Class 12 Maths Sample Papers, Test Papers, Notes | Important Questions

You can download the latest Sample Papers for CBSE Class 12 Mathematics from myCBSEguide. Chapter-related Revision Notes, Question Bank, and test papers are also available. The model papers and notes are available as PDF files for free download. Mathematics is a scoring subject provided you remember the formulas and know their application. To attain this level of competence, all you need is good practice, which is only possible if you have a well-structured question bank having a variety of questions. For this, the students can depend on class 12 Mathematics course material on myCBSEguide.

In a  world that is becoming dependent on science, technology, and engineering, Mathematics becomes an indispensable key for success not only for individuals but also for a country. To build professionals having a solid mathematics foundation it is important to begin at a basic level. Secondary and Senior Secondary Mathematics plays an important role in the overall career of a child. Hence, it should never be overlooked. 

Class 12 Mathematics Syllabus 2022-23

Students should be very sure about the one and only thing that is the syllabus. Before beginning the preparation for class 12 mathematics, students should check the detailed Class 12 Mathematics syllabus 2022-23 on myCBSEguide. Students having any doubts regarding the topic or deleted section can refer to the information available here.

The syllabus for CBSE Class 12 Mathematics 2022-23 has chapters like: Relations and Functions, Vectors and Three – Dimensional Geometry, Linear Programming, Probability, Calculus, Algebra etc. Given below is the chapter along with allotted marks.

Total time to solve this 80 marks question paper of class 12 Maths is three-hours. The CBSE has prescribed the following books for class 12 mathematics and students should follow them as the questions asked in the board examination will be based on them. 

Prescribed Books:

1. Mathematics Part I – Textbook for Class XII, NCERT Publication
2. Mathematics Part II – Textbook for Class XII, NCERT Publication
3. Mathematics Exemplar Problem for Class XII, Published by NCERT
4. Mathematics Lab Manual class XII, published by NCERT

Class 12 Maths Revision Notes

The revision notes for class 12 mathematics available on myCBSEguide has the key points of the chapters. They provide the instructions and ground rules, like basic formula with example and explanation, that will be helpful in solving the problems related to a specific chapter. We have detailed Class 12 Mathematics Revision Notes which can be easily downloaded in PDF format. Given below is the chapters list of revision notes available on our students' dashboard.  

Chapter Wise Revision Notes for Class 12 Maths

• Chapter -1 Relations and Functions
• Chapter -2 Inverse Trigonometric Functions
• Chapter -3 Matrices
• Chapter -4 Determinants
• Chapter -5 Continuity and Differentiability
• Chapter -6 Application of Derivatives
• Chapter -7 Integrals
• Chapter -8 Application of Integrals
• Chapter -9 Differential Equations
• Chapter -10 Vector Algebra
• Chapter -11 Three Dimensional Geometry
• Chapter -12 Linear Programming
• Chapter -13 Probability

Important Questions for Class 12 Mathematics

We have class 12 Maths important questions for almost every chapter in the syllabus. For example, you can find all the important questions with a complete solution for the chapter Probability by clicking on this link called Probability Class 12 Mathematics Important Questions. These questions are really helpful for the students struggling to chalk out which question needs the most attention. Likewise, we have such questions for every chapter. All you need to do is download myCBSEguide app and log it in. 

Class 12 Mathematics NCERT Solutions

For all the examinee of class 12 CSBE we advice practicing the NCERT questions (chapter-end) along with the chapter examples. NCERT becomes so important because CBSE strictly follows the NCERT books. For best results students should begin with NCERT, move on to reference books, practice previous year questions and at the end attempt class 12 full-lenght maths model question paper. Get Class 12 Maths NCERT Solutions on myCBSEguide app and website for free. Some of the chapters are listed below:

• NCERT Solutions class 12 Maths Relations and Functions
• NCERT Solutions class 12 Maths Vector Algebra
• NCERT Solutions class 12 Maths Probability
• NCERT Solutions class 12 Maths Matrices
• NCERT Solutions class 12 Maths Linear Programming

Class 12 Maths Sample Paper 2022-23

The one and only way to get good marks/grades on your boards is to practice as much as sample papers as you can. The CBSE released its sample paper for the 2022-23 examinations long back with its new marking scheme and blueprint. We, at myCBSEguide has worked on it and prepared 10 sets of class 12 mathematics sample papers for our students with cent percent genuine solutions verified by our experts. These Sample Papers are available for free download in the myCBSEguide app and website in PDF format. Our Sample Paper for Class 12 Maths 2022-23 can help students find answers to the most frequently asked question.

