Class 12 Maths Notes

Chapters in Class 12 Maths

1. Chapter 1: All Important Formula

   6 topics

   • Algebraic Formulas:
   • Factors Formula (Logarithmic Formulas)
   • Trigonometric Ratios and Formulas
   • Differentiation Formulas
   • Integration Formulas
   • Exponent Laws

2. Chapter 2: Relations and Functions

   13 topics

   • Introduction of Relations & Functions
   • Definations - Types of Relations
   • Determine whether each of the following relations are reflexive, symmetric and transitive:
   • Here's are some related questions of Relations
   • Show that the relation R
   • Find the set of all elements to 1 in each case.
   • Exercise Questions
   • Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.

3. Chapter 3: Inverse Trigonometric Functions

   8 topics

   • Introduction of Inverse Trigonometric Functions
   • Basic Concepts of Inverse Trigonometric Functions
   • Find the principal values of the following:
   • Find the values of the following:
   • Properties of Inverse Trigonometric Functions
   • Write the following functions in the simplest form
   • Find the values of each of the following:
   • A Table for Domains and Ranges (principal value branches) of inverse trigonometric functions are given in the following …

4. Chapter 4: Matrices

   27 topics

   • Introduction of Matrices
   • Definition of Matrices
   • Order of a Matrix
   • Types of Matrices
   • Exercise Questions
   • Exercise Questions
   • Find the value of a, b, c, and d from the equation:
   • Exercise Questions

5. Chapter 5: Determinants

   15 topics

   • Introduction to Determinants
   • Determinants of Different Order Matrices
   • Evaluate the Determinants
   • Find the Determinant
   • Area of a Triangle
   • Find Area of the Triangle with vertices at the point given in each of the following :
   • Show that points A (a, b + c), B (b, c + a), C (c, a + b) are collinear
   • Find values of k if area of triangle is 4 sq. units and vertices are..(i) (k, 0), (4, 0), (0, 2) , (ii) (–2, 0), (0, 4),…

6. Chapter 6: Continuity and Differentiability

   8 topics

   • Introduction to Continuity and Differentiability
   • Continuity
   • Algebra of Continuous Functions
   • Differentiability
   • Derivatives of Composite Functions
   • Derivatives of implicit functions
   • Exponential and Logarithmic Functions
   • Logarithmic Differentiation

7. Chapter 7: Application of Derivatives

   21 topics

   • Introduction of Application of Derivative
   • Rate of Change of Quantities
   • Example: Calculating Speed as Rate of Change
   • Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm , (b) r = 4 cm
   • The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an…
   • A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of…
   • Exercise Questions
   • Exercise Questions

8. Chapter 8: Integrals

   12 topics

   • Introduction of Integrals
   • Integration as an Inverse Process of Differentiation
   • Properties of Indefinite Integrals
   • Methods of Integration
   • Integration using Trigonometric Identities
   • Integrals of Some Particular Functions
   • Integration by Partial Fractions
   • Integration by Parts

9. Chapter 9: Application of Integrals

   3 topics

   • Introduction to the Application of Integrals
   • Area under Simple Curves Explained
   • Exercise Questions - 1, 2

10. Chapter 10: Differential Equations

    6 topics

    • Introduction of Differential Equations
    • Basic Concepts of Differential Equations
    • Exercise Questions
    • General and Particular Solutions of a Differential Equation
    • Methods of Solving First Order, First Degree Differential Equations
    • Exercise Questions

11. Chapter 11: Vector Algebra

    9 topics

    • Introduction of Vector Algebra
    • Some Basic Concepts of Vector Algebra
    • Types of Vectors
    • Addition of Vectors
    • Multiplication of a Vector by a Scalar
    • Components of a Vector & Section Formula
    • Exercise Questions
    • Product of Two Vectors

12. Chapter 12: Three Dimensional Geometry

    5 topics

    • Introduction of Three Dimensional Geometry
    • Direction Cosines and Direction Ratios of a Line
    • Equation of a Line in Space
    • Angle between Two Lines in 3D Geometry
    • Shortest Distance between Two Lines in 3D Geometry

13. Chapter 13: Linear Programming

    4 topics

    • Introduction of Linear Programming
    • Linear Programming Problem and Its Mathematical Formulation
    • Mathematical formulation of the problem
    • Graphical Method for Solving Linear Programming Problems

14. Chapter 14: Probability

    19 topics

    • Introduction of Probability
    • Conditional Probability
    • Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E|F) and P(F|E)
    • Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32
    • Evaluate P(A ∪ B), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5
    • Two coins are tossed once: (i) E: a tail appears on one coin, F: one coin shows head , (ii) E: no tail appears, F: no he…
    • A die is thrown three times: E: 4 appears on the third toss, F: 6 and 5 appear respectively on the first two tosses
    • Mother, father and son line up at random for a family picture: E: son on one end, F: father in middle