Higher secondary Mathematics

Kurul sınav 12. matematik hazırlanması Üretim

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topic coverd u by this app:-

**Relations and Functions:Types of relations are reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations etc

**Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

*** Algebra

**Matrices:Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices.

.** Determinants: of a square matrix , properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle and number of solutions of system of linear equations by examples.

*** Calculus

Continuity and Differentiability: derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions.

Concept of exponential and logarithmic functions.

Theorems (without proof) and their geometric interpretation :Rolle's and Lagrange's Mean Value

#Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima .

#Integrals:Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof definite integrals and evaluation of definite integrals.

##Applications of the Integrals :Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only).

5. Differential Equations :Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.

# Vectors :Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector.

2. Three - dimensional Geometry

Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance

between two lines.Cartesian and vector equation of a plane.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.

*** Probability

Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability

distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.