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Mathematics IA

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Revised Syllabus Intermediate I Year
Mathematics Ia
(Algebra, Vector Algebra & Trigonometry)

Paper I A – Algebra:

65 Periods

1	Functions of Mappings	9
2	Surds	6
3	Logs	6
4	Mathematical Induction	14
VECTOR ALGEBRA:
5	Addition of Vectors	24
6	Multiplication of Vectors	25

Trigonometry:

60 Periods

7	Graphs & Periodic Functions ) (Trigonometric ratios of Compound angles ) (Multiple & Sub-multiple angles ) ( Transformations	9
8	Trigonometric Equations	16
9	Inverse Trigonometric functions	5
10	Hyperbolic functions	5
11	Properties of triangles	10
12	Heights and distances in single plane	7
13	Complex Numbers	6
14	De-movires Theorem	5
15	Trignometric expansions	3

Intermediate Mathematics –1a (Algebra, Vector Algebra & Trignometry) :

10 Periods

S. No	Topics/Chapter	Sub-topics/Sections/Sub-sections	Periods of Instructions
1	Functions or Mappings	A. Definitions of one-one, onto, bijection functions, Identity and constant functions Equality of two functions	9 periods
		B. Definitions of Inverse function, composite Function and Inverse of composite Function Theorems with proofs F:A->B, g:B->C are bijective functions, then gof:A->C is also a bijection. Let A & B be two sets. If f:A->B is a Bijective then f –1 :B-A is also a bijective function If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1. If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1. If f:A->B is a function and IA: A->A, IB: IB: B->2B are identity functions then foIA= f=IBof If f: A->B is a bijective function Then / f -1 = IA, fof –1 = IB If f:A->B, g:B->Cand h:C->D are any 3 functions then ho(gof) = (hog) of or composition of functions is associative
		C. Definition of real valued function Definition of domain, Range Algebra of real valued functions
2	Surds	Evaluating Surds of the form
		Cube root of the surds of the form
		Rationalizing factors (upto 3rd degree)
3	Logarithms	Definitions Introduction of common logarithms	6 periods
		Theorems:
		log mn=log m+log n log (m/n) = log m – log n log m k = Klog m log a m = log b m . log a b
		Nature of Logarithms through graphs, Logarithms functions
		Types of Logarithms
4	Mathematical Induction	Principle of Mathematical Induction; Theorem of Principle of finite Mathematical Induction
		Application of Mathematical Induction S n, S n2, S n3 etc.,
		x-y devides x”-y” for all positive integral
		values of n and other divisibility problems	6 Periods

Vector Algebra

14 Periods

Addition Of Vector

Introduction of Vector as an ordered triad of real numbers- Representation of a vector as a directed line segment – Free and localized Vectors.
Classification of Vectors – Collinear or parallel, like, unlike vectors, Co-initial vectors, coplanar and non-coplanar vectors, position vector, unit vector etc.,
Addition of vectors – parallelogram and triangle laws – Properties of additions .
Multiplication of Vector by Scalar
Angle between two Non-Zero vectors. Vector of the points of division – Concurrence of Medians of a Triangle by Vector Method
Linear combination of Vectors – linearly dependent and independent vectors
Components of Vector in three dimension – Direction consines,
modulus of a vector, Right and Left hand systems – Orthogonal triad of Vectors.
Vector equation of line and plane in parametric from co linearity of three points and co planarity of four points.
Multiplication Of Vectors
Definition of the Scalar or dot product of two vectors its geometrical representation and Orthogonal projection of
Properties of Scalar product – Commutative, and distributive laws – condition for perpendicularity of two vectors a, b are perpendicular vectors, Then a.b = o.
Analytic expressions for scalar product in terms of i, j, k, angle between the two vectors. Some identities such as (a+b) 2 etc.
Proof by Vector Method of
angle in a semi-circle is a right angle
laws of cosines and projection formula in a triangle
Concurrency of the altitudes and perpendicular bisectors of sides of a triangle
= cos A cos B + sin A sin B formal form – Angle between two planes.
Vector equation of a plane in the normal form of two types:
Vector equation of sphere, angle between two planes.
Vector or Cross product of two vectors – Non-commutative vector product is distribution over addition
Vector product among i, j, k, sine or the angle between two Vectors, Unit vector perpendicular to a given pair of Vectors
Vector area of a parallelogram and a triangle – Proofs by vector method
(i) sin rule
Triple Products – Scalar triple product and its geometric interpretation. Co planarity of three vectors and deductions volume of a tetrahedron.
Vector area of a plane in different parts, skew lines – simple problems.
Vector triple product and its results.
Product of Four vectors – Scalar and vector product of Four vectors

