CBSE 2014 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 HRS, from the 2014 examination. It carries 90 marks over three hours plus 15 minutes of reading time and has 34 compulsory questions in four sections, from one-mark multiple-choice items to four-mark long answers. Calculators are not allowed. The paper covers the second-term syllabus: quadratic equations, arithmetic progressions, circles and tangents, constructions, heights and distances, probability, coordinate geometry, areas related to circles, and surface areas and volumes. Section D includes a value-based question on students planting trees to reduce air pollution. This copy has the questions only, without answers, and the last printed page is not included.

Exam

CBSE Class 10

Subject

Mathematics

Year

2014

Paper code

30/3

Maximum marks

90

Time allowed

3 hours + 15 min reading

Questions

34

Pages

14

Answers included

No, questions only

Paper pattern

• Section A

  8 marks

  Questions 1–8, multiple-choice, one mark each

• Section B

  12 marks

  Questions 9–14, two marks each

• Section C

  30 marks

  Questions 15–24, three marks each

• Section D

  40 marks

  Questions 25–34, four marks each, including a value-based question

Topics covered

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

Questions from this paper

1. Find the value of p so that the quadratic equation px(x − 3) + 9 = 0 has equal roots.
2. Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also find the coordinates of the point of division.
3. Water in a canal 6 m wide and 1.5 m deep is flowing at 4 km/h. How much area will it irrigate in 10 minutes if 8 cm of standing water is needed for irrigation?
4. From the top of a 60 m high building, the angles of depression of the top and the bottom of a tower are 45° and 60° respectively. Find the height of the tower.
5. A motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
6. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.