = 5.5 cm.

The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides.
Let the sides be x cm, y cm, and (37 - x - y) cm. Also, let the lengths of altitudes be 6a cm, 5a cm, and 4a cm.

The medians of a triangle ABC intersect each other at point G. If one of its medians is AD,
prove that:
(i) Area ( ΔABD ) = 3 x Area ( ΔBGD )
(ii) Area ( ΔACD ) = 3 x Area ( ΔCGD )
(iii) Area ( ΔBGC ) = `1/3` x Area ( ΔABC ).

Find the mean of 43, 51, 50, 57 and 54.

Find the mean of the first six natural numbers.

Find the mean of the first ten odd natural numbers.

In a series of tests, A appeared for 8 tests. Each test was marked out of 30 and averages 25. However, while checking his files, A could only find 7 of the 8 tests. For these, he scored 29, 26, 18, 20, 27, 24 and 29.
Determine how many marks he scored for the eighth test.

Find the mean of all factors of 10.

Find x if 9, x, 14, 18 x, x, 8, 10 and 4 have a mean of 11.

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination are 71,
find the ratio of the number of boys to the number of girls.

The mean weight of 120 students of a school is 52.75 kg. If the mean weight of 50 of them is 51 kg,
find the mean weight of the remaining students.

Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.

The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88.
Find the correct mean.