Trigonometry

Topics/Chapter	Sub-topics/Sections/Sub-sections	Periods of Instructions
Graph & Periodicity	Definition of Trigonometric functions with the help of unit circle	3 periods
	Particular values - Variation of sinq , cos ? ,tanq ? , Variation 3 periods in values as changes periodicity and extreme values, trigonometric ratio of any angle Graphs y=sin ? , Y=cos ? , y=tan ?
Trigonometric ratios of compound angles	Trigonometric Ratios of compound angles such as Summation Formulae Sin(A+B), Cos(A+B), Tan (A+B)	5 periods
Trigonometric ratios of Multiple and submultiples Angles	Triogonometric ratios of 2A, 3A and A/2 (Multiple and submultiple Angles angles	4 periods
Transformations and Identities	Transformation from sum to products Transformation from products to sums	4 periods
Trigonometric Equations	Trigonometric Equations Solving simple Trigonometric Equations Inverse of all the six Trigonometric functions, domains, ranges-graphs. Solving simple Equations involving Inverse trigonometric functions	5 periods
Hyperbolic functions	Meaning of e, exponential of the series Definitions Domain and Range of Hyperbolic and Inverse Hyperbolic functions Addition formulae of Hyperbolic functions Sinh(x±y), Cosh(x±y) etc.,	3 periods
Properties of triangles	Relation between the sides and angles of an triangle. Half angle formulae and area of a triangle Incircle and ex-circle of a triangle	10 periods
Heights & Distances	Angles of Elevation and Depression Problems involving one plane	10 periods
Complex Numbers	Complex number as an ordered pair of real numbers. Representation in the form of a+ib, real and imaginary part equality of Complex Numbers Fundamental operations on Complex Numbers. Conjugate Complex Numbers Modulus and amplitude of a Complex Numbers Geometrical Representation of a complex number, Argand Plane and Argand diagram	6 periods
Demovieris Theorem	Demovier's theorem for integral index and for rational index. nth root of unity and its geometrial representation. Cube roots of unity
Trigonometric Expansions	Expansion of Trigonometric functions, Sin n ? , Cos n ? as series, expansion of Tann n ? and Cos n ? Expressing Sinnq and Cosq interms of Sines and Cosines of multiples of ?	7 periods

Mathematics IB

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Revised Syllabus Intermediate I Year
Mathematics Ib
(Coordinate Geometry And Calculus)

Coordinate Geometry
Dimensions:	65 Periods)
Locus	4
Translation and rotation of axes	5
Straight lines	20
Pair of Straight lines	20
Dimensional;
Coordinates	8
Direction cosines and ratios	8

Calculus:
Functions, Limits and Continuity	16
Derivatives, first order and second order derivatives	16
Applications of derivatives	20
Partial differentiation	8

