(English Medium) ICSE Class 10 - CISCE Important Questions for Mathematics

Find the values of k for which the quadratic equation 9x² - 3kx + k = 0 has equal roots.

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.

Find the value of k for which the following equation has equal roots.

x² + 4kx + (k² – k + 2) = 0

The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.

Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)² - 3x + 4 = 0

Solve the following equation:

`x - 18/x = 6` Give your answer correct to two significant figures.

Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.

px² – 4x + 3 = 0

If 3 is a root of the quadratic equation x² – px + 3 = 0 then p is equal to ______.

Solve the following quadratic equation:

x² + 4x – 8 = 0

Give your Solution correct to one decimal place.

(Use mathematical tables if necessary.)

The roots of the quadratic equation px² – qx + r = 0 are real and equal if ______.

The roots of quadratic equation x² – 1 = 0 are ______.

The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more, then each would have got Rs. 12 less. Find ‘x’.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.

The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:

The values of x and y are:

A car travels a distance of 72 km at a certain average speed of x km per hour and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.