About Benjamin Kirk

I am a New York State Master Teacher in Mathematics at Ithaca High School. I have been teaching at Ithaca High School since 2007.

Intermediate Algebra Assignment for 5/22

Reminder: your test is on Friday, May 24. There will be calculator-forbidden and calculator-necessary components, so BRING YOUR CALCULATOR.

Your homework tonight is HW 9.20 – Test Review 2. Answers to all three test reviews will be posted tomorrow.

Lesson Video Archive

Cumulative IXL Modules



Intermediate Algebra Assignment for 5/21

We’ve started our review for our final unit test, which will be on Friday, May 24. Tonight, work on HW 9.19 – Test Review 1

Lesson Video Archive

Cumulative IXL Modules

Intermediate Algebra Assignment for 5/20 (Test Warning!)

We did some more work with Linear vs Exponential models today, and the homework is more of the same. We’ll start reviewing the unit as a whole tomorrow, with our planned Unit 9 test on Friday, May 24th

Today’s links

IXL Modules


AP Statistics Post-Exam Details

Our current plan for the last four weeks of classes can be found here: Post-exam/Final Project Schedule. Most of this time will be spent working on final projects, but we have some other tasks schedule as well, including a discussion of strategies for getting college credit for this course and learning about one last type of statistical inference!

Also, as posted before, you can review the questions from this year’s AP Statistics exam here and my responses here. Disclaimer: this is my own work, based on my own understanding of the questions. I do not guarantee that all responses would be awarded full credit (though I usually do fairly well!). Moreover, I tend to be very thorough with my responses, more than the AP rubrics generally require (especially with the hypothesis test question). Do not be nervous if you did not give quite as much detail as me.


AP Statistics Free Response Questions Posted!

You can review the questions from this year’s AP Statistics exam here. My responses are here. Disclaimer: this is my own work, based on my own understanding of the questions. I do not guarantee that all responses would be awarded full credit (though I usually do fairly well!). Moreover, I tend to be very thorough with my responses, more than the AP rubrics generally require (especially with the hypothesis test question). Do not be nervous if you did not give quite as much detail as me.

Intermediate Algebra Assignment for 5/17

Today’s assignment is about deciding whether a linear or exponential model is most appropriate for a set of data. The short version is make a scatterplot and examine the picture. If it looks straight, use a linear model. If it looks curved, use an exponential one.

Today’s links

IXL Modules

Intermediate Algebra Assignment for 5/16

More of the same today as yesterday, only this time working with exponential regression instead of linear.

Today’s links

IXL Modules

Intermediate Algebra Assignment for 5/15

Not all linear or exponential relationships are as perfectly defined as we’ve seen. Sometimes the fit of a line or a curve is a bit more approximate, and finding the equation for these functions is a bit more tricky. Fortunately, your calculator provides you with a helpful tool in doing just this: Regression. The instructions for getting your calculator to do this are in today’s notes. They’re a little tricky (lots of button pushes), but pretty straightforward.

Today’s links

IXL Modules

AP Statistics Exam Final Thoughts

Your AP Statistics Test is Thursday afternoon. Be outside York Lecture Hall by 11:50 with your calculator and pencils (non-mechanical, remember!). Do not bring your backpack, bag, or your cell phone (or any other “smart” device like watches); find somewhere to put them. You may bring a snack or water, but it must be in clear packaging and you may not have it at your desk with you. Do not expect to leave until at least 4:00!

See this post from before with the archive of review materials.

Things you should be sure to 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.
    • Related: Pay attention to which standard deviation you are being asked to calculate. The standard deviation of a sample is not the same thing as the standard deviation of a sampling distribution.
  • 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.
  • Know how to combine the standard deviations of two or more random variables. Remember: variances always add.
  • Know 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. Also remember that for a simple random sample every possible sample has the same chance of being chosen.
  • 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.
    • Related: No Naked Numbers! Every number included in any response should have a label somewhere (mean, standard deviation, p-value, etc.)
  • 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. When asked to compare two distributions, make explicit comparative statements, e.g, “Group 1 is centered at around 12, which is greater than Group 2, which is centered around 7”
  • 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.

Intermediate Algebra Assignment for 5/14

More with linear and exponential models today, specifically with interpreting what the parameters (slope, y-intercept, growth rate) mean in the context of the scenario they model.

The big takeaway is this: for both linear and exponential models, the y-intercept is the starting point or initial value. For a linear function, the slope is the unit rate of change – the change in whatever y measures per one unit increase of whatever x measures. For an exponential function, the value of b always represents the growth or decay rate – typically expressed as a percent. You’ll need to set b = 1 + r or b = 1 – r, then solve for r to get the percent change.

Don’t forget to bring your Chromebook and calculator every day for the rest of this week!

Today’s links

IXL Modules

AP Statistics Pre-exam breakfast

Ms. Seifert and I would like to invite you to a pre-exam breakfast and review session in her room, H213, on Thursday. We’ll start things up around 8:40 for those of you who don’t have 1st period free, and we’ll spend 1st period hanging out and answering any lingering, last-minute questions you may have.

We plan to get bagels, but if you have dietary restrictions (gluten free, vegan, etc.) please indicate them on this form by the end of the day!

Intermediate Algebra Assignment for 5/13

We’re in the last phase of Unit 9, which starts off by reviewing the difference between linear and exponential equations and deriving the formulas for these equations from a table of values.

Today’s links

IXL Modules

AP Statistics Assignment for Week of 5/13

Your AP exam is on Thursday, in the afternoon. Between now and then, what we do for review is largely up to you. I’ll have some ideas here and there, but I’ll expect you to ask questions and guide what we do for these last few days.

Tonight, you should take a look at the AP Exam tips on pages 608-610. We’ll do some more review with AP multiple choice questions in class tomorrow, but after that it’s up to you!

Intermediate Algebra Assignment for 5/10

We will be starting the last part of Unit 9 on Monday, some more work with exponential and linear modeling. This will include a review of Linear and Exponential Regression, so you should plan on bringing your calculator and charged Chromebook every day next week.

Today was our quiz, and we have the usual post-quiz homework assignment. Complete one page, your choice, for the homework credit. Complete both pages for an extra point on the quiz.

Intermediate Algebra Assignment for 5/9

I’ve decided to push the quiz a day to give us a little more time to review. Your homework is twofold:


Intermediate Algebra Assignment for 5/8

Your second quiz of the unit, on exponential function and compound interest word problems, is tomorrow. You got HW 9.11 – Quiz 2 Review in class today, and that will be collected tomorrow. You can find the answers here.

I also recommend you rewatch some of the lesson videos posted below and/or work on some of the highlighted IXL Modules.

Lesson Video Archive

Cumulative IXL Modules

AP Statistics Assignment for 5/8 & 5/9

By Friday, complete the 2014 released Free Response Questions. On Friday, you’ll get into grading groups and score your peers’ responses according to the scoring rubric. Note that this is a different exam from what appears on your review calendar.

This grade will not be counted towards your marking period average. Please do not review the solutions to these problems. Let this be another opportunity to practice the free response section of the exam. Spend no more than 1.5 hours, and use no resources other than your calculator and formula sheet.

Write all of your answers on blank sheets of paper. More than one solution per page is fine; we’ll staple them together in class. But please make it neat! Your peers will be reviewing your work!

AP Statistics Assignment for 5/7

We reviewed the binomial and geometric probability models today, along with sampling distribution models for proportions and for means. Tonight, please do the following

In addition, I’d recommend you look at section 10 from your review book.

Review my answers here before class tomorrow so we can address any lingering questions you may have more efficiently.