NCERT Class 12 Maths Notes

Komal MiglaniUpdated on 22 Jul 2025, 09:15 PM IST

Class 12 Mathematics plays a crucial role in broad exams, and sometimes students might feel some difficulties while solving the questions, as it contains some advanced and complex topics that require a clear understanding of concepts and regular practice. We provide you with the best notes on class 12 maths to make it easy for you. These notes help you not just for board exams but also for competitive exams like JEE, NDA, and others. Apart from this, class 12th maths is also important to solve the numerical problems in Physics. To learn these topics faster and in an organised way, having a structured summary of each chapter is very helpful. To understand the variety of questions and how hard they are, students practice with sample papers and previous year's question papers from Class 12.

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NCERT Class 12 Maths Notes
Importance of Studying NCERT Class 12 Maths Notes
NCERT Notes Subject-Wise
NCERT Solutions Subject-Wise
NCERT Exemplar Solutions Subject Wise
NCERT Books and Syllabus

These notes provide a clear and simple explanation of every chapter, helping students understand the concepts quickly. Class 12th maths comprises Relations and functions, Inverse trigonometric function, Matrices and Determinants, Differential Calculus, Integral Calculus, Vectors, 3D geometry, and Vector. These notes are useful for revision before exams and are prepared by experts as per the latest CBSE syllabus. Students can also download NCERT Solutions for Class 12 Maths chapters and other subjects to strengthen their preparation and boost their confidence.

The NCERT Class 12 Maths Notes provided here will help you to prepare for your exams. These notes cover all the important concepts in a simple, comprehensive, and detailed manner. Filled with lots of examples, these notes will explain all the topics, making it easier for students to understand. Check the table below for NCERT Class 12 Maths notes chapter-wise. Just click the link for the chapter you need!

NCERT Notes Class 12 Maths Chapter 1 Relations and Functions

NCERT Notes Class 12 Maths Chapter 2 Inverse Trigonometric Functions

NCERT Notes Class 12 Maths Chapter 3 Matrices

NCERT Notes Class 12 Maths Chapter 4 Determinants

NCERT Notes Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Notes Class 12 Maths Chapter 6 Applications of derivatives

NCERT Notes Class 12 Maths Chapter 7 Integrals

NCERT Notes Class 12 Maths Chapter 8 Applications of Integrals

NCERT Notes Class 12 Maths Chapter 9 Differential Equations

NCERT Notes Class 12 Maths Chapter 10 Vector Algebra

NCERT Notes Class 12 Maths Chapter 11 Three-dimensional geometry

NCERT Notes Class 12 Maths Chapter 12 Linear Programming

NCERT Notes Class 12 Maths Chapter 13 Probability

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Importance of Studying NCERT Class 12 Maths Notes

Class 12 Maths notes from NCERT are great for students preparing for board exams and other competitive exams like JEE Mains, Advanced, EAMCET, VIT, BITSAT, and more. These NCERT notes for class 12 Maths cover all the chapters, important concepts, formulas, giving details about problems and theories, and helping students with their exam questions. You can download the PDF version of these notes to read them easily. Here are some more reasons to read these notes.

Concept Clarity: NCERT notes simplify complex topics in a student-friendly manner so that students can learn the fundamental concepts thoroughly.
Exam-Oriented Preparation: These notes are primarily focused on board exams and help students to prepare for those exams.
Time-Saving Revision Tool: Students can revise in a short span of time with the help of these notes.
Aligned with Board Syllabus: These NCERT class 12 Maths notes strictly comply with the latest CBSE syllabus and cover all the topics related to the board exam.
Strong Foundation for Competitive Exams: The concepts explained in NCERT notes are beneficial for competitive exams like JEE, NDA, and CUET, where conceptual expertise is examined.

NCERT Notes Subject-Wise

Here, students can find subject subject-wise listing of NCERT notes. These are helpful for quickly revising all the concepts, topics, and subtopics discussed. Practice these notes to score well in the exam.

NCERT Notes Class 12 Chemistry

NCERT Notes Class 12 Physics

NCERT Notes Class 12 Mathematics

NCERT Notes Class 12 Biology

NCERT Solutions Subject-Wise

After learning the concepts of each chapter in NCERT books of class 12, students should complete the exercise dedicated to that chapter. Sometimes they get stuck in problems or need some resources to check if they have solved it correctly. The following links will help them in this purpose.

NCERT Solutions Class 12 Physics

NCERT Solutions Class 12 Chemistry

NCERT Solutions Class 12 Biology

NCERT Solutions Class 12 Mathematics

NCERT Exemplar Solutions Subject Wise

After completing the textbook exercise, students can practice the NCERT exemplar to practice and revise. The following links will take you to the NCERT exemplar solutions of different subjects.

NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Mathematics

NCERT Exemplar Class 12 Chemistry

NCERT Solution Class 12 Mathematics

NCERT Books and Syllabus

Students should always analyse the latest CBSE syllabus before making a study routine. The following links will help them check the syllabus. Students can use the following links to access more reference books.

Frequently Asked Questions (FAQs)

Q: Are these NCERT Class 12 Maths chapter-wise notes enough for competitive exams as well?

Yes, these notes act like a base to any examination, but remember competitive exams require advanced thinking, keeping basics as their aim and expanding their thinking ability. But alone, these notes cannot help you to score in a competitive exam, but for sure will be very important to act as a base.

Q: Which chapters are to be given more importance in Class 12 Maths chapter-wise notes?

Weightage of each chapter is almost equal in board exams. So, all chapters are equally important. Going through all the chapters and concepts will help you score maximum marks in your exams.

Q: How many chapters do we have in NCERT Class 12 Maths chapter-wise notes?

There are a total of 13 chapters in class 12 NCERT Maths notes. These notes are created by the expert team of Careers360, keeping in mind the needs of the students. Therefore, students can use these notes as an efficient revision tool.

Q: What are the resources that I should follow for Class 12 Maths chapter-wise notes so that I can gain maximum marks?

We have a lot of resources that are available these days on the internet, but always following government textbooks is a great idea, and going through every nook and corner of the NCERT textbook is more than enough to score a distinction. Educational sites like Careers360 also provide quality NCERT Class 12 Maths Notes.

Q: How will these notes help me in my examination point of view?

Subject matter experts designed the notes to cover all NCERT topics and save time by efficiently presenting key points. These notes help you to gain maximum marks in board examinations.

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Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

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A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

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An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

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A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

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In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

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How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

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If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

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With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

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Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

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A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is