a presentation on subject agre maths content of the class on pre-calculus (10%) fun-learning----...
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/1.jpg)
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/
![Page 2: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/2.jpg)
Key Aspects of Teaching
• Effortless & Highly condensed • Multiple exams covered • Full-of-fun • 0-memory-based • Long-termed • Root-based • Ab-initio • Practical Examples
![Page 3: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/3.jpg)
Pre- Calculus (Day 1)
• Functions (Inverse, graphs)• Analytical Geometry• Polynomial Equations • Logarithms• Trigonometry
![Page 4: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/4.jpg)
Questions
• Functions f g and f inverse• Focus of conic sections• Quad equation with complex roots• Log• Complex inverse questions on trig
![Page 5: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/5.jpg)
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)
![Page 6: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/6.jpg)
Example 1
• Example of Many one onto: If two or more students are sharing a chair and no chair remain vacant.
![Page 7: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/7.jpg)
Composite Function
• (g o f)x =g(f(x))• Example: f(x)=x2 and g(x)=x+7, then both
combinations
![Page 8: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/8.jpg)
• 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
![Page 9: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/9.jpg)
Inverse Function
• Inverse Mapping• If f(x)=y, then f-1(y)=x• Example 1.4
![Page 10: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/10.jpg)
![Page 11: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/11.jpg)
![Page 12: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/12.jpg)
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
![Page 13: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/13.jpg)
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
![Page 14: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/14.jpg)
![Page 15: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/15.jpg)
Conic Section
• Eccentricity
• (page 303 Coordinate geometry SK Goyal Arrihant)
![Page 16: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/16.jpg)
Eccentricity
• Derivation for Ellipse• (page 421 Coordinate geometry SK Goyal
Arrihant)•
![Page 17: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/17.jpg)
![Page 18: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/18.jpg)
![Page 19: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/19.jpg)
![Page 20: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/20.jpg)
![Page 21: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/21.jpg)
![Page 22: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/22.jpg)
Derivation of trigonometry
![Page 23: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/23.jpg)
Logarithmic
• Other Slide
![Page 24: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/24.jpg)
Page 26 CSGRE
![Page 25: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/25.jpg)
Page 32
![Page 26: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/26.jpg)
![Page 27: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/27.jpg)
![Page 28: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/28.jpg)
Graphs in XY Plane
• Intercept form
![Page 29: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/29.jpg)
History
• Introduction to derivation of pie in a circle• What is angle• What is distance
![Page 30: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/30.jpg)
![Page 31: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/31.jpg)
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
![Page 32: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/32.jpg)
![Page 33: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/33.jpg)
Logarithmic and Trigonometry
• Identities and formulas • Periodicities • What is log?• How is it related to exponential ?• How does e came into existence?
![Page 34: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/34.jpg)
Graph of Log Function
![Page 35: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/35.jpg)
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
![Page 36: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/36.jpg)
![Page 37: A Presentation on Subject AGRE Maths Content of the Class on Pre-Calculus (10%) Fun-learning---- Zero memorization](https://reader036.vdocuments.net/reader036/viewer/2022081604/56816785550346895ddc9b3f/html5/thumbnails/37.jpg)
Reference
• Cracking the GRE Math Test, 3rd Edition• IIT JEE Maths ML Khanna (pp 575)• GRE Math Test REA