Co-Ordinate Geometry – 2D

Locus	Definition of locus Equation of locus Illustrations
Translation & Rotation of axes	Translation of axes Rotation of axes Illustrations
Straight line	General equation of a straight line and Forms of equation of a straight line slope intercept form Intercepts form Point-slope form Two point form Normal form xCosx+ySinx=p Symmetric form x-x 1 /sinq = y-y 1 /sinq = r To reduce the general equation into different forms Point of intersection of two straight lines Family of straight lines passing through the point of intersection of two given lines.
Pair of straight lines	ax 2 +2hxy+by 2 =0 a pair of line through the origin Angle between the lines ax 2 +2hyx+by 2 =0 conditions for coincidence perpendicularities Bi-sector of the angles between the lines L 1 =0, L 2 =0 Combined equation of the bisectors of the angles between the lines ax 2 +2hxy+by 2 =0 If the general equation of the second degree in x & y i.e. ax 2 +2nxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then abc+2fgh-af 2 -bg 2 - ch 2 =0, h 2 >ab, g 2 >ac and f 2 >bc Converse of 4.5 without proof. If S=ax 2 +2hxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then ax 2 +2hxy+by 2 =0 represents the line through the origin, parallel to the above lines. Angle between the lines S=0 condition for these line to be (I) Parallel (ii) Perpendicular Point of intersection of the lines S=0 Homogenization of the second degree equation with a first degree equation in x and y
	Co-Ordinate Geometry – 3D
Co-ordinates	Co-ordinate planes – Co-ordinates of a point – Distance between two points in space. To find the Co-ordinates of a point which divides the join of two points (x, y, z), (x1 y1 z1) internally in the ratio m:n – centroid of a triangle and tetrahedron
Direction cosines and ratios	Direction cosines of a line, relation between the cosines l 2 +m 2 +n 2 =1 Direction cosines of a line, to find the direction cosines when direction ratios are given
	Calculus
Functions, Limits and Continuity	Function, Domain and Range of Continuity Function-Algebraic, Trigonometric, Inverse Trigonometric, Hyperbolic, Step function and construction of graphs of logx, e l, lxl, (x) Concepts of intervals and neighborhood Limits – Definition of right hand limit, left hand limit, limit. Limits of f+g, f/g, fog (without proof) Standard limits (Limits 3,4, and 5 without proof) Continuity – Definition and simple illustration
Differentiation	Introduction – Definition Differentiation of a function at a point and on an Interval – Derivative of a function – Differentiation of sum, difference, product and quotient of functions. Differentiation of algebraic, circular, exponential, logarithmic functions. Derivatives of composite, implicit, parametric, inverse circular, hyperbolic and inverse hyperbolic functions. Logarithmic differentiation, Derivative of a function with respect of another function. Derivatives of first and second order
Application of Derivative	Infinitesimal – Differentials Errors and approximations Geometrical interpretation of a derivative Equations of tangent, normal sub tangent, sub-normal at a point Lengths of tangent, normal sub-tangent, sub-normal at a point. Angle between two curves, orthogonally Derivative as a rate measurer Increasing and decreasing functions Maxima and minima
Partial Differentiation	Partial derivatives - First and second orders only Homogeneous functions – Euler's theorem on homogeneous functions – functions – simple applications.

Economics

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Intermediate First Year Syllabus
(With Effect From 2003-2004)

Paper-I Introductory Economic Theory

UNIT-I: Nature And Scope Of Economics

14 Periods

Brief explanation of the concepts – Origin of the word Economics – Economic problem, Economic activity – Economics as a study of wants, efforts and satisfaction. Subject matter of Economics – Broad division
Consumption, production, exchange and distribution. Income and Employment, Planning and Development.
Definition of Economics:
Explanation and criticism of: Wealth definition of Adam Smith – Welfare definition of Alfred Marshall
Scarcity definition of Lionel Robbins – Development definition of Paul Samuelson.
Divisions of Economic theory:
Micro Economics – meaning, subject matter and importance.
Macro Economics – meaning, subject matter and importance.

UNIT-II: Basic Concepts:

10 Periods

Goods: Free and Economic goods. Consumption goods and Capital goods – Intermediate goods – Perishable and Non-perishable goods, Single use goods and durable goods.
Wealth: Meaning, Characteristics and Classification.
Income: A flow concept.
Welfare: Meaning, difference between wealth & welfare.
Utility: Meaning and classification.
Value: Value in use and value in exchange.
Price: Meaning.
Wants: Characteristics and classification.

