Maths Class 12 (with NCERT Solutions)

Learn Class 12 Maths with clear concept explanations, step-by-step NCERT solutions, miscellaneous-exercise answers, important questions, MCQs and CBSE sample-paper solutions on Teachoo.

Class 12 Maths covers advanced algebra, calculus, vectors, three-dimensional geometry, linear programming and probability. These topics are important for the CBSE board examination and form a foundation for engineering, economics, statistics, computer science and other quantitative university courses.

Teachoo organises the complete Class 12 Maths course so students can either find the answer to a particular NCERT question or learn an entire chapter concept-wise. Each solution explains the formulas, substitutions, calculations and reasoning required to obtain the answer.

What You Can Learn on Teachoo

Teachoo’s Class 12 Maths resources include:

• Step-by-step NCERT exercise solutions

• Solutions to textbook examples

• Miscellaneous-exercise solutions

• Supplementary NCERT questions

• Easy concept explanations

• Video explanations for selected questions

• Multiple-choice questions or MCQs

• NCERT Exemplar MCQs

• Assertion–Reason questions

• Case-based questions

• Chapter-wise important questions

• CBSE sample-paper solutions

• Past-year board-paper resources

• Formula-based and application-based questions

The material can be used for daily study, school tests, pre-board examinations, final board revision and the development of a strong mathematical foundation for entrance examinations.

Class 12 Maths Chapters and Topics

1. Relations and Functions

Learn different types of relations, including reflexive, symmetric, transitive and equivalence relations. Study one-one, onto and bijective functions, composition of functions and inverse functions. Understand binary operations, identity elements, inverses, commutativity and associativity.

2. Inverse Trigonometric Functions

Understand inverse trigonometric functions and their domains, ranges and principal-value branches. Learn to find principal values, simplify expressions and prove identities using the properties of inverse trigonometric functions.

3. Matrices

Study the order and types of matrices, including row, column, square, diagonal, scalar, identity, symmetric and skew-symmetric matrices. Perform matrix addition, subtraction and multiplication. Learn transposition and find the inverse of a matrix using elementary transformations.

4. Determinants

Evaluate determinants of order two and three and apply their properties. Learn about minors, cofactors, adjoints and inverse matrices. Use determinants to find the area of a triangle and solve systems of linear equations.

5. Continuity and Differentiability

Check whether a function is continuous or differentiable at a point and over an interval. Learn the chain rule, implicit differentiation, logarithmic differentiation, derivatives of inverse trigonometric functions and second-order derivatives. Study Rolle’s Theorem and the Mean Value Theorem.

6. Applications of Derivatives

Use derivatives to calculate rates of change and identify increasing or decreasing functions. Find equations of tangents and normals, approximate values and local or absolute maxima and minima. Apply derivatives to numerical and geometrical optimisation problems.

7. Integrals

Learn indefinite and definite integration using standard formulas, substitution, trigonometric identities, partial fractions and integration by parts. Understand definite integrals as limits of sums and solve them using their important properties.

8. Applications of Integrals

Use integration to calculate areas under curves and areas bounded by curves and coordinate axes. Find the area between a curve and a line or between two different curves.

9. Differential Equations

Understand the order and degree of a differential equation and distinguish between general and particular solutions. Form differential equations and solve them using variable separation, homogeneous-equation methods and linear differential-equation methods.

10. Vector Algebra

Understand scalars, vectors, unit vectors, position vectors and direction ratios. Perform vector addition and scalar multiplication. Learn the scalar or dot product, vector or cross product, projections, collinearity and areas calculated using vectors.

11. Three-Dimensional Geometry

Study direction cosines and direction ratios. Find equations of lines and planes in different forms, angles between lines and planes and distances involving points, parallel lines, skew lines and planes. Understand coplanarity and other geometrical relationships in three dimensions.

12. Linear Programming

Form linear inequalities from practical situations and represent them graphically. Identify feasible regions and calculate the maximum or minimum value of an objective function. Solve diet, manufacturing, transport and resource-allocation problems.

13. Probability

Study conditional probability, the multiplication theorem, independent events, total probability and Bayes’ Theorem. Learn about random variables, probability distributions, expected values, variance, Bernoulli trials and binomial distributions.

Two Ways to Study Class 12 Maths

Teachoo organises each chapter in two useful ways.

Find an NCERT Answer

Use the serial-order section when you need the solution to a particular NCERT exercise, example or miscellaneous question. Select the chapter, exercise and required question to view the complete solution.

