(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

For the polynomial x⁵ – x⁴ + x³ – 8x² + 6x + 15, the maximum number of linear factors is ______.

If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.

If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.

The daily wages of 80 workers in a project are given below.

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1. the median wage of the workers.
2. the lower quartile wage of workers.
3. the numbers of workers who earn more than Rs. 625 daily.

Using properties of proportion, solve for x. Given that x is positive:

`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`

The weight of 50 workers is given below:

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:

1) The upper and lower quartiles.

2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.

The marks obtained by 100 students in a Mathematics test are given below:

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the:

1) Median.

2) Lower quartile.

3) A number of students who obtained more than 85% marks in the test.

4) A number of students who did not pass in the test if the pass percentage was 35.

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`

Find the fourth proportional to 1.5, 4.5 and 3.5

Find the fourth proportional to 3a, 6a² and 2ab²

Find the third proportional to `2 2/3` and 4

Find the third proportional to a – b and a² – b²

Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`

Find the mean proportional between a – b and a³ – a²b

If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

If x², 4 and 9 are in continued proportion, find x.

If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.