ICSE Class 10 Maths Important Questions

Mathematics is a subject that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. Important questions of Class 10 maths is the shortest possible preparation tester available. These important questions also provide the students with a brief knowledge of the question pattern, essential topics, and important question type. By following ICSE Class 10 Maths important questions, students can evaluate their performance and preparations so far. All the essential concepts and topics of Class 10 Maths are covered while framing the important questions to help the students to improve their conceptual learning and problem-solving skills.

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The Important Questions of ICSE Class 10 Maths are given below:

  1. Ben deposits a certain sum of money each month in a recurring deposit account of a bank. If the rate of interest is 8% per annum and Ben gets Rs. 8,088 from the bank after 3 years, find the value of his monthly instalment.
  2. A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is:
    1. a green ball
    2. a white or a red ball
    3. neither a green ball nor a white ball
  3. Find the minimum length in cm and correct to the nearest whole number of a thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. The width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m. Find the area of the metal sheet required if 10% of it is wasted in cutting, overlapping etc.
  4. Geetha repays her total loan of 1,18,000 by paying instalments every month. If the instalment for the first month is 1,000 and it increases by 100 every month, what amount will she pay as the 30th instalment of the loan? What amount of the loan has she to still pay after the 30th instalment?
  5. In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
    Question 5


    1. ∠OBD
    2. ∠AOB
    3. ∠BED
  6. Prove that
    Question 6
  7. Prove by factor theorem that

    1. (x − 2) is a factor of 2 – 7x – 2
    2. (2x + 1) is a factor of 4 + 12 + 7x +1
    3. (3x − 2) is a factor of 18 − 3 + 6x – 12
  8. Draw a histogram for the following distribution:
    Question 8
  9. Find the values of x which satisfy the inequation:
    Question 9

    Plot the solution on the number line.

  10. In the given figure. line AB meets the y-axis at point A. The line through C(2, 10) and D intersects line AB at a right angle at point R. Find
    1. equation of line AB
    2. equation of line CD
    3. co-ordinates of points E and D
  11. Find a GP for which the sum of the first two terms is −4 and the fifth term is 4 times the third term.
  12. A man invests a certain sum on buying 15% Rs. 100 shares at 20% premium. Find
    1. His income from one share
    2. The number of shares bought to have an income from the dividend as Rs. 6480
    3. The sum invested
  13. Attempt this question on a graph paper.
    1. Plot A (3, 2) and B (5, 4) on a graph paper. Take 2 cm = 1 unit on both axes.
    2. Reflect A and B in the x-axis to A’ and B’, respectively. Plot these points also on the same graph paper.
    3. Write down:
      1. the geometrical name of the figure ABB’A’
      2. the measure of angle ABB’
      3. the image of A” of A when A is reflected in the origin
      4. the single transformation that maps A’ to A”
  14. A school has 630 students. The ratio of the number of boys to the number of girls is 3:2. This ratio changes to 7:5 after the admission of 90 new students. Find the number of newly admitted boys.
  15. Prove:
    Question 15
  16. Solve for x using the quadratic formula. Write your answer correct to two significant figures.


  17. In the given figure, DE ‖ BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. Find the lengths of ME and DM.
    ICSE Class 10 Maths Important Questions-5
  18. One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.
  19. A circus tent is in the shape of a cylinder surmounted by a conical top of the same diameter. If their common diameter is 56 m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent.
  20. Ankit deposits Rs 2,250 per month in a recurring deposit account for a period of 3 years. At the time of maturity, he will get Rs 90,990.
    1. Find the rate of simple interest per annum
    2. Find the total interest earned by Ankit.

Practise This Question

If Δ is an equilateral triangle such that AD is perpendicular to BC , then AD2 =