HS First year syllabus

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MATHEMATICS
REVISED SYLLABUS FOR HIGHER SECONDARYFIRSTYEAR COURSE
TheSyllabusinthesubjectofMathematicshasundergonechanges fromtimetotime inaccordance
withgrowthofthesubject andemerging needsofthesociety.SeniorSecondarystageisalaunchingstage
from where the students go either for higher academic education in Mathematics or for professional
courses like engineering, physicaland Bioscience, commerce or computer applications. The present re-
vised syllabus has beendesigned inaccordance withNationalCurriculumFrame work 2005 and as per
guidelinesgiveninFocusGrouponTeachingofMathematics2005 whichisto meet theemerging needs
ofallcategoriesofstudents.Motivatingthetopics fromreallifesituationsandothersubject areas, greater
emphasis has been laid onapplicationofvarious concepts.
Objectives :
Thebroadobjectivesofteaching Mathematicsat seniorschoolstage intendtohelpthepupil:
 toacquireknowledgeandcriticalunderstanding, particularlybywayofmotivationand visu-
alization, ofbasic concepts, terms, principles, symbols and masteryofunderlying processes
and skills .
 to feelthe flowofreasonswhileprovingaresult orsolving aproblem.
 to applythe knowledge and skills acquired to solve problems and wherever possible, by
more thanone method .
 todeveloppositiveattitudetothink, analyzeandarticulatelogically.
 todevelopinterest inthesubject byparticipating inrelatedcompetitions.
 toacquaint studentswithdifferent aspectsofmathematicsused indailylife.
 todevelopaninterest instudentstostudymathematics asadiscipline.
 to develop awareness of the need for national integration, protection of environment,
observanceofsmallfamilynorms, removalofsocialbarriers, eliminationofsexbiases.
 todevelopreverenceandrespecttowardsgreatMathematiciansfortheircontributionstothe
fieldofMathematics.
SLLABUS FOR HIGHER SECONDARYFIRSTYEAR COURSE
One Paper Time : Three hours Marks : 100
Unitwise Distribution of Marks & Periods :
Unit Topics Marks Periods
Unit-1 SetsandFunctions 26 37
Unit-II Algebra 30 55
Unit-III CoordinateGeometry 20 36
Unit-IV Calculus 12 22
Unit-V StatisticsandProbability 12 30
Total: 100 180

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APPENDIX:
1. Infinite Series :
2. Mathematical Modelling :
Unitwise Distribution of Course contents:
Unit-I : SETS AND FUNCTIONS
1. Sets: Marks- 09 Periods-12
Sets and their representations, Emptyset, Finite and Infinite sets, Equal sets, Subsets, Subsets of
thesetofrealnumbersespeciallyintervals(withnotations),Universalset,Venndiagrams,Unionand
Intersectionofsets, Differenceofsets, Complement ofa set.
2. Relations and Functions : Marks 08 Periods-12
Cartesianproductofsets, Numberofelements inthe Cartesianproductoftwo finitesets, Cartesian
productofthereals withitself(upto R×R×R).
Definitionofrelation,pictorialdiagrams,domain,co-domainandrangeofarelation,Function
asaspecialkindofrelationfromoneset to another, Pictorialrepresentationofa function, domain,
co-domainand range ofa function, Realvalued functionofthe realvariable, domain and range of
thesefunctions,constant,identity,polynomial,rational,modulus,signumandgreatestintegerfunctions
withtheirgraphs, Sum,difference, productandquotientsoffunctions.
3.Trigonometric Functions : Marks 09 Periods-13
Positive and negative angles, Measuring angles in radians and in degrees and conversion
fromone measureto another,Definitionoftrigonometricfunctionswiththehelpofunit circle.Truth
of the identity sin2
x + cos2
x = 1, for all x. Sings of trigonometric functions and sketch of their
graphs,Expressingsin(x+y)andcos(x+y)intermsofsinx,siny,cosxandcosy,Deducingtheidentities
likefollowing:
tan(x  y) 
tan x  tan y
,
1∓ tan x tan y
cot(x  y) 
cot xcot y ∓1
,
cot y  cot x
Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x,
Unit-II : ALGEBRA
1. ComplexNumbersandQuadratic Equations: Marks 06 Periods-12
Need for complex numbers, especially 1, to be motivated by inability to solve every
quadratic equation, Brief description ofalgebraic properties ofcomplex numbers,The modulus
and the conjugate of a complex number. Argand plane and polar representation.
2. Linear Inequalities : Marks 04 Periods-06
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their
representationonthenumberline.

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3. PermutationsandCombinations : Marks 07 Periods-12
Fundamentalprincipleofcounting, Factorialn.Permutationsandcombinations,derivationof
formulaeandtheirconnections, simpleapplications.
4. BinomialTheorem : Marks 07 Periods-12
Statement and proofofthe binomialtheoremfor positive integral indices, Pascal’striangle,
simpleapplications.
5. Sequence and Series : Marks 06 Periods-13
Sequence and Series. Geometric progression (G.P.), general termofa GP., sumof n terms
ofa GP.,geometric mean(G.M.),relation betweenA.M. and GM.
Unit-III : COORDINATE GEOMETRY
1. Straight Lines : Marks 08 Periods-14
Briefrecallof2D fromearlierclasses. Slopeofa line andangle betweentwo lines,Various
forms of equations of a line, parallel to axes, point-slope form, slope-intercept form, two-point
form, intercept formandGeneralequationofa line, Distanceofapoint froma line.
2. Conic Sections : Marks 08 Periods-14
Sections ofa cone : Circle, ellipse, parabola, hyperbola, a point, a straight line and pair of
intersecting linesasadegeneratedcaseofaconicsection, Standardequationsandsimpleproperties
ofparabola, ellipseand hyperbola, Standardequation ofacircle.
3. Introduction to Three-dimensional Geometry:Marks 04 Periods-08
Coordinateaxesandcoordinateplanes inthreedimensions,Coordinatesofapoint,Distance
betweentwo points.
Unit-IV : CALCULUS
Limits and -Derivatives Marks 12 Periods-22
Intuitive idea of limits. Limits of polynomials and rational functions, trigonometric,
exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of
the curve, derivative of sum, difference, product and quotient of functions. Derivatives of
polynomial and trigonometric functions.
Unit-V : STATISTICS AND PROBABILITY
1. Statistics: Marks 07 Periods-18
MeasureofDispersion,Range,Meandeviation,varianceandstandarddeviationofungrouped/
groupeddata.
2. Probability: Marks 05 Periods-12
Events, Occurrence of events, ‘not’, ‘and’ ‘or’ events, exhaustive events, mutually exclusive
events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes,
Probabilityofanevent, probabilityof ‘not’, ‘and’& ‘or’events.
Appendix
1. Infinite Series :
Binomialtheoremforanyindex,infinitegeometricseries,exponentialandlogarithmicseries.
2. Mathematical Modelling :
Consolidating the understanding developed up to Class X. Focus on modelling problems
relatedtoreal-life(likeenvironment,travel, etc.)andconnectingwithothersubjectsofstudywhere
many constraints may really need to be ignored, formulating the model, looking for solutions,
interpretingthemintheproblemsituationandevaluatingthemodel.
Prescribed Textbook : Mathematics for Class XI, Published by NCERT.
গিণত Published by AHSEC.
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