CBSE Class 11 and 12 Maths: revision path with simulations

The CBSE Mathematics (041) syllabus for Classes 11 and 12 in NCERT chapter order, from sets and functions through calculus, vectors and 3D geometry to probability. Each topic links to simulations you can drag and explore. Topics in the theory exam are marked; those kept only for formative assessment, such as mathematical induction, are not.

40 topics · 46 simulations

Class 11

Sets, subsets, intervals, Venn diagrams and set operations Exam topicXI Ch 1 Sets
- Venn Diagrams – Set Operations
Cartesian product, relations and functions as special relations Exam topicXI Ch 2 Relations and Functions
- Function machines – inputs, outputs and rules
- Composite and inverse functions – mapping diagrams, graphs and reflection in y = x
Real functions and graphs: modulus, signum, greatest integer, exponential, logarithmic; algebra of functions Exam topicXI Ch 2 Relations and Functions
- Parent functions – domain, range, symmetry, asymptotes and piecewise functions
- Composite and inverse functions – mapping diagrams, graphs and reflection in y = x
- Exponential function y = aˣ and logarithmic function y = logₐx
Radian measure; trigonometric functions on the unit circle and their graphs Exam topicXI Ch 3 Trigonometric Functions
- Unit circle and the sine, cosine, tangent graphs
- Unit circle – sine, cosine and tangent of any angle
Compound, multiple-angle and sum–product identities Exam topicXI Ch 3 Trigonometric Functions
- Trig identities – Pythagorean, compound angle, double angle and R cos(θ − α)
General solutions of sin y = sin a, cos y = cos a, tan y = tan a Exam topicXI formative: Trigonometric equations
- Basic Trigonometric Equations on the Unit Circle
Algebra of complex numbers; Argand plane; polar form Exam topicXI Ch 4 Complex Numbers and Quadratic Equations
- Complex numbers on the Argand diagram – operations, polar form and De Moivre's theorem
Linear inequalities in one variable on the number line; two variables graphically Exam topicXI Ch 5 Linear Inequalities
- Linear inequality in one variable – solution set on a number line
- Solution region of a system of linear inequalities in two variables
Counting principle, permutations and combinations Exam topicXI Ch 6 Permutations and Combinations
- Permutations, arrangements & combinations – choosing k from n items
Binomial theorem and Pascal's triangle; general and middle terms Exam topicXI Ch 7 Binomial Theorem
- Binomial theorem, Pascal's triangle, and proof by induction
Proof by induction XI formative: Principle of Mathematical Induction
- Binomial theorem, Pascal's triangle, and proof by induction
GP, sum to n terms, infinite GP; AM and GM Exam topicXI Ch 8 Sequences and Series
- Arithmetic and geometric sequences – simple and compound interest
- Infinite geometric series – partial sums approaching the sum to infinity
Σk, Σk² and Σk³ Exam topicXI formative: Special sums
- Sequences from patterns – difference tables, the nth term and recurrence relations
Slope, angle between lines, forms of a line, distance of a point from a line Exam topicXI Ch 9 Straight Lines
- Lines and circles in the coordinate plane
- Graphing lines – slope and y-intercept
Circle, parabola, ellipse and hyperbola: standard equations and properties Exam topicXI Ch 10 Conic Sections
- Conic sections by eccentricity
- Conic sections – the reflective property (satellite dish, whispering gallery, telescope)
- Graphing quadratics – coefficients, vertex form, focus and directrix
Coordinates in 3D, distance and section formula Exam topicXI Ch 11 Introduction to Three-dimensional Geometry
- Vectors in 3D space – sum, dot product, angle
Intuitive limits; limits of polynomial, rational, trigonometric, exponential and log functions Exam topicXI Ch 12 Limits and Derivatives
- Limits of Sequences and Functions, Continuity
Derivative from first principles; slope of the tangent Exam topicXI Ch 12 Limits and Derivatives
- Secant to tangent – the derivative as a limit
- Parabola and the tangent line at a moving point
Derivative of sum, difference, product and quotient Exam topicXI Ch 12 Limits and Derivatives
- Calculus grapher – f, f′, f″ and the antiderivative
Range, mean deviation, variance and standard deviation Exam topicXI Ch 13 Statistics
- Variance, standard deviation, and IQR of grouped data
- Summary statistics of a data set – dragging data points
Events, axiomatic probability, 'not', 'and', 'or' events Exam topicXI Ch 14 Probability
- Addition and Multiplication Rules of Probability with Venn and Tree Diagrams
- Classical probability: sample space and events

