## Wednesday, December 24, 2014

### 33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions - Revision Facilitator

Sections in the chapter

33.1 Introduction
33.2 Some basic formulae
33.3 Domain and range of trigonometrical functions
33.4 Sum and difference formulae
33.5 Sum and difference into products
33.6 Product into sum or difference
33.7 T-ratios of the sum of three or more angles
33.8 Values of trigonometrical ratios some important angles and some important results.
33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.
33.10 Maximum and minimum values of trigonometrical functions

Study Plan

Day 1

33.1 to 33.4

33.1 Introduction
33.2 Some basic formulae
33.3 Doman and range of trigonometrical functions
33.4 Sum and difference formulae

Do objective type exercises 58,

Day 2

33.5 Sun and difference into products
33.6 product into sum and difference

Do objective type exercises 84,91, 92, 104, 115,

Day 3

33.7 T-ratios of the sum of three or more angles

Do objective type exercises 39, 44, 106, 113, 117,

Day 4

33.8 Values of trigonometric ratios of some important angles and some important results

Do objective type exercises 1,2,3,5,6,7,8,9,10,11

Day 5

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A

Do objective type exercises 12,13,14,15,16,17,19,20,21,22

Day 6

33.10 maximum and minimum values of trigonometrical functions

O.T.E.: 4,18,23-30

Day 7

O.T.E.: 31 to 50

Day 8

O.T.E.: 51 to 70

Day 9
O.T.E.: 71 to 90

Day 10
O.T.E.: 91 to 110

Revision Period

Day 11
O.T.E.: 111 to 120

Day 12
O.T.E.: 121 to 130

Day 13
O.T.E.: 131 to 140

Day 14
O.T.E.: 141 to 148

Day 15
Fill in the blanks type exercise: 1 to 10

Day 16
Fill in the blanks type exercise: 11 to 20

Day 17
Fill in the blanks type exercise: 21 to 30

Day 18
Fill in the blanks type exercise: 31 to 36

Day 19
True/false type exercise: 1 to 12

Day 20
Fill in the blanks type exercise: 13 to 25

Day 21
Practice Exercise: 1 to 10

Day 22
Practice Exercise: 11 to 20

Day 23
Practice Exercise: 21 to 32

Day 24
Formula Revision

Day 25
Formula Revision

Revision facilitator

33.1 Introduction
33.2 Some basic formulae
33.3 Domain and range of trigonometrical functions
33.4 Sum and difference formulae
33.5 Sum and difference into products
33.6 Product into sum or difference
33.7 T-ratios of the sum of three or more angles
33.8 Values of trigonometrical ratios some important angles and some important results.
33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.
33.10 Maximum and minimum values of trigonometrical functions

### IIT JEE Mathematics Study Guide Ch.34 Properties of Triangles and circles connected with them - Revision Facilitator

Recollect and see how many things do you remember

34.1 Introduction
34.2 Sine rule
34.3 Cosine formulae
344 Projection formulae
34.5 Trigonometrical ratios of half of the angles of a triangle
34.6 Area of a triangle
34.7 Napier’s analogy
34.8 Circumcircle of a triangle
34.9 Inscribed circle or incircle of a triangle
34.10 Escribed circles of a triangle
34.11 Orthocentre and its distances from the angular points of a triangle
34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
34.13 Area of a cyclic quadrilateral
34.14 Ptolemy’s theorem

Study Plan

Day 1

Study sections 34.1 to 34.5

34.1 Introduction
34.2 Sine rule
34.3 Cosine formulae
34.4 Projection formulae
34.5 Trigonometrical ratios of half of the angles of a triangle

Day 2

Study Sections 34.6, 34.7, 34.8, 34.9,

34.6 Area of a triangle
34.7 Napier’s analogy
34.8 Circumcircle of a triangle
34.9 Inscribed circle or incircle of a triangle

Attempt Objective Type Exercises 1 to 10

Day 3

34.10, 34.11

34.10 Escribed circles of a triangle
34.11 Orthocentre and its distances from the angular points of a triangle

Attempt objective type exercises 11 to 20

Day 4

Study 34.12 to 34.15

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
34.13 Area of a cyclic quadrilateral
34.14 Ptolemy’s theorem

Attempt obj type exercises 21 to 30.

Day 5

Attempt obj type exercises 31 to 45.

Day 6

Attempt obj type exercises 46 to 60.

Day 7

Attempt obj type exercises 61 to 75.

Day 8

Attempt obj type exercises 76 to 90.

Day 9

Attempt fill in the blanks 1 to 15.

Day 10

Attempt fill in the blanks 16 to 31.

Day 11

Practice Exercise 1 to 21

Days 12 to 20

Revision

### IIT JEE Mathematics Study Guide Ch. 35. Trigonometrical equations and Revision Facilitator

Sections in the chapter R D Sharma
35.1 Trigonometrical equations

Study Plan

Day 1

35.1 Trigonometrical equations
Objective Type Exercise: 1 to 20

Day 2
O.T.E.: 21 to 40

Day 3
O.T.E.: 41 to 60

Day 4
O.T.E.: 61 to 73

Day 5
Fill in the blanks type exercise 1 to 16

Try to recollect relevant points on the topic and if required right click on the topic if link is given and open in a new window to read the relevant material. Close the window and come back.

