XI & XII - Mathematics

8/10/2019 XI & XII - Mathematics

1/17

HIGHER SECONDARY MATHEMATICS FIRST YEAR

DRAFT SYLLABUS and ANNEXURES

S.No. Chapter Name Content Expected OutcomeNo. of

Periods

1.1 Partial Fractions : Linear factors (not repeated, repeated)

Quadratic factors (not repeated).

1. Algebra I

1.2 Permutation and

combination :

Fundamental principles of counting.

Permutation concept objects aredistinct not all distinct.

Combination concept relation between

permutation and combination properties.

Simple problems.

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2.1 Mathematical

Induction and

Binomial Theorem :

Principles of mathematical induction and

simple applications.

Binomial theorem (finite series) statement and proof for natural number

powers finding middle and particular

term.

2.2 Some special series :

2. Algebra II

Revision of arithmetic and geometric

series simple problems

Arithmetic and geometric means.

Binomial theorem infinite series(statement only) for rational index powers

(4 different cases).

Statements of exponential and logarithmic

series.

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3.1 Matrices :

Concept order types of matrices zeromatrix transpose of a matrix symmetric

and skew symmetric matrices triangular

matrices (of maximum order 3 3)

simple properties

Operations on matrices commutative

property.

3. Matrices and Determinants I

3.2 Determinants : Order minor cofactor expansions

properties of determinants product of

determinants.

Singular and non-singular matrices

simple problems.

12

4.1 Scalars and Vectors : Concept of scalars and vectors

magnitude and direction of a general

vector algebra of vectors (addition

subtraction and scalar multiple)

Types of vectors Free vector localised

vector zero vector unit vector

negative of a vector collinear vectors

coplanar vectors co-initial vectors like

vectors unlike vectors and equality of

vectors.

4. Vector Algebra I

4.2 Resolution of a vector : Illustrations direction ratios non

uniqueness property direction cosines

(unique and non uniqueness property)

position vector of a point.

Section formula to find p.v. of a point

dividing a line segment in the given ratio.

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4.3 Laws on Polygon : Triangle law parallelogram law

polygon law.

Properties of addition of vectors.

5.1 Identities : Revision of trigonometrical identities and

signs of T-ratios.

Deduction of the identities

sin (A B), cos (AB), tan (AB),

sin2A, cos2A, tan2A, sin3A, cos3A, tan3A.

Sums and products

sin CsinD, cos C cosD

sinAcosB, cosAcosB, sinA sinB

5.2 Solutions of

Trigonometrical

equations :

General solution of the trigonometrical

equations (sin = sin , cos = cos ,

tan = tan , a cos+ bsin = c)

5. Trigonometry

5.3 Properties of

Triangles :

sine cosine projection area formulae

(without proof)

18

6.1 Straight lines : Revision of Locus and various forms of

equations of a straight line (slope

point, slope intercept, two points,

intercepts, normal and parametric forms)

General equation of a line.

6. Analytical Geometry I

(Two dimensional)

6.2 Pair of straight lines : Equation of a pair of straight lines:

Problems connected with(i) distance of a point from a line.

(ii) distance between two parallel lines.

(iii) equation of lines bisecting the angle

between two lines.

(iv) angle between two lines.

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7.1 Intervals :

Intervals open, closed, neighbourhood.

7.2 Relations : Types of relations.

7.3 Functions : Various representations of a function.

Types of functions vertical and

horizontal tests.

Defining inverse of a function.

Some special functions linear functions

non-linear functions.

rational functions absolute value

functions signum and step functions

even and odd functions periodic

functions composition of functions.

Algebra of functions (sum, difference,product and quotient)

7. Relations and functions

7.4 Quadratic inequalities : Quadratic inequalities finding the

domain.

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8.1 Graphs of

trigonometrical

functions :

Graphs of sine, cosine, tangent, secant,

cosec and cot functions domain and

range.

8. Trigonometrical functions and

Inverse Trigonometrical functions

8.2 Graphs of inverse

trigonometrical

functions :

Graphs of inverse functions of sine

cosine tan secant cosec and cot

functions domain and range.

Properties of inverse trigonometrical

functions simple problems.

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9.1 Limits and Derivatives :

Introduction and some history. The calculation of limits.

