Assignments for Math S-Y

Assignments for Math SY

Precalculus - an Introduction to Mathematical Models and Expressions

Make sure you keep up with doing your homework! It's very important to work through the problems on your own to make sure you're learning the material that we cover in class. On the other hand you should free to set up study groups to work on the homework together - just be sure that you understand the solutions to the problems for yourself when you work with others.

Problem sets should be turned in at the beginning of the class in which they are due. They will be returned soon after they've been turned in.

Solution Sets:

Fifteenth Assignment: due Friday, August 11th:

Here is the last official assignment that's due this summer!

In the online textbook please read section 7.1 and section 7.2 (pages 165 through 191)

On page 176 please do problems 2, 5, 6, 9, 10 and 12

On page 191 please do problems 2, 3, 4 and 7

Fourteenth Assignment: due Wednesday, August 9th:

This is the updated assignment due Wednesday. First please read sections 6.4 and 6.5 and do the following:

at the end of section 6.4 please do problems 3, 4 and 5

at the end of section 6.5 please do problems 1 and 2

Next please answer the following additional questions:

Using the new formula for combinations (the one we found in class today for "N choose K" - i.e. the number of ways to select K objects out of N objects), calculate the following:

1) Suppose you played poker with half of the deck, throwing out all the clubs and diamonds (leaving 26 cards). Now how many possible card hands are there (dealing 5 cards out of the 26 card deck)?

2) Using the 26 card deck, what is the probability that you would end up with a flush? How does this compare to the regular 52 card deck and the probability of getting a flush there? Does the change in probability make sense to you?

3) What is the probability of ending up with a straight if you use the 26 card deck? How does this compare to the regular 52 card deck and the probability of getting a straight there? Does the change in probability make sense to you?

4) Suppose you go back to playing with a 52 card deck, but you decide to play 7 card poker (i.e. dealing 7 cards out per person instead of 5). How many possible card hands are there in 7 card poker?

5) If you were to play 7 card poker, what is the probability that in your 7 cards you would have four of a kind? (e.g. that in the 7 card hand you were dealt that you had ended up with all four aces, for instance)

Thirteenth Assignment: due Wednesday, August 2nd:

In the online textbook please read through sections 6.2 and 6.3 and read in section 6.4 up to "Expected Payoff" at the bottom of page 150 (you can read more if you'd like - we'll be picking it up from there on Wednesday). Next please do problems 1, 2 and 3 on pages 147 and 148 and questions 1 and 2 on page 154

Twelfth Assignment: due Monday, July 31st:

Please order the list of events (see the handout that was passed out in class: ProbabilityList.doc) in order of most likely to least likely as best you can and then please do problems 1, 2, 4 and 5 at the end of section 6.1 in the new online textbook (available at http://users.rcn.com/econnally/math/courses/S-Y/stats.pdf).

Eleventh Assignment: due Friday, July 28th:

Please read section 6.1 (the pages marked 129 through 136) in the new probability textbook available at

http://users.rcn.com/econnally/math/courses/S-Y/stats.pdf

We will be using this as our primary text for the rest of the summer so let me or Barusch know if you have any troubles downloading the file. You can simply read the text online or print out copies for yourself if you'd like. Note that there are no problems due from the reading as of yet - just do the reading for Friday.

For homework I'd like everyone to start getting used to probabilities by creating a couple of datasets. For the first dataset please borrow, buy or make a pair of dice. Roll the pair of dice 72 times noting the sum of the two dice each time. Record how many times each sum comes up. The minimum sum is 2 (a one plus a one) and the maximum possible is 12 (a six and a six). At this point you can probably figure out how many times you expect each sum from 2 to 12 to come up, but go ahead and do the experiment yourself and see how the data comes out. If you make your own dice you can check how close to perfectly random your homemade pair actually is by looking at the results you get. If you already rolled dice in Barusch's Wednesday section, great - just make sure you bring your results with you to class on Friday (and be sure to bring your tally up to 72 rolls if you rolled fewer times in section).

Next, use a coin and conduct the following experiment. Flip the coin 100 times and write down whether it lands heads up or tails up each time. Keep this data for a reference for later. Now using your data (which should just look like "H T T H H H T H..." etc) look through the results and record in a separate entry how many times a sequence of 2 or more heads or tails in a row occurred. For instance, if your data consisted of the following 10 flips: H T T H H H T H T T" then you would record the following:

Length 2 sequences: 2 (both T T)

Length 3 sequences: just 1 (the H H H one)

As we study probability we'll learn how often it is expected that each type of repeated sequence occurs.

Finally - this is a bit odd! - find a calendar somewhere and do the following: count the number of Friday the 13ths that have occurred (or will occur) in the years 2005 and 2006 (you can find calendars pretty easily online if you need to). Before you actually count them up you might want to guess how many you expect to see then check your guess.