35.1 Trigonometrical equations

Periodic Function

Period of a Function

General solutions of simple trigonometric equations

Join Orkut Community for more interaction

http://www.orkut.co.in/Main#Community.aspx?cmm=39291603

### IIT JEE Mathematics Study Guide 36. Inverse Trigonometrical functions and Revision Facilitator

Sections in the Chapter R D Sharma

36.1 Inverse Trigonometrical functions
36.2 Properties of inverse trigonometrical functions

Study Plan

Day 1

36.1 Inverse Trigonometrical functions
36.2 Properties of inverse trigonometrical functions

Day 2

Objective Type Exercise: 1 to 20

Day 3
O.T.E.: 21 to 40

Day 4
O.T.E.: 41 to 60

Day 5
O.T.E.: 61 to 65
Fill in the blanks 1 to 15

Day 6
Fill in the blanks 16 to 25
Practice exercise 1 to 4

Day 7 to 10
Revision

Revision Facilitator

36.1 Inverse Trigonometrical functions
36.2 Properties of inverse trigonometrical functions

Recollect the concepts and formulae

Invertible Function - Bijection

Inverse Trigometric Function

Domain and Ranges of Inverse Trigonometric Functions

sin-inv (sin θ) =
Similar relations

sin-inv x = cosec-inv(?)
Similar relations

sin-inv x = cos-inv (?)
Similar relations

sin-inv x + cos-inv x =
Similar relations

sin-inv x + sin-inv y =
Similar relations

sin-inv(-x) =?
Similar relations

2 sin-inv x =?
Similar relations

3 Sin-inv x = ?
Similar relations

Tan-inv x + Tan-inv y + Tan-inv z
Similar relations

### Ch. 37 Solution of Triangles - Revision Facilitator

Sections in the Chapter R D Sharma

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Study Plan

Day 1

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Day 2

Objective Type Exercises 1 to 20

Day 3
Revision

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

a. Right angled triangle - orthocentre
b. Distance of midpoint of the hypotenuse of a right angled triangle from the vertices of the triangle.
c. Relation between mid-point of a right angled triangle and its circumcentre

### Ch. 38 Heights and distances - Revision Facilitator

Sections in the chapter R D Sharma

38.1 Angle of elevation and depression of a point
38.2 Some useful results

Study Plan

Day 1

38.1 Angle of elevation and depression of a point
38.2 Some useful results

Day 2

Objective Type Exercises 1 to 20

### Ch.2. Cartesian Product of Sets and Relations - Part 2

Concept Review

2.2 Relation

Let A and B be two sets. Then a relation R from A to B is a subset of A×B.

R is a relation from A to B => R is a subset of A×B.

Total number of relations: If A and B are two non empty sets with m and n elements respectively, A×B consists of mn ordered pairs.
Since each subset defines a relation from A to B, so total number of relations from A to B is 2mn.

2.3 Types of relations

Void relation
Universal relation
Identity relation
Reflexive relation
Symmetric relation
Transitive relation
Antisymmetric relation
Equivalence relation

2.4 (2.5 in the book) Composition of Relations

## Tuesday, December 23, 2014

### K.V.S.S. Gangadhara Sastry, M.A., B.Ed. Passionate Teacher

_____________

_____________

He taught English and Mathematics with passion.

You were a light
that always glowed bright
You were a scholar erudite
gave your students insight

You had knowledge might
used to it well to write
notes and essays right
that brought students delight

You had the foresight
to plan and excite
your children and students to recite
poems full of  wisdom and wit

by K.V.S.S. Narayana Rao
23.12.2014

## Sunday, November 30, 2014

### JEE Main 2015 Mathematics Syllabus

JEE MAIN 2015 SYLLABUS FOR MATHEMATICS:

1 Sets, Relations And Functions

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations,functions;.
One-one, into and onto functions, composition of functions

2 Complex Numbers and Quadratic Equations

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality,
Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

3 Matrices And Determinants

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

4 Permutations And Combinations

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications

5 Mathematical Induction

Principle of Mathematical Induction and its simple applications

6 Binomial Theorem And Its Simple Applications

Binomial theorem for a positive integral index, general term and middle term,properties of Binomial coefficients and simple applications

7 Sequences And Series

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers.
Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric progression

8 Limit, Continuity And Differentiability

Real valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions.
Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions.
Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two.
Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of
quantities, monotonic increasing and decreasing functions,
Maxima and minima of functions of one variable, tangents and normals

9 Integral Calculus

Integral as an anti derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.
Integral as limit of a sum. Fundamental Theorem of Calculus.
Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form

Evaluation of simple integrals of the type:

10 Differential Equations

Ordinary differential equations, their order and degree.
Formation of differential equations. Solution of differential
equations by the method of separation of
variables, solution of homogeneous and linear differential
equations of the type

11 Coordinate Geometry

Cartesian system of rectangular coordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

Straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.

Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of
the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

12 Three Dimensional Geometry

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a
plane, coplanar lines

13 Vector Algebra

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

14 Statistics And Probability

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

15 Trigonometry

Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances

16 Mathematical Reasoning

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction,
converse and contrapositive

## Saturday, November 29, 2014

### JEE Main 2015 Information Booklet

Submission of Online Application Form: 07.11.2014 – 18.12.2014
Joint Entrance Examination (Main) - 2015
I N F O R M A T I O N I N F O R M A T I O N B U L L E T I N B U L L E T

http://jeemain.nic.in/webinfo/pdf/JEE_Main_Bulletin%202015.pdf

### JEE 2014 Advanced Mathematics Paper

49. From a point P(lambda, lambda, lambda), perpendiculars PQ and PR are drawn respectively on the lines
y = x,  z = 1 and y  = -x and  z = − 1. If P is such that ∠QPR is a right angle, then the possible
value(s) of lambda is (are)
A) SQRT (2) B) 1         C) -1           D) − SQRT (2)