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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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