Subject GRE Maths Classes A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization Subject GRE Maths Classes By: Satyadhar Joshi And Mock tests http://onlineclasses.nanotechbiz.org/

Key Aspects of Teaching Effortless & Highly condensed Multiple exams covered Full-of-fun 0-memory-based Long-termed Root-based Ab-initio Practical Examples

Pre- Calculus (Day 1) Functions (Inverse, graphs) Analytical Geometry Polynomial Equations Logarithms Trigonometry

Questions Functions f g and f inverse Focus of conic sections Quad equation with complex roots Log Complex inverse questions on trig

Mapping One-one Many one Onto ( each element can be mapped to another in the other sets ex y=2x) Into (some of the elements cannot be mapped like y=x2)

Example 1 Example of Many one onto: If two or more students are sharing a chair and no chair remain vacant.

Composite Function (g o f)x =g(f(x)) Example: f(x)=x2 and g(x)=x+7, then both combinations

Range of the function: it’s the value set that the functions points Domain of a function: it’s the value set the function takes Intervals of x-2 x-1 etc

Inverse Function Inverse Mapping If f(x)=y, then f-1(y)=x Example 1.4

Analytical Geometry How they got into existence ? Why are they the most basic structures ? Circle, Ellipse, hyperbola & Parabola Foci, vertices, axes and asymptotes Definition of the three Line= ax+by+c=0 Circle Ellipse, (x/a)2 + (y/b)2 = 1 Parabola, y= +-(1/4p)x2 Focus is the point which is used to define them

Circles Equation of circles Tangent to a circle: at point and with a given slope (page 176 Coordinate geometry SK Goyal Arrihant) Derivation using calculus method for point

Conic Section Eccentricity (page 303 Coordinate geometry SK Goyal Arrihant)

Eccentricity Derivation for Ellipse (page 421 Coordinate geometry SK Goyal Arrihant)

Derivation of trigonometry

Logarithmic Other Slide

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Graphs in XY Plane Intercept form

History Introduction to derivation of pie in a circle What is angle What is distance

Polynomial Equations Quadratic Equation Theory and roots of equations Sum and products of roots Sum of roots= - an-1/an Product of roots= (-1)n a0/a1

Logarithmic and Trigonometry Identities and formulas Periodicities What is log? How is it related to exponential ? How does e came into existence?

Graph of Log Function

Application to real work Applications in finance: Binomial asset pricing function, Brownian motion, Martingale process , Stochastic Integrals, Ito’s, Girsanov’s theorem, stochastic differential equations, continuous time financial models, Hedging strategies, Black Sholes formulas, Term structure Applications in computer Applications in marketing

Reference Cracking the GRE Math Test, 3rd Edition IIT JEE Maths ML Khanna (pp 575) GRE Math Test REA