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A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization

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

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A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization

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  1. A Presentation on Subject AGRE MathsContent 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/

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

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

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

  5. 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)

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

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

  8. 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

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

  10. 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

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

  12. Conic Section • Eccentricity • (page 303 Coordinate geometry SK GoyalArrihant)

  13. Eccentricity • Derivation for Ellipse • (page 421 Coordinate geometry SK GoyalArrihant)

  14. Derivation of trigonometry

  15. Logarithmic • Other Slide

  16. Page 26 CSGRE

  17. Page 32

  18. Graphs in XY Plane • Intercept form

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

  20. 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

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

  22. Graph of Log Function

  23. 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

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

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