The limit theorems.

The squeeze play theorem.

Infinite limits and limits at infinity.

Precise definition of limit (the theory of

limits)

Tangent lines and derivatives.

The derivative as a rate of change

9. Differential Calculus :Limit continuity

Differentiability

9.2 Continuity and

differentiability :

Continuity of a function at a point : left

hand limit right hand limit definition

of continuity of a function at a point

discontinuity of a function types of

discontinuities algebra of continuous

functions. Composite function theorem on

continuity continuity in interval

definition continuity of some standard

functions: polynomial rational

trigonometric exponential and

logarithmic functions. Relationship

between continuity and differentiability

left hand derivative and right hand

derivative (need and concept) every

differentiable function is continuous but

converse is not true.

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10. Differentiation techniques Some differentiation formulae.

The product and quotient rules.

The derivative of composite functions :

The chain rule.

The derivative of a power function.

The derivatives of trigonometric functions.

Implicit differentiation parametric

differentiation.

Higher order derivatives (restricted uptosecond order).

Differentiation of one function with

respect to another function.

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11.1 Integration : Definition of integration as anti-derivative

geometrical interpretation of indefinite

integrals algebra of integrals Integrals

of some standard functions rules of

integration.

11.2 Methods of

Integration :

Indefinite integrals methods of

integration: decomposition method

substitution method integrals of various

types integration by parts integration

by partial fractions.

11. Integral Calculus

11.3 Definite Integral

a concept :

Definite integrals (Riemann integral) as

limits of sums Statements of

fundamental theorems of integral calculus .

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12.1 Probability a classical

approach :

Classical definition random experiments

sample space.

12. Probability theory

12.2 Events : Sure impossible mutually exclusive

exhaustive

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12.3 Laws on probability : Addition and multiplication theorems

independent and dependent events

conditional probability total probability

Statement of Bayes theorem simple

problems.

Total Number of Periods

Allotted periods / week 7

Approximate transaction days 150

Approximate number of periods 150 7

5= 210.

210


8/17

HIGHER SECONDARY MATHEMATICS SECOND YEAR

DRAFT SYLLABUS and ANNEXURES

S.No. Chapter Name Content Expected OutcomeNo. of

Periods

1.1 Need for complex

numbers :

Existence of complex numbers

1.2 Properties : Complex numbers as ordered pairs of real

numbers algebra of complex numbers

conjugate of a complex number modulusof a complex number triangle inequality.

1. Complex numbers

1.3 Polar form : Polar form of a complex number

principal value of the argument simple

problems.

7

2.1 Polynomial equations : Statement of fundamental theorem of

algebra.

Relationship between roots and

coefficients. Quadratic equations and their applications.

Irrational roots, complex roots (upto 4th

degree equation), reciprocal equation (upto

4th

degree).

2. Theory of equations

2.2 Demoivres theorem : Statement of Demoivres theorem.

Solvingx3 1 = 0,x

4 1 = 0.

8

3.1 Inverse of a Matrix : Cofactor matrix, adjoint of a matrix,

inverse of a matrix, uniqueness of inverse,simple problems.

3. Matrices and Determinants II

3.2 Elementary

transformations :

Concepts rank of a matrix.

Echelon form, simple problems.

Finding inverse of a matrix using

elementary transformations.

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3.3 Solutions of system of

linear equations :

Inverse method.

Examining consistency by

(i) determinant method.

(ii) Rank method.

4.1 Product of two vectors

Scalar product :

Angle between two vectors definition of

dot product projection (geometrical

meaning of dot product) properties

applications: work done by a force to

geometry to trigonometry.

4.2 Vector product : Definition vector area (geometricalmeaning) properties of vector products.

Applications: moment of a force to

geometry to trigonometry.

4.3 Product of three

vectors

(i) Scalar triple

product :(ii)Vector triple product

Geometrical meaning determinant form

of scalar triple product.

Simple properties.

Two types of representations.

4. Vector Algebra II

4.4 Co-ordinate geometry

lines (3 dimensional):

Vector and Cartesian equations (two points

form, one point and parallel to a vector

form).

Recalling direction ratios and direction

cosines.

Angle between two lines.

Coplanar lines (intersecting, perpendicular,

parallel).

