Transcript Pre-Calculus AGRE PPT

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
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Effortless & Highly condensed
Multiple exams covered
Full-of-fun
0-memory-based
Long-termed
Root-based
Ab-initio
Practical Examples
Pre- Calculus (Day 1)
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Functions (Inverse, graphs)
Analytical Geometry
Polynomial Equations
Logarithms
Trigonometry
Questions
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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)
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Derivation of trigonometry
Logarithmic
• Other Slide
Page 26 CSGRE
Page 32
Graphs in XY Plane
• Intercept form
History
• Introduction to derivation of pie in a circle
• What is angle
• What is distance
Polynomial Equations
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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
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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