CBSE 2016 Mathematics Question Paper for Class 10

About this paper

This is the CBSE Class 10 Mathematics Summative Assessment II question paper, code 30/3 (Series JSR, Set 3), from the 2016 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, 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 triangle construction, heights and distances, probability, coordinate geometry, areas related to circles, and surface areas and volumes. Section D opens with a value-based question in which 50 schools share the cost of canvas for 1500 tents for flood victims. This copy has the questions only, without answers.

Exam

CBSE Class 10

Subject

Mathematics

Year

2016

Paper code

30/3

Maximum marks

90

Time allowed

3 hours + 15 min reading

Questions

31

Pages

15

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 ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.
2. The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.
3. Prove that the points (3, 0), (6, 4) and (−1, 3) are the vertices of a right-angled isosceles triangle.
4. A conical vessel with base radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water rises in the cylinder.
5. A motorboat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
6. Prove that the lengths of the tangents drawn from an external point to a circle are equal.