xi & xii - mathematics
TRANSCRIPT
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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.
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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)
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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.
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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.
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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.
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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.
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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
and is covered in higher classes.
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
and is covered in higher classes.
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
and is covered in higher classes.
7. Surface area and length of a curve
Integral calculus
No Boards in India includes and does not contribute for national level competitive exams
and is covered in higher classes.
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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.