MATHEMATICS (Code No. 041)
Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Bioscience, Commerce or Computer Applications. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students.
Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.
Objectives
The broad objectives of teaching Mathematics at senior school stage intend to help the students:
to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
to feel the flow of reasons while proving a result or solving a problem.
to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
to develop positive attitude to think, analyze and articulate logically.
to develop interest in the subject by participating in related competitions.
to acquaint students with different aspects of Mathematics used in daily life.
to develop an interest in students to study Mathematics as a discipline.
to develop awareness of the need for national integration, protection of environment, observance of
small family norms, removal of social barriers, elimination of gender biases.
to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.
COURSE STRUCTURE CLASS XI (2015-16)
One Paper Total Hours-Periods of 35 Minutes each
Three Hours Max Marks. 100
Topic Periods Marks
I. Sets and Functions 60 29
II. Algebra 70 37
III. Coordinate Geometry 40 13
IV. Calculus 30 06
V. Mathematical Reasoning 10 03
VI. Statistics and Probability 30 12
Total 240 100
Unit-I: Sets and Functions
1. Sets (20) Periods
Sets and their representations.Empty set.Finite and Infinite sets.Equal sets.Subsets.Subsets of a set of
real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and
Intersection of sets.Difference of sets. Complement of a set. Properties of Complement Sets.
2. Relations & Functions: (20) Periods
Ordered pairs, Cartesian product of sets.Number of elements in the cartesian product of two finite sets.
Cartesian product of the set of reals with itself (upto R x R x R). Definition of relation, pictorial
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial
representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotient of functions.
3. Trigonometric Functions: (20) Periods
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one
measure to another.Definition of trigonometric functions with the help of unit circle. Truth of the
identity sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric
functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing the identities like the following:
tanx ± tany cotxcoty 1
tan(x ± y) = , cot(x ± y) =
1 tanxtany coty ± cotx
1 1
sinα ± sinβ = 2sin (α ± β)cos (α β)
2 2
1 1
cosα + cosβ = 2cos (α + β)cos (α - β)
2 2
1 1
cosα - cosβ = -2sin (α + β)sin (α - β)
2 2
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric
equations of the type siny = sina, cosy = cosa and tany = tana.
Unit-II: Algebra
1. Principle of Mathematical Induction: (10) Periods
Process of the proof by induction, motivating the application of the method by looking at natural
numbers as the least inductive subset of real numbers. The principle of mathematical induction and
simple applications.
2. Complex Numbers and Quadratic Equations (15) Periods
Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers.Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.
3. Linear Inequalities (15) Periods
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.Graphical representation of linear inequalities in two variables.Graphical method of finding a solution of system of linear inequalities in two variables.
4. Permutations and Combinations (10) Periods
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of
formulae for 𝑛𝑃𝑟
and 𝑛𝐶𝑟
and their connections, simple applications.
5. Binomial Theorem (10) Periods
History, statement and proof of the binomial theorem for positive integral indices.Pascal's triangle,
General and middle term in binomial expansion, simple applications.
6. Sequence and Series (10) Periods
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression
(G.P.), general term of a G.P., sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums
2 3
1 1 1
,
n n n
k k k
k k and k
Unit-III:Coordinate Geometry
1. Straight Lines (10) Periods
Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slopeintercept form, two-point form, intercept form and normal form. General equation of a line.Equation of family of lines passing through the point of intersection of two lines.Distance of a point from a line.
2. Conic Sections (20) Periods
Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola.Standard equation of a circle.
3. Introduction to Three-dimensional Geometry (10) Periods
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between
two points and section formula.
Unit-IV: Calculus
1. Limits and Derivatives (30) Periods
Derivative introduced as rate of change both as that of distance function and geometrically.
Intutive idea of limit.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: Mathematical Reasoning
1. Mathematical Reasoning (10) Periods
Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words, Difference between contradiction, converse and contrapositive.
Unit-VI: Statistics and Probability
1. Statistics (15) Periods
Measures of dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
2. Probability (15) Periods
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories studied in earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.
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