# Maths

Maths

**BITSAT 2010 Syllabus | Mathematics**

**BITSAT 2010 Syllabus:**

The BITSAT-2010 test will be conducted on the basis of NCERT syllabus for 11th and 12th class. The detailed syllabus is given in the Annexure. Candidates may refer to the NCERT text books for the contents. A sample test will be made available to the registered candidates at the BITS website on which he/she can practice as many times as desired.

**BITSAT Online Test Syllabus**

**BITSAT 2010 Mathematics Syllabus**

**1. Algebra**

- Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations.
- Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, equations reducible to quadratic equations.
- Logarithms and their properties.
- Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, arithmetico-geometric series, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
- Exponential series.
- Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications.
- Binomial theorem for a positive integral index, properties of binomial coefficients.
- Matrices and determinants of order two or three, properties and evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables.
- Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.
- Mathematical Induction
- Linear Inequalities, solution of linear inequalities in one and two variables.

**2. Trigonometry**

- Trigonometric ratios, functions and identities.
- Solution of trigonometric equations.
- Properties of triangles and solutions of triangles
- Inverse trigonometric functions
- Heights and distances

**3. Two-dimensional Coordinate Geometry**

- Cartesian coordinates, distance between two points, section formulae, shift of origin.
- Straight lines and pair of straight lines: Equation of straight lines in various forms, angle between two lines, distance of a point from a line, lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrent lines.
- Circles and family of circles : Equation of circle in various form, equation of tangent, normal & chords, parametric equations of a circle , intersection of a circle with a straight line or a circle, equation of circle through point of intersection of two circles, conditions for two intersecting circles to be orthogonal.
- Conic sections: parabola, ellipse and hyperbola their eccentricity, directrices & foci, parametric forms, equations of tangent & normal, conditions for y=mx+c to be a tangent and point of tangency.

**4. Three dimensional Coordinate Geometry**

- Direction cosines and direction ratios, equation of a straight line in space and skew lines.
- Angle between two lines whose direction ratios are given
- Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines.

## Graduate Record Examination | Study Material and Sample Papers for Preparetion

**Description : **Following are some study material and sample papers for the preparation of Graduate record examination. Each practice book contains full length test, answer keys, test taking strategies.

**Syllabus for JEE-2010 Mathematics**

**Algebra: ** Algebra of complex numbers, addition, multiplication,
conjugation, polar representation, properties of modulus and principal argument,
triangle inequality,cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.

Matrices as a rectangular array of real numbers, equality of matrices,
addition, multiplication by a scalar and product of matrices, transpose of a
matrix, determinant of a square matrix of order up to three, inverse of a square
matrix of order up to three, properties of these matrix operations, diagonal,
symmetric and skew-symmetric matrices and their properties, solutions of
simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes
Theorem, independence of events, computation of probability of events using
permutations and combinations.

**Trigonometry: **Trigonometric functions, their periodicity and graphs,
addition and subtraction formulae, formulae involving multiple and sub-multiple
angles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

**Analytical geometry: **Two dimensions: Cartesian coordinates, distance
between two points, section formulae, shift of origin.

**Graduate Aptitude Test in Engineering (GATE) Syllabus | Mathematics**

**Linear Algebra:** Finite dimensional vector spaces. Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton theorem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices. Finite dimensional inner product spaces, self-adjoint and Normal linear operators, spectral theorem, Quadratic forms.

**GATE Syllabus for Mathematics**

**Linear Algebra: **Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

**GITAM University Visakhapatnam Research Admission 2009**

**GITAM University Visakhapatnam**

(*Estd u/s 3 of UGC Act, 1956*)

Gandhi Nagar Campus, Rushikonda, Visakhapatnam-530045, A.P. India, Epabx:
0891-2790101, 2840525, 2840506, Fax: 0891-2795312

**PG Admissions 2009 in Statistics & Maths - Central
University of Rajasthan**

__Central University of Rajasthan invites applications
for admissions to the following post-graduate programmes from students all over
India:
__

1. M.Sc./M.A. Statistics(Actuarial),

2. M.Sc.Tech. Mathematics,

**Eligibity Criteria**

**Event : MAA Washington Technical Festival 2009 on Maths**

Technical festival 2009 on Math at The Mathematical Association of America Washington, DC

The Mathematical Association of America(MAA)

1529 18th Street NW

Washington, DC 20036

Phone: 202-387-5200

**MathFest 2009**

**Syllabus : IIT-JEE 2007 Mathematics Syllabus**

**Algebra:** Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

**Indian Institute of Aircraft Engineering (IIAE) ADMISSIONS 2009-2010**

**Indian Institute of Aircraft Engineering (IIAE)
Approved by D.G.C.A. Govt. of India, Ministry of Civil Aviation for AME course
A 191, Road No. 4, Lane No. 8, Mahipalpur Extension, NH - 8 - New Delhi
Phone-No: 011 - 30627411, 30627412, 30627401, 26784543, Mobile: 9312438831 **

**College/Location:**

**PORTAL:**

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**Syllabus : BITSAT Exam Syllabus - mathematics**

**1. Algebra**

**1. **Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations.

**2. **Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, equations reducible to quadratic equations.

**Joint Admission Test (JAM) Syllabus for Mathematics (MA)
: 2009**

**Sequences, Series and Differential Calculus:**

- Sequences of real numbers.
- Convergent sequences and series, absolute and conditional convergence.
- Mean value theorem.
- Taylor 's theorem.
- Maxima and minima of functions of a single variable.
- Functions of two and three variables.
- Partial derivatives, maxima and minima.

**Integral Calculus:**

**Joint Admission Test (JAM) Syllabus for Mathematical Statistics (MS)
: 2009**

*The Mathematical Statistics (MS) test paper comprises of Mathematics (40%
weightage) and Statistics (60% weightage).*

**Mathematics:**

**Sequences and Series:**

- Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.

**Differential Calculus:**