Non-coplanar lines.

Distance between two parallel lines two

non-coplanar lines between a point and a

line.

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4.5 Co-ordinate Geometry

planes

(3 dimensional) :

Vector and Cartesian form of a plane

(i) normal form, (ii) 1 point and two

parallel vector (iii) 2 points and 1 parallel

vector, (iv) 3 points form, (v) passing

through intersection of two planes.

Angle between two planes

Angle between a line and a plane.

Meeting point of a line and a plane

Distance between(i) a point and a plane.

(ii) between two parallel planes.

5.1 Conic sections : Sections of a cone definition of a conic

and general equation of a conic.

5.2 Circle : General form standard form diameter

form and parametric form. Problems

connected with various forms.

Verifying the position of a given point.

5.3 Parabola : Standard equation: 4 types properties

simple problems and its applications.

5. Analytical Geometry II

(Two dimensional)

5.4 Ellipse and

Hyperbola :

Standard equation: 2 types properties

simple problems and its applications.

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6.1 Linear inequalities : Simple inequation with one and two

variables system of inequations with two

variables (all graphical).

6. Linear Programming

6.2 Linear programming

problems

Formulation

Definition of related terminology such as

constraints objective function

optimization.

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6.3 Types of L.P.

problems : different types of linear programming

(L.P.) problems graphical method of

solution for problems in two variables

feasible and infeasible regions feasible

and infeasible solutions optimal feasible

solutions (upto three non-trivial

constraints).

7. Mathematical Logic and Binary

operations

7.1 Mathematical Logic : Statements: introduction sentences and

statement truth value of statements

open sentences compound statements

quantifier and quantified statements.

Logical connectives : conjunction

disjunction negation implication

conditional biconditional.

Truth tables of compound statements

examples related to real life and

mathematics statement patterns andlogical equivalence tautology

contradiction contingency duality

negation of compound statements.

Contra-positive converse inverse

algebra of statements: idempotent law

associative law commutative law

distributive law identity law

complement law involution law DeMorgans laws difference between:

converse contrapositive contradiction

application introduction to switching

circuits (simple examples).

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7.2 Binary operations : Binary operation as a function.

Binary operation on various number

systems.

Properties associative identity

inverse and commutative.

Simple problems connected with

properties.

8.1 Interpretations ofderivatives:

Tangents and normals Rate measure and related rates.

Rolles theorem Mean value theorem

their geometrical meanings.

Indeterminate forms a Limit process.

8.2 Sketching of

elementary curves:

Increasing / Decreasing First derivative

test.

Concavity / convexity second derivative

test

Asymptotes.

Symmetrical properties.

Sketching of simple curves

rational, polynomial, trigonometrical,

exponential, logarithmic curves

8. Applications of derivatives :

8.3 Extrema of functions : Applications of Extrema (optimization

problems) first and second derivative

tests.

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9.1 Differentials : Definition and simple problems9. Differentials and Partial

Derivatives:9.2 Errors and

Approximation :

Types of errors finding approximate

values using the concepts of differentials.

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9.3 Partial differentiation : First order second order partial

derivatives.

Function of a function rule (two and three

variables)

(i) u=f(x,y) orf(x, y, z)

x, y, zare functions of t

(ii) u= f(x, y),xandyand functions of u

and v.

Simple problems.

10.1 Evaluation of definite

integrals :

By decomposition substitution

integration by parts properties of definite

integrals. Reduction formulae Gamma

integral Bernoullis formula.

Proper and improper integral definition.

10. Integral Calculus

10.2 Applications : Area under the curve : Area bounded by a

curve and axis (simple problems) area

bounded by two curves.

volume of solid of revolution-volume of

solid obtained by revolving the area under

the curve about the axis (simple problems).

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11.1 Need for differential

equations :

Ordinary / partial differential equations

definitions.

Order degree general solution

particular solution of differentialequations.

11. Differential Equations

11.2 Formation of

Differential equations :

Formation of differential equations.

Formation of differential equation by

eliminating arbitrary constants (at most

two constants).

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11.3 Solutions of

Differential Equations(first order) :

Solutions of first order and first degree

differential equations variable separablemethod, homogeneous differential

equation (equation reducible to

homogeneous form are not expected).

