CBSE Class 10 Mathematics 2022 — Set 1

Questions in this 2022 Mathematics paper (Set 1)

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 (a).
   Find the sum of first 30 terms of an A.P.: -30, -24, -18, ...
2. 2.
   A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.
3. 3 (a).
   Find the value of m for which the quadratic equation (m - 1)x^2 + 2(m - 1)x + 1 = 0 has two real and equal roots.
4. 4.
   Find the mode of the following frequency distribution: Class: 10-20, 20-30, 30-40, 40-50, 50-60 Frequency: 15, 10, 12, 17, 4
5. 5.
   The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.
6. 6.
   Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
7. 7.
   For what value of x is the median of the following frequency distribution 34.5? Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 Frequency: 3, 5, 11, 10, x, 3, 2
8. 8.
   Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters, each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.
9. 9 (a).
   The angle of elevation of the top of a building from the foot of a tower is 30 degrees and the angle of elevation of the top of the tower from the foot of the building is 60 degrees. If the tower is 50 m high, find the height of the building.
10. 10.
    Following is the daily expenditure on lunch by 30 employees of a company: Daily Expenditure (in Rupees): 100-120, 120-140, 140-160, 160-180, 180-200 Number of Employees: 8, 3, 8, 6, 5 Find the mean daily expenditure of the employees.
11. 11 (a).
    From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.
12. 12.
    In Figure 1, a triangle ABC with ∠B = 90° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.
13. 13 (a).
    (Case Study) Matchstick patterns are based on linear relations. In a pattern: Figure 1 has 4 triangles, Figure 2 has 6 triangles, Figure 3 has 8 triangles, and so on. Write the A.P. for the number of triangles used in the figures and find the nth term of this A.P.
14. 13 (b).
    (Case Study) Matchstick patterns are based on linear relations. In a pattern: Figure 1 uses 5 matchsticks, Figure 2 uses 9 matchsticks, Figure 3 uses 13 matchsticks (each figure uses 4 more matchsticks than the previous). Which figure has 61 matchsticks?
15. 14 (a).
    (Case Study) Gadisar Lake, Jaisalmer: From a point A, h m above water level, the angle of elevation of the top of Chhatri (point B) is 45° and the angle of depression of its reflection in water (point C) is 60°. Height of Chhatri above water level is 10 m. Draw a well-labelled figure based on the above information.
16. 14 (b).
    (Case Study) Gadisar Lake is in Jaisalmer, Rajasthan. From a point A above the water level, the angle of elevation of the top of a Chhatri (point B) is 45 degrees and the angle of depression of its reflection in water (point C) is 60 degrees. If the height of the Chhatri above water level is approximately 10 m, find the height (h) of point A above the water level. (Use sqrt(3) = 1.73)

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