Tripura Board Class 11 Syllabus for Mathematics
Tripura Board of Higher Secondary Education Class XI Syllabus for Mathematics with course structure are given below.
UNIT-I: SETS AND FUNCTIONS (12) Periods
1. Sets :
Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets. subsets of the set of real numbers especially intervals (with notations). Power set. Universal set.Venn diagrams. Operation on set, Union and intersection, Difference of sets, Complement of a set. Properties of complement sets. Simple problems on union and intersection on not more than three sets.
2. Relations & Functions : (14) Periods
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x Rx R). Definition of relation, pictorial diagrams, domain, codomain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain & range of a function. Real valued function of the real variable, domain and range of these functions. Constant, identity, polynomial, rational, modulus, monotone, bounded, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.
3. Trigonometric Functions: (18) 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 real value of x. Signs of trigonometric functions and sketch of their graphs. Expressing sin(x±y) and cos(x±y) in terms of sin x, sin y, cos x & cos y. Deducing the identities like the following :
Identities related to multiple and sub-multiple angles General solution of trigonometric equations of the type sin θ = sin α, cos θ = cos α and tan θ = tan α. Proof and simple application of sine and cosine formulas.
1. Principle of Mathematical induction: (06) 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: (10) Periods
Need for complex numbers, especially √-1 to be motivated by inability to solve every quadratic equation. Brief description of algebratic properties of complex numbers. Argand plane and polar representation of complex numbers, modulus and amplitude of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.
Square-root of a complex number, Cube roots of unity and their properties.
3.Linear Inequalities: (10) Periods
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables.
Solution of system of linear inequalities in two variables-graphically. Inequalities involving modulus function.
4. Permutations & Combinations: (12) Periods
Fundamental principle of counting. Factorial n(n!) permutations and combinations, derivation of formulae and their connections, simple applications.
5. Binomial Theorem: (08) Periods
History, statement and proof of the binomial theorem for positive integral indices, amazing features of 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), Geometric mean(G.M).General term of A.P and G.P, sum of n terms of A.P and G.P., Relation between A.M. and G.M of two numbers. Arithmetic, Geometric and Arithmetricogeometric series, infinite G.P and its sum. Sum to n terms of the special series ∑n, ∑n2 and ∑n3.
UNIT-III: CO-ORDINATE GEOMETRY
1.1 Introduction, distance formula, section formula, area of tangle (03) Periods
1.2. Straight Lines: (09) Periods
Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line:parallel to axes, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line, concurrence of three straight lines. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.
2. Conic Sections: (12) 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 equation of a circle; General equation of a circle: Standard equations and simple properties of parabola, ellipse and hyperbola,
3. Introduction to three-dimensional Geometry (05) Periods
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
1. Limits and Derivatives: (18) Periods
Intuitive idea of limit. Algebra of limits(statement only) some standard limit, derivative introduce as rate of change both as that of distance function and geometrically. Definition of derivative, derivative of sum algebraic and trigonometric functions from first principles with some simple applications, relate it to slope 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: (08) 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 & PROBABILITY
1.Statistics: (10) Periods
Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
2. Probability: (10) 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 the theories of earlier classes, Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.