CBSE 2015 Mathematics Question Paper for Class 10

About this paper

This is the CBSE Class 10 Mathematics Summative Assessment II question paper, code 30/2/1 (Series RLH/2, Set 1), from the 2015 examination. It carries 90 marks over three hours plus 15 minutes of reading time and has 31 compulsory questions in four sections: four one-mark short answers, six two-mark, ten three-mark and eleven four-mark questions. Calculators are not allowed. The questions cover arithmetic progressions, quadratic equations, circles and tangents, a tangent construction, heights and distances, probability, coordinate geometry, areas related to circles, and surface areas and volumes. The last question is value-based, about distributing milk in frustum-shaped containers at a camp for flood victims. This copy has the questions only, without answers.

Exam

CBSE Class 10

Subject

Mathematics

Year

2015

Paper code

30/2/1

Maximum marks

90

Time allowed

3 hours + 15 min reading

Questions

31

Pages

12

Answers included

No, questions only

Paper pattern

• Section A

  4 marks

  Questions 1–4, one mark each

• Section B

  12 marks

  Questions 5–10, two marks each

• Section C

  30 marks

  Questions 11–20, three marks each

• Section D

  44 marks

  Questions 21–31, four marks each, including a value-based question

Topics covered

• Arithmetic progressions
• Quadratic equations
• Circles and tangents
• Constructions
• Heights and distances
• Probability
• Coordinate geometry
• Areas related to circles
• Surface areas and volumes

Questions from this paper

1. A pole casts a shadow of length 2√3 m on the ground when the sun's elevation is 60°. Find the height of the pole.
2. For what values of k are the points (8, 1), (3, −2k) and (k, −5) collinear?
3. In an A.P., the 12th term is −13 and the sum of its first four terms is 24. Find the sum of its first ten terms.
4. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14)
5. Draw a circle of radius 3 cm. From a point P, 7 cm away from its centre, draw two tangents to the circle and measure the length of each tangent.
6. A vessel full of water is an inverted cone of height 8 cm with an open top of radius 5 cm. When 100 spherical lead balls are dropped in, one-fourth of the water flows out. Find the radius of a ball.