After School Regents Review

From now until the end of the school year, students taking classes that end in a regents exam (like Algebra 1!) can go to H217 after school on Mondays and Thursdays to ask questions, work on review, and generally prepare for the exam.

While the sessions are supposed to be for preparing for the exam directly, the teachers involved have stated they would be willing to help students with other work relevant to their class. This could include homework help or test corrections. Keep in mind, though, that they will need to prioritize their attention to students looking for help for their Regents exam directly.

Please take advantage of this opportunity!

Fractals and Chaos Assignment for 5/9

Now that you’ve had some opportunity to explore Devaney’s Orbit Diagram, please read the Feigenbaum Plot Article you got in class today. It will expand a bit on the work we’ve been doing in class, demonstrate a very interesting phenomenon in the pattern of bifurcations and, most importantly, answer the question of what order to cycles appear in?

Also, check out this Numberphile video about the concept of the Feigenbaum Constant, mentioned in the article.

 

AP Statistics Exam Final Thoughts

If you’re looking for the review information, you can find it here.

Your AP Statistics Test is Thursday afternoon. Be outside the new gym by 11:50 with your calculator and pencils (non-mechanical, remember!). Do not bring your bag or your cell phone; find somewhere to put them.

Things you had better remember (these are my thoughts, see pages 608-610 of your review book for some further points):

  • The formulas for the mean/standard deviation of a sampling distribution of means and a sampling distribution of proportions are on your formula sheet. Whenever you’re being asked to calculate a mean or a standard deviation, check to see if it’s one of these.
  • Probability questions will come in three categories
    • Direct calculation based on a finite sample space (like rolling dice). Write out all the possible outcomes and count which ones are the ones you want. This also includes two-way tables. Don’t try to use fancy formulas for those; just count!
    • Number of successes questions. For example: “how many model E cars would you expect to see in a 2000 car sample?” or “what’s the probability that at least one out of the four drivers is speeding?” These are applications of the binomial probability model and should be calculated appropriately using the formulas on your sheet.
    • Number of trials questions. For example: “how many chips would you expect to need to check before finding a defective one?” or “what’s the probability that the 5th donor is the first with Type-B blood?” These are applications of the geometric probability model. The formulas are not on your sheet, and so you should memorize them: q^(K-1)*p for a general probability and 1/p for the expected value.
  • How to combine the standard deviations of two or more random variables. Remember: variances always add.
  • How to read the regression output of a linear association. What do “constant,” “estimate/coefficient,” “prob” all mean? Refer to pages 111-112 in your review book or page 729 in your textbook.
  • Know the difference between stratified and cluster sampling and how to identify/use them.
  • Know the important conditions for each of the inference procedures:
    • Everything: Random Condition
    • Any z-test: Success/failure condition
    • Any t-test: Nearly Normal/Large Enough condition
    • Any chi-square test: Expected cell frequency condition
    • Any 2-sample/2-proportion test: groups are independent from each other.
    • Also: know when to use a 2-sample t-test vs. a matched pairs t-test
  • Be mindful of notation. Don’t use x-bar when you should be using µ. Don’t use p when you should use p-hat.
  • Context, context, context. Always frame your answers in the context of the situation. Don’t say, “I am 95% confident that the true proportion of success is between 22% and 37%.” Say instead: “I am 95% confident that the explosive sensor will accurately detect hidden explosives 22% to 37% of the time.”
  • Be complete with your responses. When choosing between two possibilities in a free response question, explain why one possibility is wrong and why the other one is correct.
  • At the same time, don’t give more information than is requested. If the question asks you to describe the shape of a distribution of data from a histogram, don’t discuss center and spread. If the question asks you to explain your randomization procedure for an experiment, you don’t need to explain what the response variable is, how you’re going to measure it, and what a statistically significant outcome would look like. If the question asks you to merely calculate a confidence interval, you don’t have to interpret it.

