Notes/Aarushi.txt at master · umbs/Notes · GitHub

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AARUSHI ============
- Complete Alphastar Academy AMC10 coaching classes.
- Evaluate appearing for SAT for 'testing the waters'.


Meeting with Raji M on
---
Meeting with Raji M on Feb 25, 2025
---
    - Sign up Aarushi at Alphastar Academy
    - Research International Science and Engineering Fair (ISEF)
    - IPRD Fair

    - Start preparing for AMC10, USACO

    - Look for opportunity to join City of Cupertino Youth Council.
    - Appear for PSAT in 9th grade. May be not allowed in Monta Vista HS.

Resources:
---
- SAT Preparation/Coaching: https://satnpaper.com/
- AP classes coaching (Physics, Math, Computer Science)
    ✉️ Email: nilanjan@apguidance.com
    📱 Phone: 669-302-6791
    🌐 Website: APGuidance.com
    - Nilanjan Chatterjee. IIT KGP alum.
- Aparna Lanka (408-368-0754) teaches AP Chemistry
    - Pritam Gaonkar's son took and excelled. Pritam's number: 408-768-3812
- Sanjay Tutoring
    - He runs a high school parents Whatsapp group.
    - 847-666-5699
    - Not sure if he's local/Cupertino.
    - Not sure if he himself teaches AP Chemistry or a group of parents do it.
    - "Please DM me; we are few parents whose kids have gone thru the same path and try to surface the tribal knowledge we have learned over the years. We have a high school parent WhatsApp group for discussions/questions; please feel free to join"

- Physics Tutors for AP courses
    - Mr. Giri (giridhar)
    - His flyer is in Dropbox
    - giridhar@yourphysicstutor.com
    - (973)223-6252

- Math Tutors
    - Tutor --> Monica Puthran: 610-416-2181
        - Annu (408-368-3715), Kavitha (707-685-2719), Richa Garg (650-382-9713) from MVHS Whatsapp group highly recommended her.
        - Sonali Naik Pandit (408-476-8289) has this to say:
            - Highly recommend Monica. Both my kids were her students and they both love mathematics as a subject thanks to her style of teaching!
        - Monica teaches from 9th grade, for high school kids.
    - Tutor --> Bhavika


AoPS Math Notes
---

Intermediate Algebra (4200)
---
Week 4: Quadratic Equations and Graphing Parabolas
---
"Completing The Square"
---
- How to find minimum (or maximum) value of a quadratic expression?
- Make a square of expression (Completing The Square) and you'll get the min/max value of the parabola.
- Example: What is min value of
    x^2 + 10x + 22 ==> (x+5)^2 - 3

    Hence min value is -3

- For a quadratic equation: ax^2 + bx + c = 0, the roots are
    x = (-b +- sqrt(b^2-4ac))/2a

"The Discriminant"
---
- The (b^2 - 4ac) under square root is called discriminant.
- If a, b, c are real numbers and if discriminant is positive then the roots of equation are real numbers.
- If discriminant is 0 then we get only one root (called 'double root').
- Sign of discriminant tells if quadratic has:
    - two real roots
    - two non-real roots
    - only one root

"Graphing Quadratics"
---
- Definition of Parabola: It is the set of points that are equidistant from a
  given line (called the directrix) and a point not on that line (called the
  focus).

- It turns out that every graph of an equation of the form
    y = ax^2 + bx + c
for constants a, b, and c is a parabola. (But not every parabola is an equation
of this form: if the directrix is slanted, you get a rotated parabola.)

- A parabola has a special point called the vertex, which is mid-way between
  the focus and the directrix. (That point must be on the parabola because it
is the midpoint between the focus and directrix, meaning that it has the same
distance from each.) The vertex for y = x^2 is at the origin (0,0)