AP Comp Sci A Homework - Block D

1. Go over Syllabus, Join Codes, Contract
2. Register Calculator
3. See Clip from "Hidden Figures"?
4. Class kvuruuek
5. Geogebra.org
6. Interactive Euler
7. 6.1b Notes and Examples
8. ∆Math Lab 1-1

• Syllabus
  
• Hidden Figures Clip
  
• Geogebra Example
  
• Video Explanation
  
• Khan
  
• 6.1 From Calc AB
• Euler WS 1
  
• Euler WS 2
  

1. Finish 6.1b Notes and examples with technology
2. EULERM
3. Geogebra.org
4. DeltaMath Lab on Euler Method

1. Euler WS Maximus
2. Schoop

1. Euler WS Maximus
   
2. Schoop
3. TI Program EULER
   
4. Slope Fields with Desmos
   Online version of EulerMethod.ggb
   

Many times we attempt to model the behavior of an event through an artificial simulation. This exploration will mimic the spread of a disease such as a cold. The model assumes that a person with the disease will pass it on to two other people each day.

1. Each Person will represent 10 people. Each student has their own scratch paper to keep track of which of there ten people have been infected. The first student writes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the next writes 10, 11, 22, ..., 29; The nexts writes 30, 31, 32, ..., 39; and so on
2. Using a TI-84 calculator, choose a student a random using the command RandInt(0,N) where N represents 10 ×(the number of students in the class-1. (for example, if there are 9 students, N = 89)
3. This demonstration assumes that each infected person can pass the disease to two other people each day. Press ENTER twice as many times as the number of infected people for each student. ( RandInt(0,N, M) can be used as well. eg. RandInt( 0,89,12) would return 12 random numbers from 0 to 89).
4. Plot a point (x, y) where the x coordinate is the day, and the y coordinate is the number infected.
5. Continue until all students are standing.
6. When all are infected, Using your calculator, find a good curve fit. Which model seems to fit best? Store your model in Y1.
7. In Y2 enter the command Nderiv(Y1,X,X). Graph Y2 in the same window as the data plot and Y1.
8. 6.3 b: Introduction to Logistic Equations

1. Epidemic with Logistic Model WS
   
2. Logistic Exploration.ggb
   
3. Video: Logistics Questions on the AP Exam
   

1. Quiz on Euler Method
2. Finish 6.3b Notes and Examples
3. ∆Math Lab 1-2 Logistical Model
4. Logistic Model on Past AP Exams

1. Videos and Exercise
2. Videos on Logistic differential equations
3. Logistics On The AP.pdf

1. Khan Academy Goal: 55% Mastery in Calculus AB by Sept 10 (12 HW points), 85% Mastery in Calculus AB by the End on Quarter 1 (another 12 HW Points)
2. Solving the Logistic Equation
3. Interactive Geogebra Graph of a Logistic Equation

1. Epidemic Simulation
2. KA Videos on Logistic differential equations
3. GeoGebra Logistic WS
4. Logistic_Model.ggb (install Geogebra to use this file)
   
5. Khan Academy Goal: 55% Mastery in Calculus AB by Sept 10 (12 HW points), 85% Mastery in Calculus AB by the End on Quarter 1 (another 12 HW Points)
6. Solving the Logistic Equation
7. 11 minute video proving y= M/(1 + be^(-kt) is a solution to dP/dt = kP(1-P/M) by blackPenRedPen

1. (Solving the Logistic DiffQ)
2. 7.4 Arclength
3. DeltaMath.com Practice
4. Test on Euler Method (40 min)

1. Read p 427-428
2. Start ∆Math Lab: Arc length

1. 7.4 Area of a Surface of Revolution
2. HWQ 1-6 on Logistical Model
3. 8.1 Basic Integration Rules
4. Partial Fraction Review

1. p 482
2. p 520

1. Chapter 8.0 WS
   
2. Arccos.pdf
   
3. Plus 1 - 1 Technique
   
4. Some Integration "Tricks"
5. Arccot Identity GeoGebra
   
6. 8.0 WS Solution Video
   

Ch 8.0 WS Part 2

1. Chapter 8.1 WS Solutions on PlusPortals
   
2. Plus 1 - 1 Technique
   
3. Some Integration "Tricks"
4. Arccot Identity GeoGebra
   
5. MIT Lecture "The Marriage" of Integral and Differential Calc

1. Q 1-7
2. 8.1 Review of Basic differentiation and Integration Techniques

In class

1. Integration by Parts Proof
2. Ultra Violet Voodoo WS1
   
3. Q 1-8 on Partial Fraction Decomposition (Pre-Calc) and Basic Integration Rules (8.1)
4. TabularUltraVioletVooDoo.pdf

1. UC Davis problems
2. Lab 1-4: Integration by Parts

1. uv-VooDoo Card Game Rules
   
2. Mr Tarrou Video examples
   

1. Test on Euler Method, Logistic Growth, Arc length, and Area of a Surface of Revolution

1. Video of Tabular (DI) Method ( e^x sin x is about minute 10:05)
2. Classwork 1 Level A problem 3 Level B problems
   
3. Classwork
4. UC Davis Solutions

1. Integration by Parts Proof
2. Ultra Violet Voodoo WS1
   
3. 8.3 Trigonometric Integrals Even and odd powers, Wallis' Formulas

4. Trig Powers WS
   
5. Trig Power Examples
6. Integration with Partial Fraction Decomposition
7. uv-VooDoo Card Game ( "Match" version is for COVID conditions only)
   

1. Textbook problems on 538
2. ∆ Math Lab 1-15: Partial Fractions

1. Warm-up: Deriving the Logistic (paper only)
2. Partial Fraction WS Part B (page 7) is the Calculus Part
3. Q 1-11
4. Intro to Improper integrals

1. Textbook p 557
2. ∆Math Lab 1-6: Integrating Partial Fractions

1. Video Link
   
2. PreCalc Worksheet
   
3. Integration by Partial Fractions WS (Part A is the Pre-calc part)
   
4. Video 1
   
5. Video 2
   
6. video 3
   Video 4
   

In class:

1. Q 1-12 on Delta Math (8.1, 8.2, 8.5)
2. Improper Integrals WS
   
3. Penn Slides
   

1. Textbook exercises
2. ∆Math Lab 1-16: Improper Integrals

1. Quiz on Chapter 8.1, 8.2, 8.3, and 8.5
2. Improper Integrals WS
   

1. Improper Integrals WS
   
2. Video: Basic Idea and Example
   
3. Video: MIT lecture
   
4. Penn Slides
   
5. Gabriel's Horn Paradox: finite Volume but infinite surface area
   

1. Complete Improper Integral Examples
2. Gabriels Horn Paradox
3. integral of x/tan x from 0 to pi/2

AMC 10A: November 6, 2024

AMC 12B: November 12, 2024

Free Math Jams

(not free) 2 Day Online Preparation Seminars

AMC 12 at AoPS

1. HWQ 1-17 (Improper Integrals)
2. Ch 8 Test Practice

1. Ch 8 Review Textbook problems
2. Study for Ch 8 Test

• Old FRQs
• 1997-1989 FRQs