Class 11
- Sets and their representations
- Empty set
- Finite and Infinite sets
- Equal sets
- Subsets
- Subsets of a set of real numbers especially intervals (with notations)
- Universal set
- Venn diagrams
- Union and Intersection of sets
- Difference of sets
- Complement of a set
- Properties of Complement
- 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 (up to ℝ × ℝ × ℝ)
- Definition of relation
- Pictorial diagrams of relations
- 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
- Types of real valued functions:
- Constant function
- Identity function
- Polynomial function
- Rational function
- Modulus function
- Signum function
- Exponential function
- Logarithmic function
- Greatest integer function
- Graphs of the above functions
- Sum, difference, product and quotients of 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
- Domain and range of trigonometric functions and their graphs
- Expressing sin(x ± y) and cos(x ± y) in terms of sin x, sin y, cos x, and cos y, with simple applications
- Deducing identities
- Identities related to:
- sin 2x
- cos 2x
- tan 2x
- sin 3x
- cos 3x
- tan 3x
- Need for complex numbers, especially √−1, motivated by the inability to solve certain quadratic equations
- Algebraic properties of complex numbers
- Argand plane
- Linear inequalities
- Algebraic solutions of linear inequalities in one variable
- Representation of linear inequalities on the number line
- Fundamental principle of counting
- Factorial n (n!)
- Permutations and combinations
- Derivation of formulae for nPr and nCr
- Connections between nPr and nCr
- Simple applications of permutations and combinations
- Historical perspective of the Binomial Theorem
- Statement and proof of the Binomial Theorem for positive integral indices
- Pascal’s Triangle
- Simple applications of the Binomial Theorem
- Sequence and Series
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- General term of a G.P.
- Sum of n terms of a G.P.
- Infinite G.P. and its sum
- Geometric Mean (G.M.)
- Relation between A.M. and G.M.
- Brief recall of two-dimensional geometry from earlier classes
- Slope of a line and angle between two lines
- Various forms of equations of a line:
- Parallel to axis
- Point-slope form
- Slope-intercept form
- Two-point form
- Intercept form
- Distance of a point from a line
- Sections of a cone:
- Circle
- Ellipse
- Parabola
- Hyperbola
- Point (degenerate case)
- Straight line (degenerate case)
- Pair of intersecting lines (degenerate case)
- Standard equations and simple properties of:
- Parabola
- Ellipse
- Hyperbola
- Standard equation of a circle
- Sections of a cone:
- Circle
- Ellipse
- Parabola
- Hyperbola
- Point (degenerate case)
- Straight line (degenerate case)
- Pair of intersecting lines (degenerate case)
- Standard equations and simple properties of:
- Parabola
- Ellipse
- Hyperbola
- Standard equation of a circle
- Derivative introduced as:
- Rate of change of distance function
- Geometrical interpretation (slope of the curve)
- Intuitive idea of limit
- Limits of:
- Polynomials
- Rational functions
- Trigonometric functions
- Exponential functions
- Logarithmic functions
- Definition of derivative and its relation to the slope of the tangent to the curve
- Derivative of:
- Sum of functions
- Difference of functions
- Product of functions
- Quotient of functions
- Polynomial functions
- Trigonometric functions
- Measures of Dispersion:
- Range
- Mean deviation
- Variance
- Standard deviation
- Applicable to:
- Ungrouped data
- Grouped data
- Events:
- Occurrence of events
- ‘Not’ events
- ‘And’ events
- ‘Or’ events
- Exhaustive events
- Mutually exclusive events
- Axiomatic (set theoretic) probability
- Connections with other theories studied in earlier classes
- Probability of:
- An event
- ‘Not’ an event
- ‘And’ events
- ‘Or’ events