UNIT-III: Analysis Of Demand:

10 Periods

Meaning of cordinal and ordinal utility.
The Law of Diminishing marginal utility – Statement of the Law, Illustration, assumptions, exceptions and importance.
Law of equi-marginal utility – Statement of the Law – Illustration, Assumptions and importance.
Demand – Concept of Demand, direct and derived demand, Demand function, determinants of demand, Individual demand schedule and curve, market demand schedule and curve, Law of demand and diagrammatic explanation – exceptions of the law, explanation of the downwards sloping demand curve, Income and cross demand with diagrams.
Price elasticity of demand – meaning – Measurement and Importance.

UNIT-IV: Theory Of Production:

15 Periods

Production Function – Simple illustrations.
Law of variable proportions – Statement of the Law, illustrations, assumptions and importance.
Returns to Scale – Mention of increasing, constant, diminishing returns only.

UNIT-V: Analysis Of Supply:

10 Periods

Concept of Supply – supply function – determinants of supply – Law of supply – supply schedule supply curve.
Cost and Revenue Analysis: Concept of cost – Real, money and opportunity cost – Fixed, Variable, total, average and marginal costs Average and Marginal costs Curves (short run only) concept of revenue – Total, Average and Marginal revenue – Average and Marginal Revenue Curves.

UNIT-VI: Price Determination:

25 Periods

Market: Meaning of market, types of market on the basis of area, period of time and competition.
Perfect Competition:
Features of Perfect competition and Imperfect competitions. Price Determination – Equilibrium of the Firm and Industry. Time element in Price determination (No diagrammatic representation).
Monopoly: Meaning – Features of Monopoly – Price determination.

UNIT-VII: Distribution:

10 Periods

Distribution of National Income among the four factors of production.
Rent: Meaning of economic rent, contract rent, rent as a differential surplus (Ricardo) – Scarcity rent, transfer earnings- Quasi rent.
Wages: Meaning of wages – Types of wages – Money wages, real wages and piece wages – Time wage – Factors affecting real wages.
Interest: Meaning of interest – Gross interest and Net interest.
Profit: Meaning of Profit – Gross profit and Net profit.

UNIT-VIII: National Income:

15 Periods

Definitions and concepts of National Income – Gross national Product – Gross Domestic Product Net National product – National Income at Factor prices – Personal income – Disposable income and per capita
income – Relationship between population and per capita income.
Components of National Income Consumption expenditure – Investment expenditure – Government
expenditure – net income in Foreign Trade.
Measurement of National Income :
Value added Method – Income Method – Expenditure Method.

UNIT-IX: Macro Economic Aspects:

30 Periods

Basic features of Classical theory of Employment – Basic Features of Keynesian theory of Employment.
Role of Government in Economic activities – Components of public revenue – Public Expenditure – Public Debt. (Elementary concepts only).
Role of International Trade in Economic Activities – Exports and Imports and Balance of payments (Elementary concepts only).

UNIT-X: Money And Inflation:

15 Periods

Concept of Money, Liquidity and Near Money – Functions of Money activities of Commercial Banks, Concepts of Primary Deposit, Secondary Deposit, Demand Deposit and Time Deposit – Types of Money.
Concept of Inflation – Types of Inflation – Economic Effects of Inflation.

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Intermediate First Year Syllabus
(With Effect From 2003-2004)
Economics-I

Paper-I Introductory Economic Theory

UNIT-I: Nature And Scope Of Economics:

15 Periods

Brief explanation of the concepts – Origin of the word Economics – Economic problem, Economic activity – Economics as a study of wants, efforts and satisfaction. Subject matter of Economics – Broad division
– Consumption, production, exchange and distribution. Income and Employment, Planning and Development.
Definition of Economics:
Explanation and criticism of: Wealth definition of Adam Smith – Welfare definition of Alfred Marshall
– Scarcity definition of Lionel Robbins – Development definition of Paul Samuelson.
Divisions of Economic theory:
Micro Economics – meaning, subject matter and importance.
Macro Economics – meaning, subject matter and importance.

UNIT-II: Basic Concepts:

10 Periods

Goods: Free and Economic goods. Consumption goods and Capital goods – Intermediate goods – Perishable and Non-perishable goods, Single use goods and durable goods.
Wealth: Meaning, Characteristics and Classification.
Income: A flow concept.
Welfare: Meaning, difference between wealth & welfare.
Utility: Meaning and classification.
Value: Value in use and value in exchange.
Price: Meaning.
Wants: Characteristics and classification.

