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August 25th, 2016, 01:36 PM
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TMISAT Syllabus

Would you please give here syllabus for Mathematics subject for Tolani Maritime Institute’s Science Aptitude test (TMISAT) ?

As per your requirement I am here giving you syllabus for Mathematics subject for Tolani Maritime Institute’s Science Aptitude test (TMISAT).

TMI SAT Syllabus mainly comprises subjects namely:
Physics
Chemistry
Mathematics
English
Verbal Reasoning & Ability

Syllabus of Mathematics:
Sets:

Sets and their representations; Empty Sets; Finite and Infinite Sets; Equal sets; Subsets. Subsets of a set
of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union
and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets.
Practical problems based on sets.

Relations & Functions:
Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets.
Cartesian product of the sets of real (upto RxR). Definition of relation, pictorial diagrams, domain, codomain
and range of a relation. Function as a special kind of relation from one set to another. Pictorial
representation of a function, domain, co-domain and range of a function. Real value functions, domain
and range of these functions: constant, identity, polynomial, rational, modulus, signum and greatest
integer functions with their graphs. Sum, difference, product and quotients of functions.
Trigonometric Functions:
Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into
another. Definition of trigonometric functions with the help of unit circle. Signs of trigometric functions.
Domain and range of trigonometric functions and their graphs. Expressing sin and cos in terms of sinx,
cosx & cosy and their simple application. General solution of trigonometric equations of the type.

Algebra:

Principles of Mathematical Induction:
Principle of Mathematical Induction:
Process of the proof by induction, motivating the application of the method by looking at natural
numbers as the least inductive subset of real numbers. The principle of mathematical induction and
simple applications.

Complex Numbers and Quadratic Equations:
Need for complex numbers, especially to be motivated by inability to solve some of the quadratic
equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex
numbers. Statement of Fundamental theorem of Algebra , solution of quadratic equations in the
complex number system. Square root of a complex number.

Linear Inequalities:
Linear inequalities, algebraic solutions of linear inequalities in one variable and their representations on
the number line. Graphical solution of linear inequalities in two variables. Graphical solution of linear
inequalities in two variables. Graphical solution of system of linear inequalities in two variables.

Permutations and Combinations:
Fundamental principle of counting. Factorial n Permutations and combinations, derivation of formulae
and their connections, simple applications.
Binomial Theorem:
Histor , state e t a d proof of the i o ial theore for positive i tegral i di es. Pas al’s tria gle,
General and middle term in binomial expansion, simple applications.
Sequence and Series:
Sequence and Series. Arithmetic Progression (A.P) Arithmetic Mean (A.M) Geometric Progression and
general Term of a G.P. sum of n terms of a G.P. Arithmetic and Geometric series infinite G.P. and its
sum; geometric mean; relation between A.M. and G.M. formula

Coordinate Geometry:

Straight lines: Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a
line and angle between two lines. Various forms of equations of a line: parallel to axis; point slope form,
slope intercept form; two point form; intercept form and normal. General equation of a line. Equation of
family of lines passing through the point of intersection of two lines. Distance of a point from a line.
Conic Sections: Sections of a cone; circles, ellipse; parabola; hyperbola; a point; a straight line and a pair
of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties
of parabola; ellipse and hyperbola. Standard equation of a circle.
Introduction to Three-dimensional Geometry: Coordinate axes and coordinate planes in three
dimensions. Coordinates of a point. Distance between two points and section formula.
Calculus:

Limits and Derivatives:

Derivative and introduced as rate of change both as that of distance function and geometrically.
Intuitive idea of limit. Limit of polynomials and rational functions, trigonometric; exponential and
logarithmic functions. Definitions of derivatives, relate it to slope of tangent of a curve, derivative of
sum; difference; product and quotient of functions. The derivative of polynomial and trigonometric
functions.

TMISAT MATH Syllabus




Last edited by Neelurk; June 9th, 2020 at 11:26 AM.
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