Linear differential equations applications

: Population growth bacterial colony

growth Newtons laws of cooling

radioactive decay.

11.4 Solutions ofDifferential Equations

(second order) :

Second order linear equations withconstant coefficients (particular integral

connected withf(x) = ex, sin x, cosx).

12.1 Randam Variables : Discrete and continuous random variables

probability mass function probability

density function probability distribution

function properties.

12.2 MathematicalExpectation :

Mathematical expectation variancestandard deviation of a random variable.

12. Probability Distribution

12.3 Theoretical

distribution :

Binomial Poisson normal

distributions.

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Total Number of Periods

Allotted periods / week 7

Approximate transaction days 150

Approximate number of periods

150 7

5= 210.

210


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MATHEMATICS DRAFT SYLLABUS ANNEXURE I

(I) Curriculum Development and Syllabus in Higher Secondary Mathematics done based on the following needs :

(1) It must cater to the needs of aspirants who pursue their higher education in Mathematics and in Pure Basics Sciences.

(2) It is based on the need for those aspirants who pursue their higher education in Science and Technology / Engineering.

(3) It must act as a level playing field for various Higher Secondary Boards in India.

(4) It is aimed at facing the competitive examination JEE.

(II) Justification for exclusion :

(1) Existing / revised X Standard Mathematics Syllabi covers part of existing Higher Secondary Mathematics curriculum.

(2) Certain portions that have been included as a tradition but not required for the current development.

(III) Justification for Inclusion :

(1) To maintain the flow of continuity.

(2) To maintain quality / competition at the national level.

(3) To maintain equilibrium at 210 periods level.


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MATHEMATICS DRAFT SYLLABUS ANNEXURE II

Sl.No. Portions Excluded Justification

XI Standard

1. Sequences and Series Already exists in the revised X Standard Mathematics content.

2. Circular Permutations No Boards in India includes and does not contribute for national level competitive exams

and is covered in higher classes.

3. Fundamentals of Matrices Already exists in the revised X Standard Mathematics content.

4. Fundamentals of Trigonometry Already exists in the revised X Standard Mathematics content.5. Solutions of Triangles Not required for current develoipment.

6. Derivation of different forms of

straight lines

Already exists in the revised X Standard Mathematics content.

XII Standard

1. Applications of Demoivres Theorem No Boards in India includes and does not contribute for national level competitive exams


2. Vector four products and scalar fourproducts.

No Boards in India includes and does not contribute for national level competitive examsand is covered in higher classes.

3. Non-standard conic sections, shifting

the origin, tangents and normals,

asymptotes and rectangular hyberbola

No Boards in India includes and does not contribute for national level competitive exams


4. Group theory Too abstract to be taught at higher secondary level and is included in the higher education

curriculum.

5. Extension of mean value theorems,Maclaurins series, Inequalities

No Boards in India includes and does not contribute for national level competitive examsand is covered in higher classes.

6. Eulers Theorem and its applications No Boards in India includes and does not contribute for national level competitive exams


7. Surface area and length of a curve

Integral calculus

No Boards in India includes and does not contribute for national level competitive exams



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MATHEMATICS DRAFT SYLLABUS ANNEXURE III

Sl.No. Portions Included Justification

XI Standard

1. Convergence and divergence in

Algebra II

For facilitating the understanding of infinite series and existance of imrproper integrals

2. Section formula in Vector Algebra I Required for J.E.E. / National level competitive examinations.

3. Geometrical interpretatons for one to

one and onto functions

in Relations and Functions

For better understanding / clarity of one to one correspondence.

4. Inverse trigonometrical functions Required for J.E.E. / National level competitive examinations.

5. Theory of limits and squeeze play

theorems.

For deeper understanding of limit concepts required for National level curriculum / J.E.E.

XII Standard

1. Theory of Equations For completing the conceptual understanding of polynomial equations.2. Inverses of matrices by elementary

transformations

Other national boards include and becomes a part of J.E.E. syllabus.

3. Linear Programming Other Boards and national curriculum include as a part of the syllabi.

4. Extension of Mathematical Logic Boards of other states and national level include in their curriculum.

5. Partial differential equations limited

to 4 elementary problems.

To enrich the understanding of partial differentiation.

XI & XII - Mathematics

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