Mathematics – Class XII Student Support Material (2025–26)

1️⃣ Relations and Functions

This chapter introduces different types of relations such as reflexive, symmetric, transitive, and equivalence relations. It also explains various types of functions like one-one (injective), onto (surjective), and bijective functions.

Students learn how to determine the number of relations and functions between sets and solve multiple-choice, assertion-reason, and descriptive questions.

2️⃣ Inverse Trigonometric Functions

This section focuses on inverse trigonometric functions such as sin⁻¹x, cos⁻¹x, and tan⁻¹x. It explains:

Principal value branches

Domain and range

Important identities

Graphs and properties

Students learn how to simplify expressions and solve equations involving inverse trigonometric functions.

3️⃣ Matrices

This chapter covers:

Types of matrices (row, column, square, zero, identity)

Matrix operations (addition, multiplication, transpose)

Properties of matrix multiplication

Students also learn how matrices are used to solve systems of linear equations.

4️⃣ Determinants

This section explains:

Determinants of order 2 and 3

Properties of determinants

Adjoint and inverse of a matrix

Solving system of linear equations using determinants

It builds strong algebraic manipulation skills.

5️⃣ Continuity and Differentiability

This is an important calculus chapter. It explains:

Concept of limits

Continuity of functions

Differentiation of composite, inverse trigonometric, implicit, and parametric functions

Logarithmic differentiation

Students also learn about derivatives of exponential and trigonometric functions.

6️⃣ Applications of Derivatives

This chapter applies differentiation in real-life contexts such as:

Increasing and decreasing functions

Tangents and normals

Maximum and minimum values

Rate of change

It helps students understand optimization problems.

7️⃣ Integrals

This chapter introduces integration as the reverse process of differentiation.

It covers:

Indefinite integrals

Standard integrals

Integration by substitution

Integration by parts

Partial fractions

Integration techniques are developed step by step.

8️⃣ Applications of Integrals

This section explains how integrals are used to find:

Area under curves

Area between two curves

It connects calculus with geometrical interpretation.

9️⃣ Differential Equations

This chapter introduces:

Formation of differential equations

Methods of solving first-order differential equations

Applications in growth and decay problems

It links calculus with real-world modeling.

🔟 Vector Algebra

This chapter explains three-dimensional vectors including:

Position vectors

Addition and scalar multiplication

Dot product and cross product

Direction cosines and direction ratios

It builds foundation for 3D geometry.

1️⃣1️⃣ Three-Dimensional Geometry

This section focuses on:

Direction cosines and direction ratios

Equation of line in space

Shortest distance between two lines

Angle between lines

Students learn geometric interpretation in 3D space.

1️⃣2️⃣ Linear Programming Problem (LPP)

This chapter introduces optimization techniques using:

Formulation of LPP

Graphical method

Feasible region

Optimal solution

It is useful for business and economics applications.

1️⃣3️⃣ Probability

This chapter explains:

Conditional probability

Bayes’ theorem

Random variables

Mean and variance

Probability distributions

Students learn how to calculate probabilities in complex situations.

1️⃣4️⃣ Exercises and Answers (All Chapters)

This section provides chapter-wise practice questions along with answers for revision and self-assessment.

1️⃣5️⃣ Sample Question Papers with Answers

It includes complete model question papers based on the latest CBSE pattern to help students prepare effectively for board exams.

1️⃣6️⃣ Useful Links

This final section provides additional resources and reference materials for further learning.