A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%)
Fun-learning---- Zero memorization
Subject GRE Maths ClassesBy: Satyadhar Joshi
And Mock testshttp://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
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
• 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
