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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
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Key Aspects of Teaching
Effortless & Highly condensed Multiple exams covered Full-of-fun 0-memory-based Long-termed Root-based Ab-initio Practical Examples
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Pre- Calculus (Day 1) Functions (Inverse, graphs) Analytical Geometry
Polynomial Equations Logarithms Trigonometry
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Questions Functions f g and f inverse Focus of conic sections
Quad equation with complex roots Log Complex inverse questions on trig
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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)
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Example 1 Example of Many one onto: If two or more students are sharing a chair and no chair remain vacant.
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Composite Function (g o f)x =g(f(x))
Example: f(x)=x2 and g(x)=x+7, then both combinations
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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
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Inverse Function Inverse Mapping If f(x)=y, then f-1(y)=x Example 1.4
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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
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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
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Conic Section Eccentricity
(page 303 Coordinate geometry SK Goyal Arrihant)
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Eccentricity Derivation for Ellipse
(page 421 Coordinate geometry SK Goyal Arrihant)
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Derivation of trigonometry
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Logarithmic Other Slide
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Page 26 CSGRE
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Page 32
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Graphs in XY Plane Intercept form
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History Introduction to derivation of pie in a circle What is angle
What is distance
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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
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Logarithmic and Trigonometry
Identities and formulas Periodicities What is log? How is it related to exponential ? How does e came into existence?
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Graph of Log Function
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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
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Reference Cracking the GRE Math Test, 3rd Edition
IIT JEE Maths ML Khanna (pp 575) GRE Math Test REA
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