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

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.

If different values of variable x are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5 and 11.1;
find
(i) the mean ` barx `

(ii) the value of  ` sum (x_i - barx)`

The mean of 100 observations is 40. It is found that an observation 53 was misread as 83.
Find the correct mean.

If the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11,
find:
(i) The value of x;
(ii) The mean of first three observations.

The mean of 5 numbers is 18. If one number is excluded, the mean of the remaining number becomes 16. Find the excluded number.

Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: divided by 2.

In the following figure, write BC, AC, and CD in ascending order of their lengths.

Find ‘x’, if:

Find 'x', if :

Find 'x', if: