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
 Halfangle and doubleangle formulas
 Law of sines/cosines
 Area of triangle, given one angle and 2 adjacent sides
Linear Algebra
 Types of linear systems
 GaussJordan elimination, GaussJordan 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
