CBSE Class 10 Mathematics 2022 — Set 3

Questions in this 2022 Mathematics paper (Set 3)

All 14 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   Solve the quadratic equation for x: x^2 - 2ax - (4b^2 - a^2) = 0
2. 2.
   Find the sum of first 20 terms of an AP in which d = 5 and a_20 = 135.
3. 3.
   Find the mode of the given frequency distribution: Class: 15-25, 25-35, 35-45, 45-55, 55-65, 65-75 Frequency: 6, 11, 22, 23, 14, 5
4. 4.
   150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and are completely immersed in water. Find the rise in the level of water in the cylindrical vessel.
5. 5.
   For what value of 'n', are the nth terms of the APs: 9, 7, 5, ..... and 15, 12, 9, ..... the same?
6. 6.
   In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠OPR = 45°, then prove that ORPQ is a square.
7. 7.
   Draw a line segment AB of length 8 cm and locate a point P on AB such that AP : PB = 1 : 5.
8. 8.
   The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance between the two poles.
9. 9.
   The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained: Weight (kg): 100-110, 110-120, 120-130, 130-140, 140-150 Number of animals: 4, 12, 23, 8, 3 Find the mean weight (in kg) of animals, using assumed mean method.
10. 10.
    For the following frequency distribution, find the median: Class: 1400-1550, 1550-1700, 1700-1850, 1850-2000 Frequency: 6, 13, 25, 10
11. 11.
    In Figure 3, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A chord AB of the bigger circle meets the smaller circle at C. Show that C bisects AB.
12. 12.
    A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Ten seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
13. 13 (a).
    Case Study: A rectangular in-ground swimming pool is installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq m. (a) Based on the information, form a quadratic equation in terms of x.
14. 13 (b).
    Case Study: A rectangular in-ground swimming pool is installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq m. (b) Find the width of the sidewalk around the pool.
15. 14 (a).
    Case Study: John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps and to buy a cake from a bakery shop. The dimensions are: Cake: Cylindrical shape with diameter 24 cm and height 14 cm. Cap: Conical shape with base circumference 44 cm and height 24 cm. (a) How many square cm paper would be used to make 4 such caps?
16. 14 (b).
    Case Study: John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps and to buy a cake from a bakery shop. The dimensions are: Cake: Cylindrical shape with diameter 24 cm and height 14 cm. Cap: Conical shape with base circumference 44 cm and height 24 cm. The bakery shop sells cakes by weight (0.5 kg, 1 kg, 1.5 kg, etc.). To have the required…

Class 10 Mathematics exam pattern (80 marks)

The theory paper carries 80 marks over 3 hours (38 questions, with internal choice in some). Section-wise structure:

Structure per the CBSE 2023-24 sample-paper design; question wording varies by set.

Prepare with

How to use these papers

1. 1Start chapter-wise early in the year — solve only the Mathematics questions from a chapter you have just finished.
2. 2Switch to full timed papers 2–3 months before the exam: one complete set in the real time limit, no notes.
3. 3Self-mark against the marking scheme, then fix every mistake with our free NCERT solutions.
4. 4Re-attempt your weakest chapters until the recurring question types feel routine.

CBSE Class 10 Mathematics 2022 paper — FAQ