Class 12

One-one and onto functions Exam topicXII Ch 1 Relations and Functions
- Composite and inverse functions – mapping diagrams, graphs and reflection in y = x
Principal value branches and graphs Exam topicXII Ch 2 Inverse Trigonometric Functions
- Composite and inverse functions – mapping diagrams, graphs and reflection in y = x
- Unit circle and the sine, cosine, tangent graphs
Types of matrices, operations, transpose, symmetric and skew-symmetric Exam topicXII Ch 3 Matrices
- 2 × 2 matrices as transformations – determinant, composition, inverse and eigenvectors
Invertible matrices; non-commutativity of multiplication Exam topicXII Ch 3 Matrices
- 2 × 2 matrices as transformations – determinant, composition, inverse and eigenvectors
Determinants, minors, cofactors, adjoint, inverse; area of a triangle; solving systems Exam topicXII Ch 4 Determinants
- 2 × 2 matrices as transformations – determinant, composition, inverse and eigenvectors
- Systems of Three Linear Equations – Planes and Gaussian Elimination
Continuity and differentiability Exam topicXII Ch 5 Continuity and Differentiability
- Continuity of a function at a point
- Limits of Sequences and Functions, Continuity
Chain rule, implicit, inverse-trig, log and exponential, parametric and second derivatives Exam topicXII Ch 5 Continuity and Differentiability
Rate of change of quantities Exam topicXII Ch 6 Application of Derivatives
- Related rates – sliding ladder, filling cone, ripple, balloon and shadow
Increasing and decreasing functions; maxima and minima tests Exam topicXII Ch 6 Application of Derivatives
- Cubic and rational function analysis – derivatives, extrema, asymptotes
Real-life optimisation problems Exam topicXII Ch 6 Application of Derivatives
- Real-world optimization with derivatives
Integration as the inverse of differentiation Exam topicXII Ch 7 Integrals
- Calculus grapher – f, f′, f″ and the antiderivative
Fundamental theorem of calculus; properties of definite integrals Exam topicXII Ch 7 Integrals
- Integrals as a limit of rectangle areas
Area under lines, circles, parabolas and ellipses Exam topicXII Ch 8 Application of Integrals
- Area between two curves
- Integrals as a limit of rectangle areas
Order, degree, general and particular solutions; separation of variables; linear and homogeneous equations Exam topicXII Ch 9 Differential Equations
- Differential equations – slope fields, particular solutions and Euler's method
Vectors, direction cosines, components, addition, section formula Exam topicXII Ch 10 Vector Algebra
- Vectors in 3D space – sum, dot product, angle
- Vector addition – tip-to-tail and parallelogram rules
Scalar (dot) product and projection Exam topicXII Ch 10 Vector Algebra
- Vectors – sum, difference, scalar multiple and dot product
- Vectors in 3D space – sum, dot product, angle
Equations of a line, angle between lines, skew lines and shortest distance Exam topicXII Ch 11 Three-dimensional Geometry
- Vector equations of lines in 3D – intersecting, parallel and skew lines
Graphical method, feasible region and optimal corner points Exam topicXII Ch 12 Linear Programming
- Solution region of a system of linear inequalities in two variables
Conditional probability, multiplication theorem, independence, total probability, Bayes' theorem Exam topicXII Ch 13 Probability
- Conditional probability and Bayes' theorem: disease testing
- Addition and Multiplication Rules of Probability with Venn and Tree Diagrams

Topics follow the published curriculum; the mapping to simulations is by Simulic. Simulic is not affiliated with CBSE or NCERT.