If you are searching for the best CBSE Sample Papers Class 12 Mathematics 2023, you must visit our student dashboard. For all the above-mentioned products, myCBSEguide is an unmatched one-stop solution.

Class 12 Maths Case Study Questions

The main focus of our latest education policy is competency-based education. One of the best ways to inculcate this competency-based learning is through case-based questions. Hence, of late the CBSE has introduced case study questions in the CBSE curriculum.  Section E of the official class 12 Maths sample paper is devoted to case-based questions. It has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub-parts.

However, you may find such questions over the internet or in any publication books, we do not guarantee their authenticity. We have selected the best of Case Study Questions for Class 12 Mathematics which have been value-added by our genius experts. Download myCBSEguide App, if you wish to access them. Unlike last year where the sub-parts of these CBQs had objective questions, this year subjective questions have been asked with internal choice. 

Ideally, these types of questions prepare our children to face real-life challenges with the knowledge acquired in their classrooms. The idea is to make the students apply or use, whatever they are learning, in their day-to-day life. Therefore, with this noble intent, the CBSE is emphasizing case studies and competency-based education.

Subjective Case Study Question for Class 12 Maths

In a street two lamp posts are 600 feet apart. The light intensity at a distance d from the first (stronger) lamp post is 1000d2, the light intensity at distance d from the second (weaker) lamp post is 125d2 (in both cases the light intensity is inversely proportional to the square of the distance to the light source). The combined light intensity is the sum of the two light intensities coming from both lamp posts.

1. If l(x) denotes the combined light intensity, then find the value of x so that I(x) is minimum.
2. Find the darkest spot between the two lights.
3. If you are in between the lamp posts, at distance x feet from the stronger light, then write the combined light intensity coming from both lamp posts as function of x.
   OR

4. Find the minimum combined light intensity?

What makes Maths an important subject?

Senior Secondary or Class 12 is a crucial stage in a student's life. They have to be serious, they should have clear goals and objectives. Even if they are confused, all they need to do is play their current role (of being a student) in genuine terms, without cheating, without feigning. Be honest with your subjects, give your 100% and the output will surely surprise you. Take, for example, a subject like Mathematics may be complex at the same time easy for some. It is not important whether you will continue with it in your further studies or not. What is important is knowing it, and doing justice to the subject. Hence, by this time students should be having a clear picture of the purpose behind the existence of these subjects and their importance in life. Here's the perspective that a senior secondary student should be having if they have studied Mathematics.

• Common Language: Mathematics cuts across any other language boundaries and can be considered a common language. It is also called the language of science. It holds importance as a 'universal language' because it is universally understood across different cultures, countries, and languages.
• Analytical Skills: Mathematics develops the skills of posing hypotheses, experimentation, analysis, recognizing patterns, finding proofs, deducing conclusions, and problem-solving. It hones the curiosity of a child and encourages abstract thinking.
• Universally Applicable: Mathematics is applicable in each and every aspect of our life. It is not limited to sums and numbers. It is involved in our day-to-day life. It is a set of logical ideas.
• Leads the Way: We can understand Mathematics to be like a toolbox that has every necessary tool needed while pursuing any discipline like science, engineering, and technology. 
• A New Perspective: Being good in mathematics is a choice, knowing/studying it is enough. If you are studying mathematics with genuine intent, it allows you to understand the world better. Unravelling the nuances behind how mathematics works can open your eyes and help you see the world around you in a new way.