Advanced

Exam prep. with rigourous approach to computational techniques.

College Algebra

Review
Linear Equations
Quadratic Equations
Radical Equations
Absolute value Equations
Solving Quadratic Inequalities
Solving Abs. Value Ineq.
Applications to Business and Science
Lines- Slope, intercepts, Symmetry
Distance and Midpoint
Circles
Functions
Graphs of Functions
Properties of Functions
Types of Functions
Polynomials
Rational Functions
Solving Polynomial and Rational Inequalities
Finding Real Zeros of Polynomials
Complex numbers
Finding Complex Zeros
Composition of Functions
One-to-One and Inverse Functions
Exponential Functions
Logarithmic Functions
Exponential Growth and Decay models
Systems of Linear Equations
Solving system of Linear equations using-
Matrices
Row-Echelon and Reduced Row Echelon
Sequences
Arithmetic
Geometric
Binomial Theorem

Pre Calculus

Prerequisites
Functions and Properties
Basic functions
Combining and
-Composition of Functions
Transformations
Linear and Quadratic
Power functions
Polynomial functions
Real Zeros of Poly.
Complex zeros
Graphs of Rational functions
Exponential and Logistic
Logarithmic Functions
Properties of Logs
Solving Log and Exp
Trigonometric Funct.
Angles and Measures
Trig functions of Acute angles
Circular functions
Graphs of Sine & Cosine
Graphs of Tan.Cotangent & Secant
Composite Trig. Functions
Inverse Trig. Functions
Trig Identities
Proving Trig. Identities
Multiple Angle Identities
Law of Sines
Law of Cosines
Vectors
Dot product of Vectors
De Moivres Theorem and nth Roots
Matrices
Solving System of Two equations
Matrix Algebra
Linear Systems-Gaussian,Row Echelon
-Reduced Row Echelon
Binomial Theorem
Sequences
Intro Limits, Derivatives, Integrals

Calculus

Prerequisites for Calculus
Limits and Continuity
Derivatives
Derivatives of functions
Differentiability implies Continuity
Rules of Differentiation
Velocity and Rates of Change
Derivatives of Trig. Function
Chain Rule
Implicit Differentiation
Derivatives of Inverse Trig.
Derivatives of Exp. and Log.
Applications of Derivatives
Extreme Values of Functions
Mean Value Theorem
First and Second Derivative Tests.
LHopitals Rule
Definite Integrals
Definite Integrals
Definite Integrals and Antiderivatives
Fundamental Th. of Calculus
Integration by Substitution
Product rule of Integrals
Application to Areas and Volumes
Average rate of Change
Infinite Series
Power series
Taylor Series
Convergence
Differential Equations
Seperable

Trigonometry

Trigonometric Funct.
Angles and Measures
Trig functions of Acute angles
Circular functions
Graphs of Sine & Cosine
Graphs of Tan.Cotangent & Secant
Composite Trig. Functions
Inverse Trig. Functions
Trig Identities
Proving Trig. Identities
Multiple Angle Identities
Law of Sines
Law of Cosines
Vectors
Dot product of Vectors
De Moivres Theorem and nth Roots

Analytical Geometry

Part I

This course is the study of Locus, Transformation of axes, Straight lines, Pair of straight lines, Three dimensional geometry, Direction cosines , The plane.

Part II

Circles, System of Circles, Conics( Parabola, Hyperbola, Ellipse) Polar Coordinates.

SAT

Number Systems,Operation with Fractions
Word problems involving fractions
Inverse Variations,Percentages
Arithmetic and Geometric Sequences
Algebra: Linear Equations,Quadratic, Radicals,Roots,
Monomials,Polynomials,
Inequalities, Solving Inequalities
Solving Linear and Quadratic Functions, Rational functions
Solving Rational Inequalities
Geometry: Areas, Volumes, Perimeter, word problems
Properties of Triangles, Coordinate Geomentry
Lines- parallel and perpendicular
Data Analysis, Statistics, Basics of probability,Average, central tendencies,Permutations, counting principles