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 
7 
Graphs & Periodic Functions ) (Trigonometric ratios of Compound angles ) (Multiple & Submultiple 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 
Demovires Theorem 
5 
15 
Trignometric expansions 
3 
Intermediate Mathematics –1a (Algebra, Vector Algebra & Trignometry) : 
10 Periods 
S. No 
Topics/Chapter 
Subtopics/Sections/Subsections

Periods of Instructions

1 
Functions or Mappings 
A. Definitions of oneone, 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 :BA 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., 



xy 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, Coinitial vectors, coplanar and noncoplanar vectors, position vector, unit vector etc.,
 Addition of vectors – parallelogram and triangle laws – Properties of additions .
 Multiplication of Vector by Scalar
 Angle between two NonZero 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 semicircle 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 – Noncommutative 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 
Subtopics/Sections/Subsections

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, rangesgraphs. 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 excircle 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

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 
CoOrdinate 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 Pointslope form Two point form Normal form xCosx+ySinx=p Symmetric form xx 1 /sinq = yy 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 Bisector 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+2fghaf 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 

CoOrdinate Geometry – 3D 
Coordinates 
Coordinate planes – Coordinates of a point – Distance between two points in space. To find the Coordinates 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 FunctionAlgebraic, 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, subnormal at a point Lengths of tangent, normal subtangent, subnormal 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. 
Intermediate First Year Syllabus (With Effect From 20032004)
PaperI Introductory Economic Theory
UNITI: 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.
UNITII: Basic Concepts: 
10 Periods 
 Goods: Free and Economic goods. Consumption goods and Capital goods – Intermediate goods – Perishable and Nonperishable 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.
UNITIII: 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 equimarginal 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.
UNITIV: 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.
UNITV: 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.
UNITVI: 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.
UNITVII: 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.
UNITVIII: 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.
UNITIX: 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).
UNITX: 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.
Intermediate First Year Syllabus (With Effect From 20032004) EconomicsI
PaperI Introductory Economic Theory
UNITI: 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.
UNITII: Basic Concepts: 
10 Periods 
 Goods: Free and Economic goods. Consumption goods and Capital goods – Intermediate goods – Perishable and Nonperishable 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.
UNITIII: 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 equimarginal 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.
UNITIV: 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.
UNITIV: 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.
UNITV: 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.
UNITVI: 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.
UNITVII: 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.
UNITVIII: 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
UNITIX: 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).
UNITX: 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.
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 reallife situations. Main Reader
PartA 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.
PartB The total number of prose lessons shall be eight (8). Of the eight, one shall be a skit or oneact 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 / oneact play shall be on the following themes: Empowerment of women /Information technology/biotechnology / 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, leavetaking, requesting, seeking permission, asking for / giving information, agreeing, disagreeing)
PartC The total number of poems shall be give (5). The poems chosen shall be modern and native or nonnative. 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
PartD All Lessons (Prose8 and Poetry5) 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 writeup 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 NeverNever 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: Nondetailed 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
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: Nondetailed Text Book “ NETAJI ”
