#
TN State Board 12th Maths Tuition

Draw and color amazing backgrounds for your comics, concept art, and more. Plus learn composition

- The broad objectives of teaching Mathematics at senior school stage intend to help the students:
- To acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
- To feel the flow of reasons while proving a result or solving a problem.
- To apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
- To develop a positive attitude to think, analyse and articulate logically.
- To develop interest in the subject by participating in related competitions.
- To acquaint students with different aspects of Mathematics used in daily life.
- To develop an interest in students to study Mathematics as a discipline.

- Assignments every week
- 200+ MCQs
- Courseware prepared by experts
- Assessments to give you the level of improvement

Class 12 is an essential year in school education. It's when basic arithmetic principles should be firmly established. Students will benefit from a firm grasp of class 12^{th} maths since they will have momentum for the following year, allowing them to do well in the class 12^{th} board exams. Finding a grade 12^{th} mathematics teacher who can give all the attention and assistance students need to succeed in this essential discipline may be difficult for many pupils. However, with LITAA online programs, one-on-one sessions at a low cost are now a reality.

This program has been designed by LITAA to meet the requirements of Tamilnadu State Board class 12^{th} maths using SCERT solutions. You will begin preparing for important competitive examinations in Class 12 so that you can keep your career options open. The subject specialists and solutions of maths class 12^{th} provide you with a thorough syllabus and study materials, which you may access anywhere without prior knowledge. The study material will be conveyed to you carefully. You can pick up the phone and call an expert to clear up any doubts you may have anytime.

## Course Features

## Course Structure

Units |
Topics |

I | Matrices and determinants -II |

II | Complex Numbers |

III | Theory of Equations |

IV | Trigonometric functions and Inverse Trigonometric functions |

V | Two Dimensional Analytic Geometry - II |

VI | Vectors - II |

VII | Applications of Derivatives |

VIII | Differentials and Partial Derivatives |

IX | Applications of integration |

X | Differential equations |

## Course Lessons

Inverse of a Matrix - cofactor of a matrix, adjoint of a matrix, inverse of a matrix, uniqueness of inverse; Elementary Transformations - rank of a matrix, echelon form, inverse of a matrix using elementary transformations; System of linear equations - linear equations in matrix form, solving equations using Matrix Inverse method, consistency of the system of equations by Determinant method and Rank method

Introduction to Complex Numbers - the need for complex numbers; complex numbers as ordered pairs of real numbers; basic arithmetic operations on complex numbers; Algebra of complex numbers - conjugate of a complex number, modulus of a complex number, triangle inequality, problems; Polar form - argand plane as an extension of the real number line, a geometrical representation of complex numbers, conjugate, modulus, addition and subtraction, polar form of a complex number and principal value of the argument; Demoivre’s theorem - statement of Demoivre’s theorem, Euler’s formula, notation and polar form of unit circle, square roots, cube roots and fourth roots of unity, problems involving the cube roots of unity

Quadratic Equations - relation between roots and coefficients, conditions for rational, irrational, and complex roots, solving equations reducible to a quadratic equation, the graph of a quadratic function, minimum and maximum values, quadratic inequalities, and a sign of quadratic expression; Polynomial equations - fundamental theorem of algebra, formation of the equation for the given roots, equations with rational coefficients when some of the irrational or complex roots are given, roots of third or higher degree polynomial equations when given in partly factorized form; Graphical approach to equations - using continuity of polynomial functions to find real roots by finding where the function changes sign, counting the number of positive, negative and complex roots using Descartes’ rule of signs (no proof)

Periodic functions - definition and examples, domain and Range of a function; Odd and Even functions - definitions and examples; Graphs of Trigonometric functions - graphs of sine, cosine, tangent, secant, cosecant, cotangent functions; Properties and graphs of inverse Trigonometric functions - domain and Range of Inverse Trigonometric functions, properties of Inverse Trigonometric functions, Simple problems, graphs of Inverse of sine, cosine, tangent, secant, cosecant, cotangent functions

Conic sections - definition of a conic, general equation of a conic, sections of a cone; Circle - general form, standard forms, parametric form, verifying the position of a given point; Parabola - standard equation: four types, properties, parametric form, simple problems, and applications; Ellipse and Hyperbola - standard equation, parametric form, properties, simple problems and applications

Scalar Triple Product - definition of the scalar triple product, geometric meaning and determinant form, properties, problems, and applications; Vector Triple Product - definition of vector triple product, geometric meaning, properties, problems, and applications; Straight lines - vector and cartesian equations of a straight line: two points form, one point and parallel to a vector form, direction ratios, and cosines, angle between two lines, coplanar lines (intersecting, perpendicular, parallel), non-coplanar lines, the distance between two parallel lines, two non–coplanar lines, a point, and a line; Planes - vector and cartesian equations of a plane (Normal form, given one point and two parallel vectors, given two points and one parallel vector, given three points, passing through the intersection of two planes), angle between two planes, the angle between a line and a plane, meeting point of a line and a plane, the distance between a point and a plane, the distance between two parallel planes

Derivatives as Slope and Rate of Change - meaning of derivative as slope, equations of tangent and normal, the meaning of derivative as a rate of change and related rates; Mean Value Theorem - Rolle’s theorem, Lagrange’s Mean Value Theorem, geometrical meaning, applications; Indeterminate forms - a limit process - l’ Hôpital Rul, evaluating the limits; Sketching of elementary curves - increasing/decreasing – first derivative test, concavity/convexity – second derivative test, Asymptotes, and symmetry, sketching of polynomial, rational, trigonometric, exponential and logarithmic curves; Extrema of functions - Extrema: Maxima and Minima using first and second derivative test, applications to optimization

Differentials - definition and simple problems; Errors and Approximations - types of errors – finding approximate values, concepts of differentials; Partial Differentiation - First-order and second-order partial derivatives, Function of function rule (two and three variables), simple problems

Evaluation of definite integrals - geometric meaning of definite integrals, definite integrals (Riemann integral) as a limit of sums, fundamental theorem of integral calculus, evaluation of definite integrals by evaluating the anti-derivative, reduction formulae, Bernoulli’s formula, Gamma integral, properties of definite integrals; Areas and Volumes - area bounded by a curve and coordinate axes (simple problems), area bounded by two curves, the volume of a solid obtained by revolving area about an axis (simple problems)

Introduction to differential equations - definition of ordinary differential equations, order and degree of the ODE, general and particular solutions; Formation of differential equations - formation of differential equations by eliminating arbitrary constants (at most two constants), Modeling problems of Population growth, Bacterial growth, Newton’s law of cooling, Radioactive decay; Solutions of linear differential equations (First order) - solutions of first-order and first-degree differential equations: variable separable method, homogenous differential equation, linear differential equations, applications to modeling: Solving the differential equations that were formed for population growth, bacterial colony growth, Newton’s laws of cooling and radioactive decay

Introduction to Probability - classical definition, random experiment, sample space and events, sure-impossible-mutually exclusive–exhaustive events; Laws on probability - addition and multiplication theorems, independent and dependent events, conditional and total probability, Bayes’ theorem, simple problems; Probability distributions - introduction to random variables, probability mass function, probability density function, probability distribution functions, probability, general distribution, mathematical expectation, Mean and Variance, binomial distribution