This method is useful for:

• Completing school assignments

• Checking an NCERT answer

• Finding a specific exercise solution

• Understanding a difficult textbook example

• Correcting an algebraic or calculation error

• Revising an exercise before an examination

Learn a Concept

Use the concept-wise section when learning or revising a chapter properly. Each chapter is divided into smaller topics. The concept is explained first, after which related questions are arranged from easier to more challenging levels.

This method is useful for:

• Learning a chapter for the first time

• Revising weak concepts

• Connecting questions that use the same method

• Preparing for application-based board questions

• Building a foundation for entrance examinations

Do not open a solution immediately when a question appears difficult. Identify the chapter, write the relevant formulas and attempt a complete method first.

Important Questions for Class 12 Maths

Teachoo provides chapter-wise important questions covering all 13 Class 12 Maths chapters. These questions help students revise frequently tested formulas, standard methods and examination-oriented applications.

Important questions are available for:

• Relations and Functions

• Inverse Trigonometric Functions

• Matrices and Determinants

• Continuity and Differentiability

• Applications of Derivatives

• Integrals and Applications of Integrals

• Differential Equations

• Vector Algebra

• Three-Dimensional Geometry

• Linear Programming

• Probability

Important questions should be attempted after completing the NCERT exercises. They are a revision tool, not a replacement for the textbook.

CBSE Class 12 Maths Sample-Paper Solutions

Teachoo provides step-by-step solutions to CBSE Class 12 Maths sample papers from multiple examination years. Sample papers help students understand the question-paper structure, marks distribution, competency-based questions and the time required for different sections.

Use sample papers correctly:

1. Complete the NCERT course.

2. Revise all formulas.

3. Attempt the paper under timed conditions.

4. Do not view the solution during the test.

5. Check every answer after finishing.

6. Classify each mistake as conceptual, calculation-based or careless.

7. Reattempt the incorrect questions after one or two days.

Reading a solved sample paper is not equivalent to attempting it. Board-exam performance improves through written, timed practice.

Why Class 12 Maths Needs Consistent Practice

Class 12 Maths contains several chapters that depend directly on Class 11 concepts. Functions support calculus, trigonometric identities appear in differentiation and integration, and vectors support three-dimensional geometry.

Calculus carries significant conceptual weight. Students must learn to recognise whether a problem requires differentiation, substitution, integration by parts, partial fractions or another method. This recognition develops only through varied practice.

For every chapter:

1. Learn the definitions and formulas.

2. Study the NCERT examples.

3. Complete every exercise.

4. Attempt the miscellaneous questions.

5. Solve chapter-wise important questions.

6. Practise MCQs and case-based questions.

7. Attempt sample papers.

8. Reattempt every incorrect question without assistance.

Maintain a short mistake notebook containing incorrect formulas, missed conditions and recurring calculation errors. Revising this notebook is more useful than repeatedly reading questions you already know.

Class 12 Maths for Boards and Entrance Examinations

NCERT is the essential starting point for the CBSE Class 12 Maths board examination. It also provides the foundational theory required for engineering and other entrance examinations.

However, NCERT solutions alone are not complete entrance-exam preparation. First master the NCERT concepts, examples and exercises. Then solve higher-level, multi-concept and timed questions.

Teachoo’s concept-wise arrangement helps students identify the exact method behind a question before moving to more advanced problem sets.

Frequently Asked Questions

Does Teachoo cover all Class 12 Maths NCERT chapters?

Yes. Teachoo covers all 13 Class 12 Maths chapters with exercise-wise and concept-wise explanations.

Are miscellaneous-exercise solutions available?

Yes. Regular exercises, examples, miscellaneous exercises and available supplementary questions are solved step by step.

Are Class 12 Maths solutions explained in detail?

Yes. The solutions show formulas, substitutions, algebraic steps, diagrams and intermediate calculations instead of giving only the final answer.

Does Teachoo provide Class 12 Maths MCQs?

Yes. MCQs, NCERT Exemplar questions, assertion–reason questions and case-based questions are available for different chapters.

Are Class 12 Maths sample-paper solutions available?

Yes. Teachoo provides detailed solutions to CBSE Class 12 Maths sample papers from multiple examination years.

How should I prepare for the Class 12 Maths board exam?

Complete NCERT first, including examples and miscellaneous exercises. Then solve chapter-wise important questions and attempt full sample papers under timed conditions. Analyse and reattempt every incorrect question.

Select a Class 12 Maths chapter and begin with its concept explanation. Solve each question independently before checking the answer. Board-exam confidence comes from repeated written practice—not from reading solutions passively.