From chapter 16, read pages 418-423, up to the section titled “The Normal Model to the Rescue!”
From the exercises on pages 430-432, do 7, 10, 12, 17
From page 430, do exercises 1, 2, 4, 9. That’s all!
As we continue to explore the use of i to represent the square root of -1, and the consequences that such a definition involves, we revisited the topic of rationalizing today, and noted that since i is a square root, the rules of Simplest Radical Form require that we not leave i in the denominator of a fraction.
Our test on Unit 4 will be on Friday, January 18th. Please do not be absent on that day! If you know for some reason that you will be absent on that day, please arrange a time before the 18th to take the test! Otherwise, we will have to schedule a time for you to take the test during exam week.
Tonight, after today’s quiz, please start reading Chapter 16: pages 413-418, up to the section “The Binomial Mode: Counting Successes”
More work with imaginary numbers today, in particular simplifying expressions that involve multiplying them or with higher powers. We saw in the videos we watched yesterday that powers of i don’t increase like other real numbers, but instead cycle through the numbers 1, i, -1, -i, and then back to 1 again.
Your quiz on Chapter 15 will be on Monday, January 14. There is no special review sheet for this quiz, this time I advise you work on the following problems from Chapter 15’s exercises: 19, 20, 21, 36, 38, 41, 42, 52. You can find my solutions here.
Download Fractal Zoomer.exe from here (don’t click the green button, that downloads something else). Use the navigation guidelines posted yesterday to help you use the program.
Play around with the program, but do so with intent. I have a few things I want you to explore:
- Take unusual values of C from the Complex Paint worksheet and verify the connected/disconnectness of the corresponding Julia Set
- Explore: Where in the Mandelbrot Set can we find values of C that correspond to area versus string Julia Sets?
- Explore: What is the relationship between the location of C in the Mandelbrot Set and the orbit pattern within the corresponding Julia Set?
- Challenge: We saw earlier that orbits of quadratics can contain up to Nine 6-cycles. Some are attracting, some are repelling, but most are complex. Can you find all nine of them in the Mandelbrot Set?
Also, if you’re interested in learning a bit more about three dimensional fractals, check out the game or information linked here.
We’ve started the second section of Unit 4, learning about complex and imaginary numbers. This is a new category of number, much like irrational or negative numbers, that mathematicians developed to handle equations that they previously had no ability to solve. We watched two videos to introduce this topic, but I recommend you watch the full story found here.
From pages 409-411, do exercises 32, 43, 49, and 53.
There will be a Chapter 15 Quiz on Monday, January 14. I would advise you also start working on the quiz review questions of: 19, 20, 21, 36, 38, 41, 42, 52
After today’s quiz, you have the usual post-quiz assignment. Complete either page – your choice – for a homework credit. Complete both pages for extra credit on the quiz.
Finish reading chapter 15 – pages 400-407
From the exercises on pages 409-411, do 39, 45, 47 (skip part c), and 55.
Continue reading through chapter 15, pages 395-400 (up to the section on Continuous Random Variables)
From the exercises on pages 407-408, do 5, 23, 27, 29, and 35.
First, a reminder of the homework protocol.
- Homework is assigned every day and due the following day. Homework is assigned every day and due the following day.
- Late assignments will be accepted ONE day late for half-credit.
- If you are ABSENT FROM CLASS, you are expected to turn in the assignment you would have submitted on that day on the day that you return. You will be given one additional day per day of absence to turn in the assignments you missed.
- For example: Goofus is present on Monday and absent on Tuesday. On Wednesday, he must turn in Monday’s homework, and he has until Thursday to turn in Tuesday’s assignment. He gets no extra time on Wednesday’s assignment; that is due Thursday also.
- If you are having difficulty with an assignment, it is your responsibility to arrange extra help. We usually have time to discuss one or two topics in class, but if that’s not enough please come and see me!
- New for 2019: Any student who has 3 or more unexcused missing assignments will be assigned a lunch or after school detention to make up the missing work. This work will or will not be accepted for credit based on my discretion!
Your quiz on the first part of Unit 4, all about rewriting radical expressions in Simplest Radical Form, is tomorrow. We made a study guide today, linked below, and got a review sheet that will be collected for homework tomorrow. The solutions are posted below as well.
Start reading Chapter 15, pages 389-395, up to the section “More about mean and variances”
From Chapter 14 (page 388), do exercise 52
From Chapter 15 (pages 407-407), do exercises 3, 7, 9, 12.
Still more work with simplifying radical expressions today, now with expressions that include variable components. The method of dealing with these terms, fortunately, is fairly straightforward.
We will have a quiz on our work in this unit so far on Tuesday, January 8th.
Finish reading chapter 14, pages 371-383. From the exercises on pages 384-388, do 16, 22, 36, 51
Radical expressions aren’t just for undoing powers of two, there are in fact roots for every conceivable power you might use as an exponent. Our lesson today was evaluating “n-th” (pronounced “ennth”) roots.
From chapter 14, read pages 363-371, up to the section on Tables vs Venn Diagrams, then work on exercises 3, 4, 9, 11 from pages 383-384.
Please post here or email me with questions!