Go Back   2023 2024 MBA > MBA > Main Forum

  #1  
Old 31st October 2012, 01:34 PM
shashank shahn
Guest
 
Default TGT UP syllabus Maths

Please provide me the Maths subject syllabus of Uttar Pradesh Trained Graduate Teacher recruitment exam because I have need of its syllabus for do prepation of this recruitment exam so please provide me its syllabus.
Reply With Quote Quick reply to this message
  #2  
Old 1st November 2012, 09:51 AM
Super Moderator
 
Join Date: May 2012
Default Re: TGT UP syllabus Maths

Here I am giving you syllabus of the Maths subject of Uttar Pradesh Trained Graduate Teacher recruitment exam as below:-

Real Numbers:
Representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification.

Rational numbers as recurring / terminating decimals. Examples of non-recurring / non terminating decimals. Existence of non-rational numbers (irrational numbers) and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.

Laws of exponents with integral powers. Rational exponents with positive real bases. Rationalization of real numbers. Euclid's division lemma, Fundamental Theorem of Arithmetic. Expansions of rational numbers in terms of terminating / non-terminating recurring decimals.

Elementary Number Theory:
Peano’s Axioms, Principle of Induction; First Principle, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function, Test of Divisibility, Euclid’s algorithm, The Unique Factorisation Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a number . Euler’s totient function, Theorems of Fermat and Wilson.

Matrices
R, R2, R3 as vector spaces over R and concept of Rn. Standard basis for each of them. Linear Independence and examples of different bases. Subspaces of R2, R3. Translation, Dilation, Rotation, Reflection in a point, line and plane. Matrix form of basic geometric transformations. Interpretation of eigenvalues and eigenvectors for such transformations and eigenspaces as invariant subspaces. Matrices in diagonal form. Reduction to diagonal form upto matrices of order 3. Computation of matrix inverses using elementary row operations. Rank of matrix. Solutions of a system of linear equations using matrices.

Polynomials:
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros / roots of a polynomial / equation. Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of quadratic and of cubic polynomials using the Factor Theorem. Algebraic expressions and identities and their use in factorization of polymonials. Simple expressions reducible to these polynomials.

Linear Equations in two variables:
Introduction to the equation in two variables. Proof that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, Algebraic and graphical solutions.

Pair of Linear Equations in two variables:
Pair of linear equations in two variables.
Geometric representation of different possibilities of solutions /

inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication.

Quadratic Equations:
Standard form of a quadratic equation. Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. Relation between roots and coefficients, Symmetric functions of the roots of an equation. Common roots.

Arithmetic Progressions:
Derivation of standard results of finding the nth term and sum of first n terms.

Inequalities:
Elementary Inequalities, Absolute value, Inequality of means, Cauchy-Schwarz Inequality, Tchebychef’s Inequality.

Combinatorics;
Principle of Inclusion and Exclusion, Pigeon Hole Principle, Recurrence Relations, Binomial Coefficients.

Calculus:
Sets. Functions and their graphs: polynomial, sine, cosine, exponential and logarithmic functions. Step function. Limits and continuity. Differentiation. Methods of differentiation like Chain rule, Product rule and Quotient rule. Second order derivatives of above functions. Integration as reverse process of differentiation. Integrals of the functions introduced above.

Euclidean Geometry:
Axioms / postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Relationship between axiom and theorem. Theorems on lines and angles, triangles and quadrilaterals, Theorems on areas of parallelograms and triangles, Circles, theorems on circles, Similar triangles, Theorem on similar triangles. Constructions.

Ceva’s Theorem, Menalus Theorem, Nine Point Circle, Simson’s Line, Centres of Similitude of Two Circles, Lehmus Steiner Theorem, Ptolemy’s Theorem.

Coordinate Geometry:
The Cartesian plane, coordinates of a point, Distance between two points and section formula, Area of a triangle.

Areas and Volumes:
Area of a triangle using Hero's formula and its application in finding the area of a quadrilateral. Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders / cones. Frustum of a cone.

Area of a circle; area of sectors and segments of a circle.
Trigonometry:
Trigonometric ratios of an acute angle of a right-angled triangle. Relationships between the ratios.
Trigonometric identities. Trigonometric ratios of complementary angles. Heights and distances.

Statistics:
Introduction to Statistics: Collection of data, presentation of data, tabular form, ungrouped / grouped,bar graphs, histograms, frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data. Mean, median and mode of grouped data. Cumulative frequency graph.

Probability:
Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson and Normal distribution. Sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and Regression.
Reply With Quote Quick reply to this message
Reply

Similar Threads
Thread Thread Starter Forum Replies Last Post
Thiruvalluvar university B.Sc maths syllabus sandeep marwaha Main Forum 2 27th September 2019 01:51 PM
MS University B.Sc Maths Syllabus Unregistered Main Forum 2 27th February 2018 02:56 PM
IIT Bombay Maths Olympiad Syllabus Unregistered Main Forum 1 5th December 2016 01:29 PM
NATA MATHS Syllabus Unregistered Main Forum 1 5th November 2016 05:42 PM
CCS University Msc Maths Syllabus Unregistered Main Forum 1 1st November 2016 03:56 PM
Syllabus of Maths for Cat Exam Unregistered Main Forum 1 26th October 2016 03:56 PM
Vikram University MSC Maths Syllabus Unregistered Main Forum 1 25th October 2016 05:02 PM
BPSC Maths Syllabus Unregistered Main Forum 1 15th October 2016 03:37 PM
Bsc Maths Syllabus Of Lucknow University Unregistered Main Forum 1 4th October 2016 06:39 PM
SSC CHSL Maths Syllabus Unregistered Main Forum 0 17th July 2015 05:19 PM
BHU B.Sc Maths Entrance Exam Syllabus Unregistered Main Forum 0 16th July 2015 04:58 PM
AUCET Maths Syllabus Unregistered Main Forum 0 15th July 2015 01:44 PM
MP PET Maths Syllabus Unregistered Main Forum 0 14th July 2015 05:27 PM
M.Sc Maths Syllabus BAMU Unregistered Main Forum 0 7th July 2015 12:54 PM
Mp Board 10th Maths Syllabus bijay arjuna Main Forum 1 15th March 2013 04:55 PM
Syllabus for B.Sc Maths H avdeshmishra 789 Main Forum 1 4th February 2013 12:17 PM
VTU Maths Syllabus raghvendra kumar.r Main Forum 1 25th September 2012 11:31 AM
BCA Maths Syllabus Pune University Monika68 Main Forum 1 7th September 2012 05:31 PM
SAT Syllabus for Maths chandan kumar pod Main Forum 1 17th August 2012 11:19 AM
B.Sc Maths Syllabus Mumbai University sudhir katoch Main Forum 1 28th June 2012 05:37 PM


Quick Reply
Your Username: Click here to log in

Message:
Options

Thread Tools Search this Thread



All times are GMT +5.5. The time now is 04:54 AM.


Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2024, vBulletin Solutions, Inc.
Search Engine Friendly URLs by vBSEO 3.6.0 PL2

1 2