CBSE Class 10 Maths (Standard) Previous Year Question Paper 2022 - Set 1

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This is the CBSE Class 10 Mathematics (Standard) Previous Year Question Paper from the Term-II 2022 board exams, Set 1 (Code 30/2/1). The paper is designed for a duration of 2 hours and carries a maximum of 40 marks. It contains a total of 14 compulsory questions, divided into three sections: Section A, Section B, and Section C. Section A includes 6 questions worth 2 marks each, with internal choices in two questions. Section B comprises 4 questions of 3 marks each, featuring internal choice in one question. Section C consists of 4 questions, each carrying 4 marks, including internal choice in one question and two case study-based questions. Solving this previous year's board question paper is crucial for students to understand the exam pattern, question types, and marking scheme, thereby enhancing their preparation and performance.

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Quick info

BoardCBSE
Class10
SubjectMaths
Session2022
LanguageEnglish
TypePrevious Year Question Paper
Exam typeBoard Exam

Paper pattern

The question paper contains 14 questions divided into 3 sections (A, B, C). Section A has 6 questions (2 marks each), Section B has 4 questions (3 marks each), and Section C has 4 questions (4 marks each).

Topics covered

Paper topics

  • Quadratic Equations
  • Arithmetic Progressions
  • Coordinate Geometry
  • Circles
  • Constructions
  • Trigonometry
  • Surface Areas and Volumes
  • Statistics and Probability

Important topics

  • Quadratic Equations
  • Arithmetic Progressions
  • Circles
  • Surface Areas and Volumes
  • Case Study Questions

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Question paper text

Date: 05/05/2022

Question Paper Code

30/2/1

Time: 2 Hrs.

Class-X

Max. Marks: 40

MATHEMATICS (Standard) Term-II (CBSE 2022)

GENERAL INSTRUCTIONS

  1. This question paper contains 14 questions. All questions are compulsory.
  2. This question paper is divided into 3 Sections – Section A, B and C.
  3. Section-A comprises of 6 questions (Q. Nos. 1 to 6) of 2 marks each.

Internal choice has been provided in two questions.

  1. Section-B comprises of 4 questions (Q. Nos. 7 to 10) of 3 marks each.

Internal choice has been provided in one question.

  1. Section-C comprises of 4 questions (Q. Nos. 11 to 14) of 4 marks each. An internal choice has been provided in one question. It also contains two case study based questions.
  2. Use of calculator is not permitted.

SECTION A

Question Numbers 1 to 6 carry 2 marks each.

  1. Solve the quadratic equation : <math>x^2 + 2\sqrt{2}x - 6 = 0</math> for x.

Solution

<math>x^2 + 2\sqrt{2}x - 6 = 0</math> <math display="block">\therefore x^2 + 3\sqrt{2}x - \sqrt{2}x - 6 = 0</math> <math display="block">x\left(x+3\sqrt{2}\right)-\sqrt{2}\left(x+3\sqrt{2}\right)=0</math> <math display="block">\left(x+3\sqrt{2}\right)\!\left(x-\sqrt{2}\right)=0</math> <math>\Rightarrow</math> <math>x = -3\sqrt{2}, \sqrt{2}</math> [1] [1]

2. (a) Which term of the A.P. <math>-\frac{11}{2}</math>, -3, <math>-\frac{1}{2}</math>,.... is <math>\frac{49}{2}</math>?

OR

  1. Find a and b so that the numbers a, 7, b, 23 are in A.P.

Solution

  1. Given A.P.

<math>-\frac{11}{2}</math>, -3, <math>-\frac{1}{2}</math>, .....

Here,

<math>a = -\frac{11}{2}</math>, <math>d = -3 + \frac{11}{2} = \frac{11 - 6}{2} = \frac{5}{2}</math>

[\frac{1}{2}]

<math>t_n = \frac{49}{2}</math>

<math display="block">a+(n-1)d=\frac{49}{2}</math>

[\frac{1}{2}]

or <math>-\frac{11}{2} + (n-1)\left(\frac{5}{2}\right) = \frac{49}{2}</math>

or <math>-11 + 5n - 5 = 49</math> <math>\Rightarrow</math> 5n = 49 + 16 <math>\Rightarrow</math> 5n = 65 <math display="block">\Rightarrow n = \frac{65}{5} = 13</math> <math>\Rightarrow</math> <math>n = 13</math>

[\frac{1}{2}]

[\frac{1}{2}]

Frequently asked questions

What is this document?

This is the official CBSE Class 10 Mathematics (Standard) Previous Year Question Paper from the 2022 Term-II board examinations, Set 1.

What is the duration and maximum marks for this paper?

The total time allotted for this paper is 2 hours, and the maximum marks are 40.

How is the question paper structured?

The paper is divided into three sections: Section A (6 questions, 2 marks each), Section B (4 questions, 3 marks each), and Section C (4 questions, 4 marks each), including case study questions.

How can solving previous year papers help?

Solving previous year question papers helps students understand the exam pattern, difficulty level, and marking scheme, improving their confidence and performance.

What are the key topics covered in this paper?

The paper covers topics such as Quadratic Equations, Arithmetic Progressions, Circles, Trigonometry, Surface Areas and Volumes, and Statistics, among others.

Important links

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