11th Standard - old Maths / கணிதம் Subjects Question Paper Software Subscription

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11th Standard - old Maths English Medium Chapters / Lessons 2022-2023


Matrices and Determinants

Vector Algebra

Algebra

Sequence and Series

Analytical Geometry

Trigonometry

Functions and Graphs

Differential Calculus

Integral Calculus

Probability



11th Standard - old Maths English Medium Chapters / Lessons 2022-2023


Matrices and Determinants
Vector Algebra
Algebra
Sequence and Series
Analytical Geometry
Trigonometry
Functions and Graphs
Differential Calculus
Integral Calculus
Probability

11th Standard - old Maths English Medium Chapters / Lessons 2022-2023 Syllabus

MATRICES AND DETERMINANTS

Matrix Algebra – Definitions, types, operations, algebraic properties. Determinants − Definitions, properties, evaluation, factor method, product of determinants, co-factor determinants.

VECTOR ALGEBRA

Definitions, types, addition, subtraction, scalar multiplication, properties, position vector, resolution of a vector in two and three dimensions, direction cosines and direction ratios.

ALGEBRA

Partial Fractions − Definitions, linear factors, none of which is repeated, some of which are repeated, quadratic factors (none of which is repeated). Permutations − Principles of counting, concept, permutation of objects not all distinct, permutation when objects can repeat, circular permutations. Combinations, Mathematical induction, Binomial theorem for positive integral index−finding middle and particular terms.

SEQUENCE AND SERIES

Definitions, special types of sequences and series, harmonic progression, arithmetic mean, geometric mean, harmonic mean. Binomial theorem for rational number other than positive integer, Binomial series, approximation, summation of Binomial series, Exponential series, Logarithmic series (simple problems).

ANALYTICAL GEOMETRY

Locus, straight lines – normal form, parametric form, general form, perpendicular distance from a point, family of straight lines, angle between two straight lines, pair of straight lines. Circle − general equation, parametric form, tangent equation, length of the tangent, condition for tangent. Equation of chord of contact of tangents from a point, family of circles – concetric circles, orthogonal circles.

TRIGONOMETRY

Trigonometrical ratios and identities, signs of T-ratios, compound angles A ± B, multiple angles 2A, 3A, sub multiple (half) angle A/2, transformation of a product into a sum or difference, conditional identities, trigonometrical equations, properties of triangles, solution of triangles (SSS, SAA and SAS types only), inverse trigonometrical functions.

FUNCTIONS AND GRAPHS

Constants, variables, intervals, neighbourhood of a point, Cartesian product, relation. Function − graph of a function, vertical line test. Types of functions − Onto, one-to-one, identity, inverse, composition of functions, sum, difference product, quotient of two functions, constant function, linear function, polynomial function, rational function, exponential function, reciprocal function, absolute value function, greatest integer function, least integer function, signum function, odd and even functions, trigonometrical functions, quadratic functions. Quadratic inequation − Domain and range.

DIFFERENTIAL CALCULUS

Limit of a function − Concept, fundamental results, important limits, Continuity of a function − at a point, in an interval, discontinuous function. Concept of Differentiation − derivatives, slope, relation between continuity and differentiation. Differentiation techniques − first principle, standard formulae, product rule, quotient rule, chain rule, inverse functions, method of substitution, parametric functions, implicit function, third order derivatives.

INTEGRAL CALCULUS

Concept, integral as anti-derivative, integration of linear functions, properties of integrals. Methods of integration − decomposition method, substitution method, integration by parts. Definite integrals − integration as summation, simple problems.

PROBABILITY

Classical definitions, axioms, basic theorems, conditional probability, total probability of an event, Baye’s theorem (statement only), simple problems.

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11th Standard - old Maths English Medium Chapters / Lessons 2022-2023

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