CBSE Class 10 Mathematics Term 2 Sample Paper (Set-3)

CBSE Class 10 Mathematics Term 2 Sample Paper

Class – X Exam 2021-22

Mathematics Standard (041)

Time Allowed: 120 minutes (Maximum Marks: 40)

General Instructions:

  1. The question paper consists of 14 questions divided into 3 sections A, B,
  2. All questions are
  3. Section A comprises of 6 questions of 2 marks Internal choice has been provided in two questions.
  4. Section B comprises of 4 questions of 3 marks Internal choice has been provided in one question.
  5. Section C comprises of 4 questions of 4 marks An internal choice has been provided in one question. It contains two case study based questions. (08)


1. Find the positive value of k for which x2 − 8x + k = 0, will have real roots.


If x2 + y2 = 25, xy = 12, then what is the value of x ?

2. If seven times the 7th term of an AP is equal to eleven times the 11th  term, then what will be its 18th  term.

3. In figure, O is the centre of the circle and LN is a If PQ is a tangent to the circle at K and +KLN = 30º, find +PKL.

4. A metallic sphere of total volume π is melted and recast into the shape of a right circular cylinder of radius 5 cm. What is the height of cylinder?

5. The data regarding the height of 50 girls of class X of a school is given below :

Height (in cm) 120-130 130-140 140-150 150-160 160-170 Total
Number of girls 2 8 12 20 8 50

Change the above distribution to ‘more than type’ distribution.

6. Convert the following distribution to more than type, cumulative frequency distribution :

Class 50-60 60-70 70-80 80-90 90-100
Frequency 12 18 10 15 5


Find the median for the given frequency distribution:

Class 40-45 45-50 50-55 55-60 60-65 65-70 70-75
Frequency 2 3 8 6 6 3 2

Section B

7. Find the sum of the following series.

8. Two points A and B are on the same side of a tower and in the same straight line with its base. The angle of depression of these points from the top of the tower are 60c and 45c If the height of the tower is 15 m, then find the distance between these points.

9. Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the Measure the length of a tangent and verify it by actual calculation.

10. A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.


The radii of two right circular cylinders are in the ratio of 2 | 3 and their height are in the ratio of 5 | 4. Calculate the ratio of their curved surface area and radio of their volumes.

Section C

11. In figure PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and +QOR is a diameter. If +POR = 130c and S  is a point on the circle, find +1 + +2.

12. If the mean of the following frequency distribution is 91, and sum of frequency is 150, find the missing frequency x and y: 

Class 0- 30 30- 60 60- 90 90-120 120-150 150-180
Frequency 12 21 x 52 y 11


Daily wages of 110 workers, obtained in a survey, are tabulated below :

Daily Wages (in<) 100-120 120-140 140-160 160-180 180-200 200-220 220-240
Number of Workers 10 15 20 22 18 12 13

Compute the mean daily wages an modal daily wages of these workers.


11. Nidhi and Ria are very close friends. Nidhi’s parents own a Maruti Alto. Ria’s parents own a Toyota Liva. Both the families decide to go for a picnic to Somnath temple in Gujrat by their own cars.

Nidhi’s car travels x km/h while Ria’s car travels 5 km/h more than Nidhi’s car. Nidhi’s car took 4 hrs more than Ria’s car in covering 400 km.

  • Which of the following quadratic equation describe the speed of Nidhi’s car?
  • How much time did Ria take to travel 400 km?

12. From the observation deck of a seaside building 200 m high, Jignesh sees two fishing boats in the The angle of depression to the nearer boat is 60c while for the boat farther away the angle is 45c .

    • How far out to sea is the nearer boat?
    • How far apart are the two boats?

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