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  Grade XI-Math

The following is the list of topics covered under Grade 11.  However it can be customized according to each student’s requirements.   

Algebra I

  • Sets
  • Relations and functions
  • Logarithms
  • Complex numbers
  • Linear Inequalities
  • Quadratic Equations
  • Sequences and Series
  • Partial Fractions
  • Mathematical Induction
  • Binomial Theorem
  • Monomials and polynomials
  • Hypothesis, counterexamples
  • Patterns, relations, functions
  • Radical equations/inequalities
  • Limits and infinity

Geometry and Measurement

  • Locus
  • Straight Lines
  • Circle
  • Tangent
  • Geometric proofs
  • Pythagorean Theorem
  • Congruence
  • Similarity
  • Triangle inequality theorem
  • Angles of triangles and polygons
  • Basic constructions
  • Coordinate geometry
  • Properties of inscribed/circumscribed polygons of circles
  • Rotations, translations, reflections

Probability and Statistics

  • Fundamental principle of counting
  • Types of events
  • Statistical experiments (more than one variable)
  • Factorial notation
  • Permutations
  • Combinations
  • Mean deviation
  • Variance and Standard Deviation
  • Measures of central tendency/dispersion, quartiles
  • Conditional probability
  • Total probability of an event
  • Theoretical/empirical probability

AP Probability and Statistics

  • Standard distributions
  • Probability problems with finite sample spaces
  • Discrete/continuous random variables

Algebra II

  • Operations on polynomials
  • Operations on rational expressions
  • Operations on complex numbers
  • Factoring polynomials/trinomials
  • Graphing quadratic equations
  • Absolute value equations/inequalities
  • systems of linear equations/inequalities
  • Conic sections
  • Ellipse, parabola, hyperbola
  • Composition of functions
  • Inverse of a function

Trigonometry

  • Angles, compound Angles
  • Properties of Triangles
  • Trigonometric Ratios and Identities
  • Trigonometric Equations
  • Trigonometric functions of sum or difference
  • Trigonometric functions of multiples
  • Conditional Identities
  • Tables and Graph of Trigonometric functions
  • Inverse trigonometric functions
  • Solutions of Triangles
  • Formulas for sines and cosines
  • Law of Sines/Cosines, area formulas
  • Area of triangle (one angle and 2 adjacent sides)
  • Polar/rectangular coordinates

Precalculus

  • Functions and operations
  • Sequences and series
  • Limits of sequences, series
  • Continuity, end behavior, asymptotes, limits
  • Regression
  • Parametric/rectangular forms of functions
  • Vectors, Types of Vectors
  • Operations on Vectors
  • Position Vector
  • Resolution of a Vector
  • Scalar (dot) product
  • Direction Cosines and Direction Ratios
  • Even/odd functions, significant values

Calculus

  • Limit of a function
  • Fundamental results on limits
  • Continuity of a function
  • Concept of differentiation
  • Concept of derivative
  • Slope of a curve
  • Intermediate value, extreme value theorem
  • Derivatives, differentiability
  • Derivatives of functions
  • Derivatives of inverse functions
  • Differentiation of parametric and implicit functions
  • Logarithmic differentiation
  • Method of substitution
  • Higher order derivatives
  • Chain rule
  • Maxima, minima, inflection points, intervals
  • Rolle’s theorem, mean value theorem, and L’Hôpital’s rule
  • Simpson’s rule, Newton’s method
  • Methods of Integration
  • Integrals of functions containing linear functions
  • Decomposition method
  • Method of substitution
  • Integration by parts
  • Definite/indefinite integrals
  • Riemann sums
  • Fundamental theorem of calculus
  • Improper integrals (limits of definite integrals)
  • Power series
  • Tests for convergence/divergence of sequences/series

    
Linear Algebra

  • Types of linear systems
  • Gauss-Jordan elimination, Gauss-Jordan method
  • Matrices and Determinants
  • Rectangular matrices to row echelon form
  • Row reduction methods, Cramer’s rule
  • Inverse to a square matrix
  • Matrix multiplication
  • Determinants of 2 by 2 and 3 by 3 matrices

Mathematical Models with Applications

  • Studying patterns and analyzing data
  • Probability models
  • Problems related to personal income, credit, financial planning
  • Rates, linear functions, direct/inverse variation
 
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