Tenth Assignment: due Wednesday, July 26th:

Please read section 5.3 and do the following problems:

from section 5.2 please do 17, 20, 31, 33

from section 5.3 please do 1, 3, 13, 16, 18, 19, 31, 43, 44, 46

Ninth Assignment: due Monday, July 24th:

Please read sections 5.1 and 5.2 and do the following problems:

from section 5.1 please do problems 11, 13, 25, 26, 27, 29, 35, 40, 41

from section 5.2 please do problems 14, 19, 22, 24, 30, 34, 35, 38

Eighth Assignment: due Friday, July 21st:

Please read sections 4.2 and 4.3 by Friday. Note that we haven't talked about completing the square in class yet (covered on pages 173-176) so if that's not familiar to you, don't worry about it at this point. My apologies for including a problem last time (#18 on 4.2) that required tricks we hadn't covered in class yet - I hadn't meant to include that particular one (on the other hand, several of you were creative in your approaches to solving it!)

from section 4.1 (one last time!) please do problem 26

from section 4.2 please do 1 through 8, 21, 23, 25, 27, 35, 38, 39, 42, 43, 46

from section 4.3 please do 29, 30 and 56

Seventh Assignment: due Wednesday, July 19th:

Here's the full set of problems due on Wednesday (this includes the set that was posted last week)

Please read section 4.1 in the textbook and do the following: (note that you're not being asked to read sections 4.2 and 4.3 at this point - you should feel free to skim through them if you want, but we'll be going over this material in class on Wednesday and you don't need to read them to do the problems in the assignment below - you should be able to do them all based on your class notes from class on Monday!) Note that there's a bunch of algebra on this problem set, so use the time to review any algebraic issues you need to cover with Barusch in Tuesday's section if you're stuck.

at the end of section 4.1 do problems 5, 7, 9, 11, 12, 16, 20, 28, 29, 33 and 37

also from the same section (4.1) do problems 25, 31, 32

from the end of section 4.2 please do problems 9, 12, 13, and 18

and from the end of section 4.3 please do problems 6, 7, 18, 19, 20, 38 and 55

Sixth Assignment: due on Wednesday, July 12th

Please read sections 2.4 and 2.5 in the textbook and do the following problems: (if you are interested you can also take a look at section 2.6 on solving simultaneous linear equations, but this section is not required reading and it does get somewhat involved)

at the end of section 2.4 please do 1, 6, 8, 15, 23, 50, 55, 57, 59, 68

at the end of section 2.5 please do 3, 13, 15, 18, 32, 36, 38, 39

also please do problem 35 on page 107

Finally, please read and do the problem on Tax schedules in Tax Graphs

Fifth Assignment: due on Monday, July 10th

Please read sections 2.1, 2.2 and 2.3 in the textbook and do the following problems:

at the end of section 2.1 please do 4, 5, 12, 22, 31, 34, 37, 39, and 44

at the end of section 2.2 please do 35, 37, 45, 53, and 56

and at the end of section 2.3 please do 4, 5, 33, 38, 59 and 60

Fourth Assignment: due on Friday, July 7th

As we didn't make it particularly into chapter 2 yet, the reading for Friday goes back to the chapter zero review material, which you should finish off now - note that this is most likely review for everyone, but the reason going over these basics is that these algebra skills are key for so many math classes. If anything feels rusty, then now is the time to really go over it well. Barusch should be able to help you with this on Thursday as well.

So - please finish off the algebra review by working through sections 0.3 and 0.4 as well as the "Tools for Chapter Zero" section starting on page 27, and then do the following:

do problems 36, 37, 39, 41, 45, 46, 52, and 56 on pages 25 and 26 and

also do problems 5, 10, 15, 21, 25, 27 and 28 on page 32

Third Assignment: due on Wednesday, July 5th

Please read sections 1.4 and do problems 15, 17, 19, 21, 23, 26 and 31 at the end of section 1.4.

Also, for a few bonus points on the homework assignment due Wednesday, please write down a coherent argument concerning the following question (around a paragraph or two is fine). As we saw in class, the function f(x) = x² (whose graph is a parabola) is a sometimes decreasing, sometimes increasing function. For positive x the graph is concave up (i.e. that part of the graph that's in the first quadrant). Is the part of the parabola that's in the second quadrant concave down or concave up? Recall that we defined a function to be concave up whenever the rate of change of the function (i.e. its slope) was itself increasing. For example the graph of the slow starting runner, given by S(t) in today's class was concave up, but the graph of the fast starter - given by F(t) was concave down.

Second Assignment: due on Monday, July 3rd

We've gotten underway in chapter 1, so over the weekend please read sections 1.2 and 1.3. When you read, you should be sure to go through the examples they give carefully - much of the math that's covered in the textbook is worked out through the examples, so they're crucial to your reading.

Next, please do:

from section 1.2 problems 1, 5, 7, 17, 21, 24, 35

from section 1.3 problems 3, 4, 9, 12, 16, 19, 23

First Assignment: due on Friday, June 30th