NDSS Academy

Class 12 Mathematics

Class 12 Mathematics: full syllabus tuition with regular tests (CBSE / UP Board).

12 MonthsDuration 13Chapters64Topics
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Syllabus · पाठ्यक्रम

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01Relations and Functions 5 topics
  1. Types of relations: reflexive, symmetric, transitive
  2. Equivalence relations
  3. One-one and onto functions
  4. Composition of functions
  5. Invertible functions
02Inverse Trigonometric Functions 4 topics
  1. Definition, domain and range
  2. Principal value branches
  3. Graphs of inverse trigonometric functions
  4. Elementary properties
03Matrices 5 topics
  1. Types of matrices
  2. Operations on matrices
  3. Transpose
  4. Symmetric and skew-symmetric matrices
  5. Invertible matrices
04Determinants 5 topics
  1. Determinant of a square matrix
  2. Area of a triangle
  3. Minors and cofactors
  4. Adjoint and inverse of a matrix
  5. Solving linear equations by matrix method
05Continuity and Differentiability 7 topics
  1. Continuity
  2. Differentiability
  3. Chain rule
  4. Derivatives of inverse trigonometric functions
  5. Exponential and logarithmic functions
  6. Logarithmic and parametric differentiation
  7. Second order derivatives
06Application of Derivatives 5 topics
  1. Rate of change of quantities
  2. Increasing and decreasing functions
  3. Maxima and minima
  4. First and second derivative tests
  5. Applied maxima-minima problems
07Integrals 6 topics
  1. Integration as inverse of differentiation
  2. Integration by substitution
  3. Integration by partial fractions
  4. Integration by parts
  5. Definite integrals and fundamental theorem
  6. Properties of definite integrals
08Application of Integrals 3 topics
  1. Area under simple curves
  2. Area bounded by a curve and a line
  3. Area of circles, parabolas and ellipses (standard forms)
09Differential Equations 5 topics
  1. Order and degree
  2. General and particular solutions
  3. Variable separable method
  4. Homogeneous differential equations
  5. Linear differential equations
10Vector Algebra 6 topics
  1. Types of vectors
  2. Addition and scalar multiplication
  3. Components of a vector
  4. Section formula
  5. Scalar (dot) product
  6. Vector (cross) product
11Three Dimensional Geometry 4 topics
  1. Direction cosines and direction ratios
  2. Equation of a line in space
  3. Angle between two lines
  4. Shortest distance between two lines
12Linear Programming 4 topics
  1. Formulation of LPP
  2. Graphical method
  3. Feasible and unbounded regions
  4. Corner point method
13Probability 5 topics
  1. Conditional probability
  2. Multiplication theorem
  3. Independent events
  4. Total probability
  5. Bayes' theorem

About

You will be able to

  • Work with relations, functions, inverse trigonometric functions, matrices and determinants
  • Test continuity and differentiability and find derivatives of all standard function types
  • Use derivatives for rates of change, increasing / decreasing functions and maxima-minima
  • Evaluate indefinite and definite integrals and find areas under curves
  • Form and solve first order differential equations
  • Solve problems on vectors, 3D lines, linear programming and probability (including Bayes' theorem)
  • Present complete step-wise solutions as expected in CBSE / UP Board exams

Who it is for

  • Class 12 students of CBSE and UP Board taking Mathematics (PCM / PCMB)
  • Students who want regular practice and tests in calculus and algebra
  • Students preparing for JEE Main basics along with board exams

What you need

  • Class 11 Mathematics (functions, trigonometry, limits and derivatives basics)
  • NCERT Class 12 Mathematics Part I and II textbooks

Questions

Which syllabus is followed?

The current rationalised NCERT Class 12 Mathematics syllabus, which is used by both CBSE and UP Board.

How much practice is given?

Every chapter covers NCERT exercises, examples, miscellaneous questions and previous year board questions, followed by a chapter test.

Is calculus given extra time?

Yes. Continuity, derivatives, integrals and differential equations carry the most marks, so they get the most classes and tests.

Are mock board papers conducted?

Yes. Full-length board-pattern papers are conducted in the last two months with step-marking feedback.

Download the syllabus (PDF)

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