UNIT-III: Analysis Of Demand:

25 Periods

Meaning of cordial and ordinal utility.
The Law of Diminishing marginal utility – Statement of the Law, Illustration, assumptions, exceptions and importance.
Law of equi-marginal utility – Statement of the Law – Illustration, Assumptions and importance.
Demand – Concept of Demand, direct and derived demand, Demand function, determinants of demand, Individual demand schedule and curve, market demand schedule and curve, Law of demand and
diagrammatic explanation – exceptions of the law, explanation of the downwards sloping demand curve, Income and cross demand with diagrams
Price elasticity of demand – meaning – Measurement and Importance.

UNIT-IV: Theory Of Production:

15 Periods

Production Function – Simple illustrations.
Law of variable proportions – Statement of the Law, illustrations, assumptions and importance.
Returns to Scale – Mention of increasing, constant, diminishing returns only.

UNIT-IV: Theory Of Production:

15 Periods

Production Function – Simple illustrations.
Law of variable proportions – Statement of the Law, illustrations, assumptions and importance.
Returns to Scale – Mention of increasing, constant, diminishing returns only.

UNIT-V: Analysis Of Supply:

10 Periods

Concept of Supply – supply function – determinants of supply – Law of supply – supply schedule supply curve.
Cost and Revenue Analysis:
Concept of cost – Real, money and opportunity cost – Fixed, Variable, total, average and marginal costs Average and Marginal costs Curves (short run only) concept of revenue – Total, Average and Marginal
revenue – Average and Marginal Revenue Curves.

UNIT-VI: Price Determination:

10 Periods

Market: Meaning of market, types of market on the basis of area, period of time and competition.
Perfect Competition:
Features of Perfect competition and Imperfect competitions. Price Determination – Equilibrium of the Firm and Industry. Time element in Price determination (No diagrammatic representation).
c) Monopoly: Meaning – Features of Monopoly – Price determination.

UNIT-VII: Distribution:

10 Periods

Distribution of National Income among the four factors of production.
Rent: Meaning of economic rent, contract rent, rent as a differential surplus (Ricardo) – Scarcity rent, transfer earnings- Quasi rent.
Wages: Meaning of wages – Types of wages – Money wages, real wages and piece wages – Time wage – Factors affecting real wages.
Interest: Meaning of interest – Gross interest and Net interest.
e) Profit: Meaning of Profit – Gross profit and Net profit.

UNIT-VIII: National Income:

15 Periods

Definitions and concepts of National Income – Gross national Product – Gross Domestic Product Net National product – National Income at Factor prices – Personal income – Disposable income and per capita
income – Relationship between population and per capita income.
Components of National Income Consumption expenditure – Investment expenditure – Government
expenditure – net income in Foreign Trade.
Measurement of National Income :
Value added Method – Income Method – Expenditure Method

UNIT-IX: Macro Economic Aspects:

30 Periods

Basic features of Classical theory of Employment – Basic Features of Keynesian theory of Employment.
Role of Government in Economic activities – Components of public revenue – Public Expenditure – Public Debt. (Elementary concepts only).
Role of International Trade in Economic Activities – Exports and Imports and Balance of payments (Elementary concepts only).

UNIT-X: Money And Inflation:

15 Periods

Concept of Money, Liquidity and Near Money – Functions of Money activities of Commercial Banks, Concepts of Primary Deposit, Secondary Deposit, Demand Deposit and Time Deposit – Types of Money.
Concept of Inflation – Types of Inflation – Economic Effects of Inflation.

English

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Syllabus:

Objective
To equip the learners with the skills (language, study, communication, and literary) required to function fluently, accurately, and appropriately in the target language in a variety of academic and real-life situations.
Main Reader

Part-A
Literary appreciation skills shall be imparted and tested for 50 Marks. Language skills, Study skills, and Communication skills shall be imparted and tested for 50 Marks.

