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  Grade XII-Math

The following is the list of topics covered under Grade 12.  However it can be customized according to each student’s requirements.   
Algebra I

  • Integers
  • Rational and irrational numbers
  • Rules of exponents
  • Absolute value equations/inequalities
  • Linear equations/inequalities
  • Parallel and perpendicular lines
  • Operations on monomials and polynomials
  • Factoring of second/third degree polynomials
  • Fractions
  • Rational expressions/functions
  • Quadratic equations
  • rate problems, work problems, and percent mixture problems
  • Relation and function
  • Domain and range of functions

Geometry

  • Theorems on congruence, similarity
  • Pythagorean Theorem
  • Interior and exterior angles of triangles and polygons
  • Properties of quadrilaterals and circles
  • Coordinate geometry
  • Rotations, translations, reflections
  • Properties of inscribed/circumscribed polygons of circles
  • Vector and Cartesian equation of a line in space
  • Angle between two lines
  • Shortest distance between two lines
  • Plane
  • Angle between two planes
  • Angle between a line and a plane
  • Distance of a point from a plane
  • Sphere

Algebra II

  • Factoring polynomials/trinomials
  • Real and complex numbers
  • Operations on complex numbers
  • Operations on rational expressions
  • Graphing quadratic equations
  • Maxima, minima and zero of quadratic function
  • Laws of logarithms
  • Exponential growth/decay
  • Properties of logarithms
  • Graph of conic sections
  • Circle, Ellipse, parabola, hyperbola
  • Counting principles
  • Permutations and combinations
  • Binomial theorem
  • Mathematical Induction
  • Arithmetic and geometric series
  • Inverse functions
  • Operations on functions

Trigonometry

  • Graphs of sine and cosine functions
  • Trigonometric Identities
  • Graphing trigonometric functions
  • Inverse trigonometric functions
  • Addition formulas for sines and cosines
  • Half-angle and double-angle formulas
  • Law of sines/cosines
  • Area of triangle, given one angle and 2 adjacent sides

Linear Algebra

  • Types of linear systems
  • Gauss-Jordan elimination, Gauss-Jordan method
  • Rectangular matrices to row echelon form
  • Types of Matrices
  • Transpose of a Matrix
  • Adjoint and inverse of a matrix
  • Symmetric and Skew Symmetric Matrices
  • Elementary Operation (Transformation) of a Matrix
  • Applications
  • Determinants
  • Properties of Determinants

Probability and Statistics

  • Random experiments and sample spaces
  • Events
  • Probability of an event
  • Mutually exclusive events
  • Multiplication Theorem on Probability
  • Independent events and experiments
  • Conditional probability
  • Random variables and probability distributions
  • Discrete random variables
  • Bayes' Theorem
  • Bernoulli Trials and Binomial Distribution
  • Bivariate frequency distributions
  • Marginal and conditional frequency distributions
  • Definition of correlation
  • Positive and negative correlation
  • Scatter diagram method
  • Spearman’s rank correlation method
  • Introduction of regression
  • Regression lines
  • Regression equations

Advanced Placement Probability and Statistics

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

Precalculus

  • Parametric/rectangular forms of functions
  • Sequences and series
  • Continuity, end behavior, asymptotes, limits
  • Law of Sines/Cosines, area formulas
  • Even/odd functions, significant values
  • Vectors, Types of Vectors
  • Addition of Vectors
  • Multiplication of a Vector by a Scalar
  • Product of Two Vectors
  • Functions and operations

Calculus

  • Domain and range of a function
  • Graph of a function
  • Inverse of a function
  • Real functions and their graphs
  • Operations on real functions
  • Limit of a function
  • Limit at infinity and infinite limits
  • Left and right limits
  • Continuity and discontinuity at a point
  • Continuous functions
  • Derivative of a point
  • Interpretation of a derivative at a point
  • Derivative of a function
  • Differentiability
  • Derivative of some important functions
  • Product rule for Differentiation
  • Quotient rule for Differentiation
  • Derivative of implicit functions
  • Derivative of a function of a function
  • Derivative of inverse trigonometric functions
  • Derivatives of functions in parametric forms
  • Differentiation of logarithmic and exponential functions
  • Logarithmic differentiation
  • Differentiation by substitution
  • Second order derivative
  • Rate of change of quantities
  • Increasing and decreasing functions
  • Maxima and minima
  • Tangents and normals
  • Rolle’s theorem
  • Lagrange’s Mean Value Theorem
  • Differentials, errors and approximations
  • Constant of integration
  • Elementary integration formulas
  • Methods of integration
  • Integration by decomposition of integrand
  • Integration by substitution
  • Integration by parts
  • Integration through partial fractions
  • Definite integral as the limit of a sum
  • Fundamental theorem of calculus
  • Evaluation of definite integrals using properties
  • Calculating area under a plane curve
  • Area between two curves
  • Differentiation Equations
  • Methods of Solving First order, First Degree Differential Equations
  • General and Particular Solutions of a Differential Equation
 
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