12thMat-1 Course Topics
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Unit 7 : Applications of Derivatives |
7.1 Derivatives as Slope and Rate of Change -
meaning of derivative as slope, equations of
tangent and normal, meaning of derivative as
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 |
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Unit 6 : Vectos-2 |
6.1 Scalar Triple Product - definition of 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, 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 intersection of two
planes), angle between two planes, angle
between a line and a plane, meeting point of a
line and a plane, distance between a point
and a plane, distance between two parallel
planes |
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Unit 5 :Two Dimensional Analytic Geometry - II |
5.1 Conic sections - definition of a conic,
general equation of a conic, sections of a
cone; Circle - general form, standard forms,
parametric form, verifying 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 |
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Unit 4 : Trigonometric
functions and Inverse Trigonometric functions |
4.1 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 |
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Unit-3 Theory Equations |
Quadratic Equations - relation
between roots and coefficients,
conditions for rational, irrational and
complex roots, solving equations
reducible to quadratic equation, graph of
a quadratic function, minimum and
maximum values, quadratic inequalities
and sign of quadratic expression |
Polynomial equations - fundamental
theorem of algebra, formation of 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 factorised
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) |
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Unit-2 Complex Numbers |
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
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Unit-2 Complex Numbers |
Introduction to Complex Numbers - 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, geometrical representation
of complex numbers, conjugate, modulus,
addition and subtraction, polar form of a
complex number and principal value of the
argument |
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Unit-1 Matrices and determinants -II |
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 |
