#
TN State Board 11th Maths Tuition

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- 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 11 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 11^{th} maths since they will have momentum for the following year, allowing them to do well in the class 11^{th} board exams. Finding a grade 11^{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 11^{th} maths using SCERT solutions. You will begin preparing for important competitive examinations in Class 11 so that you can keep your career options open. The subject specialists and solutions of maths class 11^{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 | Basic Algebra |

II | Sets, Relations, and Functions |

III | Trigonometry |

IV | Combinatorics |

V | Finite and Infinite Series |

VI | Two Dimensional Analytic geometry – I |

VII | Matrices and Determinants - I |

VIII | Vectors –I |

IX | Limits, Continuity, and Differentiability |

X | Differential Calculus |

XI | Integral Calculus |

## Course Lessons

Real Numbers - Revision: Rational, Irrational Numbers, Expressing inequalities like or using intervals; Absolute value of x; Exponents - Revision: Properties of exponents, Converting radicals/surds to exponents. Rationalizing fractions with surds; Polynomials - Addition, multiplication, and factorization of polynomials, Identities for, Method of undetermined coefficients to find a polynomial of given degree; Rational Expressions - Simplification of rational expressions by factorization, Partial fractions: linear and quadratic factors; Graphs - Graphical representation of data, Interpreting a graph and answering questions based on it; Equations and simple inequalities roots of Linear Equations, quadratic equations, roots of a factored polynomial equation; solving equations with radicals and absolute value; solving simple linear inequalities, graphical representation of equations and inequalities

Sets - recalling: Definitions and Examples, types of sets, algebra of sets, De Morgan Laws, Venn diagrams, practical problems; Intervals - open and closed intervals, other types of intervals, a neighborhood of a Point; the Cartesian product of sets - definition and examples; Relations - special relations: reflexive, symmetric, transitive, antisymmetric and equivalence relations; Functions and Graphs of Algebraic functions - functions as a formula, real-valued functions, identity function, polynomial functions, rational functions, absolute value functions, Signum functions, greatest integer functions; Algebra of functions - addition, subtraction, multiplication, and quotient of functions, the composition of functions, one to one and onto functions, Inverse of a function

Basic concepts - angles, signs of an angle, degree and radian measures, trigonometric ratios for all angles, basic trigonometric identities; Formulae for the sum of angles and sum and products of trigonometric ratios - formulae for sin(A ± B), cos (A ± B), tan(A±B), sin2A, cos2A, tan2A, sin3A, cos3A, tan3A, sum and product formulae: sinC ± sinD, cosC± cosD sinAcosB, cos A cos B, sinAsinB; Trigonometric equations - general solutions of the trigonometric equations: sin θ = sin α, cosθ = cosα, tanθ = tan α, a cosθ + b sin θ = c; Properties of Triangles - sine and cosine rule: Projection and area formulae, application to triangles; Inverse trigonometric functions - definitions, Identities, and simple problems

Factorials - definition and examples; Permutations - a fundamental principle of counting, permutation of distinct objects, not all distinct objects, simple problems; Combinations - definition, the relation between Permutation and combinations, properties, simple problems; Mathematical Induction - principles, simple problems

Binomial theorem - Binomial theorem for positive integral index (proof using combinations and also by induction), applications of binomial theorem; Sequence and Series - AP, GP, HP: Terms and Sum of AP and GP, Arithmetic and Geometric means. Problems on the sum of finite series, Arithmetic-geometric progression. Infinite Series - Infinite Geometric Series; Infinite Arithmetic - Geometric Series; Infinite series using the principle of telescopic sums; Exponential and logarithmic series (without proof); Binomial theorem for all rational index as an infinite series (without proof)

Locus of a point - definition and simple examples; Straight lines - various forms of the equation: Slope – point, Slope – intercept, two points, intercepts, normal and parametric forms; general form; related problems; Pair of Straight lines - equation of a pair of straight lines, problems related with the distance of a point from a line, the distance between two parallel lines, equation of a line bisecting the angle between two lines

Matrices - definition, concept, and types of matrices, operations of transpose, scalar multiplication, multiplying a row or column by a number, adding two rows/columns, reducing a matrix into triangular and echelon form, addition and multiplication of matrices, solving simultaneous linear equations by Gaussian Elimination Method; Determinants - definition of a determinant and its evaluations, properties of determinants, using properties of determinants to evaluate the value, product of determinants, determinant of a square matrix, singular and non-singular matrices

Scalars and Vector - Concept of scalars and vectors, Magnitude and direction of a general vector, free vectors, localized vectors, zero vector, unit vector, negative of a vector, algebra of vectors, resolution of a vector, vector Arithmetic in space (3D) direction ratios, and direction cosines; Vector Algebra - equality of vectors, collinear vectors, co-planar vectors, co-initial vectors, like vectors, unlike vectors, triangle law, parallelogram law, Polygon law; Applications of Vector Algebra - position vector of a point, the distinction between position vectors and free vectors, section formulae, problems; Product of two vectors - the angle between two vectors, definition of the dot product, geometrical meaning, properties, the definition of the cross product, geometrical meaning, properties, applications to geometry, trigonometry and physics

Left-hand limits and Right-hand limits, the definition of Limit, properties of limit, Limit theorems, Evaluation of limits; Continuity - graphical meaning of continuity of a function, visual identification of continuity and discontinuity, formal definition of continuity, examples, points of discontinuity, kinds of discontinuity, algebra of continuous functions, composite function theorem, standard problems; Slope as Limits - finding the slope of straight lines and curves, the definition of a derivative as the limit, evaluation of simple derivatives; Differentiability - graphical understanding of differentiability and non-differentiability, formal definition of differentiability and examples, the relation between continuity and differentiability, evaluation of derivatives using first principle, properties of derivatives, derivatives as a rate of change, the slope of a straight line

Methods of differentiation - differentiation formulae: addition, product, quotient rules, derivative of composite functions, power functions, trigonometric functions, derivative of implicit functions, parametric differentiation, the meaning of second, third, and higher-order derivatives (with problems restricted to second-order), differentiation of functions with respect to another function

Indefinite integral as Anti-derivative - integration as antiderivative, properties of integrals and integrals of standard functions and also functions Methods of Integration - properties of integration, indefinite integrals: decomposition, substitution, partial fractions and integration by parts methods