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Math Tutoring for Grade/class 11-Find Math home Tutors, Online Tutors, home Tuition & Private Tutors for Class XI


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Topics Covered by our Math Home Tutoring Program:


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Pre-Algebra
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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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