Algebra 1 Assignment for 5/8

Your test is tomorrow! Here’s what you should do to prepare:

  • Review your vocabulary notes. There’s a lot of vocabulary in this unit that have very particular and important definitions. Make sure you know them well.
  • Do some more review with Statistics Review 2, or with the review exercises in your workbook. Answers to the review you got in class can be found here, while answers to the textbook review can be provided by email (just send me a message).
  • Work on some IXL review. I’ve bolded the ones that would be particularly useful.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 5/5

We’ve started to review for the test on Tuesday, May 9th. The first review, Statistics Review 1, is based on the student survey data we gathered from the beginning of the unit. Refer to that data to answer the questions in the review.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 5/4

Today we did part 2 of the Global Stats Project, comparing the Gender Inequality Index data for each country you researched previously to the GDP (Gross Domestic Product) of the country. Your homework tonight is to finish this work. If you weren’t in class, please check your email for a scan of your data from part 1 (you’ll obviously need it to finish part 2).

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

 

 

Fractals & Chaos Assignment for 5/3

We’ve spent some time exploring the logistic function analyzers linked at right, and have found some patterns. For example, when a = 3.0, we have a fixed point attractor, but at a = 3.1, there’s a 2 cycle. There’s a 4 cycle at a = 3.5, and while there appear to be separate bands of chaos at a = 3.6, they’ve merged by the time we get to a = 3.7. Please investigate the logistic function some more, with the following questions in mind:

  1. Where between 3.0 << 3.1 does the first bifurcation occur? When is the 2-cycle born?
  2. Can a 3 cycle be found in the interval 3.4 << 3.5? If so, this would suggest that one part of a cycle can bifurcate before the other. If not, perhaps bifurcation is an all or nothing thing.
  3. Is there only chaos to be found for a > 3.6? Or is there something else hidden in there?

Algebra 1 Assignment for 5/3

The second part of the pick Unit 10 rewrite is today: Lesson 7 – Evaluating Appropriateness and Reliability of Linear Models. The notes are posted below, as is a video discussing how to calculate and understand residuals and the correlation coefficient.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 5/2

Some of the biggest rewrites in the unit are happening now: we’ve essentially taken all of the remaining lessons and condensed them into two. Today, do the modified version of Homework 6: Bivariate Data Analysis. You may want to refer to the calculator reference sheet for a refresher on how to get a linear model on your calculator, or view the video linked below.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 5/1

In class today, please refer to the student survey data found here.

Complete the homework assignment for Unit 10, Lesson 5 – Two Way Frequency Tables. This assignment is also an edited version of the original version from the workbook, but it’s close enough to the original version that Kirk’s video should still be useful.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 4/28

Now that we have some statistics tools, we took some time today to practice them with a project analyzing the Gender Inequality Index for countries around the world. If you did not finish the Global Stats Project Day 1 sheet, please do so this weekend. This will be collected for a quiz grade on Monday. If you weren’t in class, you’ll also need to refer to this Country List to select your sample.

For a homework grade, please complete IXL module N.5 – Interpret box-and-whisker plots up to a score of 90 or better.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Algebra 1 Assignment for 4/27

In class today, please refer to the student survey data found here.

Tonight’s homework is for the modified Unit 10, Lesson 4 – Mean and Standard Deviation. This is the modified version of pages 431-432.

IXL Review Modules for Unit 10 (modules relevant to today’s lesson are in bold)

Fractals & Chaos Assignment for 4/26

Use the cobweb diagram apps on MathInsight.org to analyze the non-linear functions of Part 4 of the Iterated Functions sheet (use this Supplement to record your answers). Work up to 4g.

We’re working on some more iterating functions in class, but tonight I want you to read this article from Scientific American: Chaos and Fractals in Human Physiology. It talks about many of the same ideas discussed in the NOVA documentary we watched, but there’s some very important clues on some upcoming phenomena that I want you to pay attention to also.