CBSE 2018 Maths Question Paper for Class 10

About this paper

This is the CBSE Class 10 Mathematics question paper, code 30/3 (Set 3), from the 2018 board examination. It carries 80 marks over three hours plus 15 minutes of reading time and has 30 compulsory questions in four sections: six one-mark, six two-mark, ten three-mark and eight four-mark questions. There is no overall choice, but internal choices are given in four three-mark and three four-mark questions, and calculators are not allowed. The paper covers the full-year syllabus, from real numbers and polynomials to statistics, including a median-salary table and an ogive. One frustum question also asks why buckets made of ordinary plastic should be avoided. This copy has the questions only, without answers.

Exam

CBSE Class 10

Subject

Mathematics

Year

2018

Paper code

30/3

Maximum marks

80

Time allowed

3 hours + 15 min reading

Questions

30

Pages

11

Answers included

No, questions only

Paper pattern

• Section A

  6 marks

  Questions 1–6, one mark each

• Section B

  12 marks

  Questions 7–12, two marks each

• Section C

  30 marks

  Questions 13–22, three marks each; internal choice in four

• Section D

  32 marks

  Questions 23–30, four marks each; internal choice in three

Topics covered

• Real numbers
• Polynomials
• Pair of linear equations
• Quadratic equations
• Arithmetic progressions
• Triangles and similarity
• Coordinate geometry
• Trigonometric identities
• Heights and distances
• Circles and constructions
• Areas, surface areas and volumes
• Statistics and probability

Questions from this paper

1. Given that √2 is irrational, prove that 5 + 3√2 is an irrational number.
2. Find all zeroes of the polynomial 2x⁴ − 9x³ + 5x² + 3x − 1 if two of its zeroes are 2 + √3 and 2 − √3.
3. A plane left 30 minutes late and, to reach its destination 1500 km away on time, had to increase its speed by 100 km/h. Find its usual speed.
4. If tan 2A = cot (A − 18°), where 2A is an acute angle, find the value of A.
5. From the top of a 100 m high lighthouse, the angles of depression of two ships on the same side are 30° and 45°. If one ship is exactly behind the other, find the distance between them.
6. Prove that in a right triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.