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Mathematics Syllabus for Grade 11
UNIT I: SETS AND FUNCTIONS
Sets
- Sets and their representations
- Empty set
- Finite and Infinite sets
- Equal sets
- Subsets
- Subsets of the 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
Relations and Functions
- 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 × R × R)
- Definition of relation
- Pictorial diagrams
- Domain, co-domain 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 and range of a function
- Real valued function of the real variable
- Domain and range of these functions
- Constant, identity, polynomial, rational, modulus
- Signum and greatest integer functions with their graphs
- Sum, difference, product and quotients of functions
Trigonometric Functions
- 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 and sketch of their graphs
- Expressing sin (x+ y) and cos (x + y) in terms of sin x, sin y, cos x and cos y
- Deducing the identities
- Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x
- General solution of trigonometric equations of the type sinθ = sin α, cosθ = cosα and tanθ = tan α
- Proofs and simple applications of sine and cosine formulae
UNIT II : ALGEBRA
Principle of Mathematical Induction
- 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
Complex Numbers and Quadratic Equations
- Need for complex numbers, especially −1, to be motivated by inability to solve every quadratic equation
- Brief description of algebraic properties of complex numbers
- Argand plane and polar representation of complex numbers
- Statement of Fundamental Theorem of Algebra
- solution of quadratic equations in the complex number system
- Square-root of a Complex number
Linear Inequalities
- 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 - graphially
Permutations and Combinations
- Fundamental principle of counting
- Factorial n
- Permutations and combinations
- derivation of formulae and their connections, simple applications
Binomial Theorem
- History, statement and proof of the binomial theorem for positive integral indices
- Pascal’s triangle
- general and middle term in binomial expansion
- simple applications
Sequence and Series
- Sequence and Series
- Arithmetic Progression (A.P.)
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- general term of a G.P
- sum of n terms of a G.P
- Arithmetic and geometric series
- infinite G.P. and its sum
- geometric mean (G.M.)
- Relation between A.M. and G.M
- Sum to n terms of the special series : 2 3 Σn, Σn and Σn
UNIT III : COORDINATE GEOMETRY
Straight Lines
- Brief recall of 2-D from earlier classes
- 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, intercepts 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
Conic Sections
- Sections of a cone: Circles, ellipse, parabola, hyperbola
- a point, a straight line and 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
Introduction to Three-dimensional Geometry
- Coordinate axes and coordinate planes in three dimensions
- Coordinates of a point
- Distance between two points
- section formula
UNIT IV : CALCULUS
Limits and Derivatives
- Derivative introduced as rate of change both as that of distance function and geometrically
- intuitive idea of limi Definition of derivative
- 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
- 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
Statistics
- Measure of dispersion
- mean deviation
- variance
- standard deviation of ungrouped/grouped data
- Analysis of frequency distributions with equal means but different variances
Probability
- Random experiments: outcomes, sample spaces (set representation)
- Events: Occurrence of events, ‘not’, ‘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
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