Part-B
The total number of prose lessons shall be eight (8). Of the eight, one shall be a skit or one-act play in modern English and the other seven selections from modern prose. The maximum length of each lesson shall not exceed six pages.
The four prose passages and one skit / one-act play shall be on the following themes:
Empowerment of women /Information technology/bio-technology / scientific temper / Human emotions/qualities/values such as courage, love, honesty etc., Indian Culture and tradition / Human rights /
humanism.

Three lessons shall be customized for teaching language skills, communication skills, and study skills exclusively. The customized lessons shall focus on the teaching / learning of:
Skimming
Scanning
Reference skills
Information transfer
Listening (listen and repeat, listen and draw, listen and complete, listen and do, listen for gist, listen for specific information etc.,)
Writing (paragraph writing etc.,)
Speaking (greeting, introducing, thanking, leave-taking, requesting, seeking permission, asking for / giving information, agreeing, disagreeing)

Part-C
The total number of poems shall be give (5). The poems chosen shall be modern and native or non-native. The maximum length of each poem shall not exceed thirty lines. The themes for the poems shall be:
Values (human/moral)
Culture and heritage
Patriotism and world view
Adventure
Emotions
Triumph of good over evil

Part-D
All Lessons (Prose-8 and Poetry-5) in the main reader shall be exploited to the extent possible to teach the language skills study skills, literary appreciation skills, and communicative functions specified in this document.
All selections shall be culturally familiar, and of relevance to the learner.
The teacher shall present and give practice in the grammatical items relevant to each lesson in a graded manner.
Selections wherever possible may be preceded by a brief write-up about the author. All selections shall be accompanied by a glossary and relevant types of tasks / activities (essay writing, answering comprehension questions, dialogues, games, role playing, information gap, problem solving etc.,) The
teacher shall employ participatory, and interactive techniques to teach the
lessons.
First Book: “ Petals Of Poetry And Prose ”
Lessons:

Prose	Visionary Teachers and Scientists – Abdul Kalam From Ignited Minds. Energy – Isaac Asimov A Nation's Strength – Karan Singh An ordinary Man in an Extraordinary Way – Gandhi – Humayun Kabir. The Never-Never Nest (One act play) – Cedric Mount
Customized passages	TV. should never be held out as a carrot The name spells Magic – Kapil Dev She Ignited Aspirations: Kalpana Chawla
Poetry	All the World Is a Stage – Shakespeare The Road Not Taken – Robert Frost The Gift of India – Sarojini Naidu The Talisman – Har Prasad Sharma Character of Happy Life – H. Wotton

Second Book:
Non-detailed Text Book “ Insights – A Collection Of Short Stores ”
- A Flowering Tree
- A Hero
- The Cherry Tree
- Lalajee
- After Twenty Years
- Marriage is a Private Affairs

Third Book:
“Intermediate English Grammar” – Grammar, Study Skills & Communication skil

Sanskrit

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First Book: “ Gyrvani Vilasah ”

A. Poetry:

Epic Litt. – Valmiki Ramayana – Ayodhya Kanda 75th Canto 25 Slokas.
Descriptive Poetry – Kalidasa – Kumara Sambhavam 1 Canto – 17 Slokas.
Subhashitas – Bhatrihari – 15 Slokas.
Modern Poetry – Vasa Suryanarayana Sastry – Lokamanya Charitam – 25
Slokas.
Modern Poetry – Dr. Arka Somayaji – Purabharata Medini – 8 Slokas.
Selected Verses for Translation – Recitation – 15 Slokas

B. Prose:

Ancient Sanskrit Literature Bhoja Prabandha - 2 Stores 5 pages
6 stories from selected Katha Vali - 5 pages

Scientific Story – Antariksha Vijayaha (Sansmskrita Bhasha Prachara Samithi) Dr. P. Sri Ramachandrudu - 4 Pages
Patriotic Lesson – Story – Manava Sevaiva Madhava Seva
Communication Skills – Yuktisali Vanik – Comedy Satire – 6 pages

C. Grammar

Sabdas - 15
Conjugations - 15
Sandhis - 06

Second Book: Non-detailed Text Book “ NETAJI ”

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