CBSE Class 12 Board Exam Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in CBSE Class 12 Board Exam, not a summary of it.

1. 1

   Relations, Functions and Algebra

   3 topics

   • Relations and Functions
     • Types of relations and functions
     • One-one, onto and bijective functions
     • Composition of functions
   • Inverse Trigonometric Functions
     • Domain, range and principal value branch
     • Properties and graphs
   • Matrices and Determinants
     • Matrix operations and types
     • Determinants and properties
     • Adjoint, inverse and applications
     • Solving systems of linear equations
2. 2

   Calculus

   4 topics

   • Continuity and Differentiability
     • Continuity and differentiability of functions
     • Chain rule and implicit differentiation
     • Logarithmic differentiation
     • Rolle's and Mean Value theorems
   • Applications of Derivatives
     • Rate of change and tangents and normals
     • Increasing and decreasing functions
     • Maxima and minima
   • Integrals
     • Methods of integration
     • Definite integrals and properties
     • Fundamental theorem of calculus
   • Applications of Integrals and Differential Equations
     • Area under simple curves
     • Order, degree and formation of differential equations
     • Variable separable and linear differential equations
3. 3

   Vectors and Three-Dimensional Geometry

   3 topics

   • Vector Algebra
     • Types of vectors and components
     • Scalar (dot) product
     • Vector (cross) product
   • Three Dimensional Geometry
     • Direction cosines and ratios
     • Equation of a line in space
     • Equation of a plane and distances
   • Linear Programming
     • Formulation of LPP
     • Graphical method of solution
     • Feasible region and optimal solution
4. 4

   Probability

   3 topics

   • Conditional Probability
     • Conditional probability and multiplication theorem
     • Independent events
   • Bayes' Theorem and Total Probability
     • Theorem of total probability
     • Bayes' theorem and applications
   • Random Variables and Distributions
     • Random variable and probability distribution
     • Mean of a probability distribution

Mathematics flashcards for CBSE Class 12 Board Exam

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is the definition of a reflexive relation R on a set A?

   A relation R on A is reflexive if (a, a) belongs to R for every element a in A.

2. State the conditions for a relation R on set A to be an equivalence relation.

   R must be reflexive, symmetric, and transitive simultaneously.

3. What does it mean for a function f to be injective (one-one)?

   f is one-one if f(x1) = f(x2) implies x1 = x2; distinct inputs give distinct outputs.

4. What does it mean for a function f to be surjective (onto)?

   f is onto if every element of the codomain is the image of at least one element of the domain (range = codomain).

5. When is a function called bijective, and what does it guarantee?

   A function is bijective if it is both one-one and onto; this guarantees the existence of an inverse function.

6. What is the principal value range of sin^(-1) x?

   [-pi/2, pi/2], with domain [-1, 1].

7. What is the principal value range of cos^(-1) x?

   [0, pi], with domain [-1, 1].

8. What is the principal value range of tan^(-1) x?

   (-pi/2, pi/2), with domain all real numbers.

9. State the identity for sin^(-1) x + cos^(-1) x.

   sin^(-1) x + cos^(-1) x = pi/2, for x in [-1, 1].

10. What is the formula for tan^(-1) x + tan^(-1) y when xy < 1?

    tan^(-1) x + tan^(-1) y = tan^(-1)((x + y)/(1 - xy)), when xy < 1.

11. What is a symmetric matrix?

    A square matrix A such that A' = A, i.e., a_ij = a_ji for all i, j.

12. What is a skew-symmetric matrix and what are its diagonal elements?

    A square matrix with A' = -A (a_ij = -a_ji); all its diagonal elements are zero.

13. What is the condition for a square matrix A to be invertible, and the formula for its inverse?

    A is invertible if det(A) is not 0; then A^(-1) = (1/det(A)) adj(A).

14. State the property det(AB) for square matrices A and B.

    det(AB) = det(A) x det(B).

15. How is the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) expressed using determinants?

    Area = (1/2) |determinant of the matrix with rows (x1,y1,1), (x2,y2,1), (x3,y3,1)|.

16. What is the relationship between A(adj A) and the identity matrix?

    A(adj A) = (adj A)A = det(A) I, where I is the identity matrix of the same order.

17. State the three conditions for a function f to be continuous at a point x = c.

    f(c) is defined, the limit of f(x) as x approaches c exists, and that limit equals f(c).

18. State the product rule for differentiation of u(x)v(x).

    d/dx[uv] = u(dv/dx) + v(du/dx).

19. State the quotient rule for differentiation of u(x)/v(x).

    d/dx[u/v] = (v(du/dx) - u(dv/dx)) / v^2.

20. State the chain rule for the derivative of a composite function f(g(x)).

    d/dx[f(g(x))] = f'(g(x)) x g'(x).

21. What does Rolle's Theorem state?

    If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists c in (a, b) with f'(c) = 0.

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