🇮🇳 CBSE Class 12 Board Exam · subject

CBSE Class 12 Board Exam Mathematics Syllabus

The Mathematics syllabus for CBSE Class 12 Board Exam in full: 4 chapters, 13 topics and 37 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.

4Chapters

13Topics

37Sub-topics

50Flashcards

Mathematics syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

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
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
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
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

CBSE Class 12 Board Exam Mathematics flashcards — 50 questions with answers

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.
State the conditions for a relation R on set A to be an equivalence relation.
R must be reflexive, symmetric, and transitive simultaneously.
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.
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).
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.
What is the principal value range of sin^(-1) x?
[-pi/2, pi/2], with domain [-1, 1].
What is the principal value range of cos^(-1) x?
[0, pi], with domain [-1, 1].
What is the principal value range of tan^(-1) x?
(-pi/2, pi/2), with domain all real numbers.
State the identity for sin^(-1) x + cos^(-1) x.
sin^(-1) x + cos^(-1) x = pi/2, for x in [-1, 1].
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.
What is a symmetric matrix?
A square matrix A such that A' = A, i.e., a_ij = a_ji for all i, j.
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.
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).
State the property det(AB) for square matrices A and B.
det(AB) = det(A) x det(B).
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)|.
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.
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).
State the product rule for differentiation of u(x)v(x).
d/dx[uv] = u(dv/dx) + v(du/dx).
State the quotient rule for differentiation of u(x)/v(x).
d/dx[u/v] = (v(du/dx) - u(dv/dx)) / v^2.
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).

Show the other 30 Mathematics flashcards

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.
State the Mean Value Theorem (Lagrange).
If f is continuous on [a, b] and differentiable on (a, b), then there exists c in (a, b) with f'(c) = (f(b) - f(a))/(b - a).
What is the first derivative test for a local maximum at x = c?
f'(c) = 0 and f' changes sign from positive to negative as x increases through c.
In the second derivative test, what indicates a local minimum at x = c?
f'(c) = 0 and f''(c) > 0 indicate a local minimum at c.
How is a function determined to be increasing on an interval using derivatives?
f is increasing on an interval if f'(x) >= 0 (and > 0 except at isolated points) throughout that interval.
What is the integration formula for x^n dx (n not equal to -1)?
Integral of x^n dx = x^(n+1)/(n+1) + C.
What is the integral of 1/x dx?
Integral of 1/x dx = ln|x| + C.
State the integration by parts formula.
Integral of u dv = uv - integral of v du.
In integration by parts, what does the ILATE rule help decide?
It gives the priority order (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential) for choosing the first function u.
State the fundamental theorem of calculus (evaluation part) for a definite integral.
Integral from a to b of f(x) dx = F(b) - F(a), where F is an antiderivative of f.
What is the integral of 1/(x^2 + a^2) dx?
(1/a) tan^(-1)(x/a) + C.
What is the formula for the area between a curve y = f(x) and the x-axis from x = a to x = b (f >= 0)?
Area = integral from a to b of f(x) dx.
What is the order of a differential equation?
The order is the order of the highest derivative appearing in the differential equation.
What is the degree of a differential equation?
The degree is the power of the highest-order derivative, when the equation is polynomial in derivatives and free from radicals/fractions in them.
What is the integrating factor for a linear differential equation dy/dx + Py = Q?
I.F. = e^(integral of P dx).
What is the dot (scalar) product of two vectors a and b in terms of magnitudes and angle?
a . b = |a| |b| cos(theta), where theta is the angle between them.
What is the magnitude of the cross product of vectors a and b?
|a x b| = |a| |b| sin(theta), where theta is the angle between them; it equals the area of the parallelogram they form.
How do you determine if two non-zero vectors a and b are perpendicular?
They are perpendicular if and only if a . b = 0.
What is a unit vector in the direction of vector a?
a-hat = a / |a|, the vector a divided by its magnitude.
What is the formula for the projection of vector a on vector b?
Projection of a on b = (a . b) / |b|.
What are direction cosines of a line?
The cosines (l, m, n) of the angles the line makes with the positive x, y, z axes; they satisfy l^2 + m^2 + n^2 = 1.
State the vector equation of a line through point a parallel to vector b.
r = a + lambda b, where lambda is a scalar parameter.
What is the formula for the angle between two lines with direction ratios (a1,b1,c1) and (a2,b2,c2)?
cos(theta) = |a1a2 + b1b2 + c1c2| / (sqrt(a1^2+b1^2+c1^2) x sqrt(a2^2+b2^2+c2^2)).
State the equation of a plane in normal form (vector).
r . n-hat = d, where n-hat is the unit normal vector and d is the perpendicular distance from the origin.
What is the shortest distance between two skew lines r = a1 + lambda b1 and r = a2 + mu b2?
d = |((a2 - a1) . (b1 x b2))| / |b1 x b2|.
In linear programming, what is the feasible region?
The common region determined by all the constraints (including non-negativity) of a linear programming problem.
State the corner point theorem in linear programming.
If a feasible region is bounded, the optimal value of the objective function occurs at a corner (vertex) of the feasible region.
What is the formula for conditional probability P(A|B)?
P(A|B) = P(A and B) / P(B), provided P(B) > 0.
State Bayes' Theorem for events A and E_i (a partition).
P(E_i | A) = [P(E_i) P(A | E_i)] / [sum over j of P(E_j) P(A | E_j)].
What are the mean and variance of a binomial distribution with n trials and success probability p?
Mean = np; Variance = npq, where q = 1 - p.

CBSE Class 12 Board Exam Mathematics FAQ

What is in the CBSE Class 12 Board Exam Mathematics syllabus?

CBSE Class 12 Board Exam Mathematics is split into 4 chapters: Relations, Functions and Algebra, Calculus, Vectors and Three-Dimensional Geometry and Probability. Together they contain 13 topics and 37 sub-topics.

How many chapters are in CBSE Class 12 Board Exam Mathematics?

4 chapters, containing 13 topics and 37 sub-topics. The largest chapter is Calculus, with 4 topics.

Are there flashcards for CBSE Class 12 Board Exam Mathematics?

Yes — a 50-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.