TS Intermediate Mathematics Syllabus 2024-25: Check TS Inter 2nd Year Mathematics Syllabus

Complex Numbers

Complex number as an ordered pair of real numbers and fundamental operations, Representation of complex numbers in the form a+ib, Modulus and Amplitude of complex numbers, illustrations, geometrical and polar representation of complex numbers in argand plane, argand diagram.

De Moivre's Theorem

De moivre's theorem, integral and rational indices, nth roots of unity, geometrical interpretations, illustrations.

Quadratic Expressions

Quadratic expressions, equations in one variable, sign of quadratic expressions, change in signs, maximum and minimum values, quadratic in-equations.

Theory Of Equations

Relation between the roots and coefficients in an equation, solving equations when two or more roots of it are connected by certain relations, equation with real coefficients, occurrence of complex roots in conjugate pairs and its consequences, transformation of equations, reciprocal equations.

Permutations And Combinations

Fundamental principle of counting - linear and circular permutations, permutations of 'n' dissimilar things taken 'r' at a time, permutations when repetitions allowed, circular permutations, permutations with constraint repetitions, combinations-definitions and certain theorems.

Binomial Theorem

Binomial theorem for positive integral index, binomial theorem for rational index (without proof), approximations using binomial theorem.

Partial Fractions

Partial fractions of f(x) / g(x) when g(x) contains non -repeated linear factors, partial fractions of f(x)/g(x) when g(x) contains repeated and/or non-repeated linear factors, partial fractions of f(x)/g(x) when g(x) contains irreducible factors.

Measures Of Dispersion

Mean deviation, variance and standard deviation of ungrouped/grouped data, coefficient of variation, analysis of frequency distributions with equal means but different variances.

Probability

Random experiments and events, classical definition of probability, axiomatic approach and addition theorem of probability, independent and dependent events, conditional probability multiplication theorem, bayee's theorem, random variables and probability distributions, random variables, theoretical discrete distributions, binomial and poisson distributions.

Circle

Circle in standard form

centre and radius of a circle

length of tangent,

conditions for a line to be tangent,

chord joining two points on a circle, equation of the tangent at a point on the circle,

point of contact, etc

System Of Circles

Angle between two intersecting circles, radical axis of two circles, properties of common chord and common tangent of two circles, radical centre, intersection of a line and a circle.

Parabola

Conic sections, parabola, equation of parabola in standard form, different forms of parabola, parametric equations, equations of tangent and normal at a point on the parabola ( cartesian and parametric), conditions for straight line to be a tangent.

Ellipse

Equation of ellipse in standard form, parametric equations, equation of tangent and normal at a point on the ellipse (cartesian and parametric), condition for a straight line to be a tangent.

Hyperbola

Equation of hyperbola in standard form, parametric equations, equations of tangent and normal at a point on the hyperbola (cartesian and parametric), conditions for a straight line to be a tangent, asymptotes.

Integration

Integration as the inverse process of differentiation, standard forms, properties of integrals, method of substitution, integration of algebraic expressions, exponential, logarithmic, trigonometric and inverse trigonometric functions, integration by parts, integration by partial fractions method, reduction formulae.

Definite Integrals

Definite integral as the limit of sum, interpretation of definite integral as an area, fundamental theorem of integral calculus, reduction formulae, application of the definite integral to areas.

Differential Equations

Formation of a differential equation, degree and order of an ordinary differential equation, solving differential equations by various methods.