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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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