Happy Summer!

We’re done now – even the teachers!! – so I wanted to take a second to say thanks to everyone here for three great years at WECHS, and wish you a good summer.

For those who took the Accuplacer to try to place out of AFM for the fall, most of the results are good.  If you have not already, check in with Mr. Wonsavage to see about changing your schedule and adding a college math class.

A few people are taking college classes in the summer, but there are a lot of other interesting things you could do to keep learning between now and August:

• Learn computer programming! Code Academy has several different programs (no pun intended) to help you start from absolute zero and learn the programming language of your choice.  This could pay off in a lot of unexpected ways – there are a lot of non-programming fields where no the basics of computer logic could help you with things like building spreadsheets and websites.
• Learn a foreign language! Duolingo now has six different languages – they count English as one (so you could work on that), but they also have Spanish, French, German, Italian, and Portuguese.  The exercises are fun, you don’t have to know anything at all before you start, and you can help translate the entire internet.  It really is a great way to get started – it could make your Spanish classes next year a lot easier.
• Don’t forget all the math we learned!  O.k., maybe you don’t find Khan Academy exciting, but simply practicing some of the things we did late in the year will put you way ahead of the game when you start math in the fall.  Or watch some of his videos about the French Revolution, which I don’t know much about either, so I’ll go look at that this week.

Have fun!  And whatever your summer holds, stay safe and come back happy in August!

Assignments – April 22

First Period

Complete the Great Lakes problem.  Each person should complete the function for the lake they are in charge of, then share with their group so every person has a set of functions for all three lakes.  If your group is not sure having trouble figuring out the right formulas, or if you aren’t sure, try this process:

• Begin with year zero.  Figure out for your lake how much flows out.
• Erie should get from Huron the amount flowing in.  Ontario should get from Erie how much is flowing in.
• Add any new pollution that is created on your lake (if any).
• Use your new total to as the initial value for the next year.  Repeat the previous three steps.
• Do this process for five years.

Your recursive function should capture this process in equations, so you should get the same values from the functions.

Once you have a formula you think is correct, create an Excel spreadsheet that calculates the pollution in each lake based on how much was in the lakes the previous year.  Use this to calculate out to 40 years.  Use this to help answer the rest of the questions on the assignment sheet.   You can do one spreadsheet per group, but every individual should write down complete answers to everything in the assignment.  Anything that is not a complete sentence – especially anything that is just a number, or “yes” or “no” – is not a complete answer.

When you finish – do problems 1 and 2 on page 499.

Second period

Do Problems 1 & 2 on p.499, and Problems 5 & 6 on p.501.  Do complete answers (showing work and explaining steps) following the rubric we used in the last two units.  Also do Problem 16 on p.506.

Finish Problem 6 on p.521 – note that you are supposed to try several different starting values, and you should split the work up among members of your group.  After you finish this, try Problem 7 on p.521 – it asks you to consider how the fixed point varies depending on the function.

Third Period

Khan Academy – do the following exercises: Trigonometry 0.5, Trigonometry 1 (remember they do not want you to leave a radical in the denominator), Trigonometry 1.5 (write out the ratio containing the desired side and the known side), Trigonometry 2 (similar to 1.5).

When you finish this, work on the Right Triangles Word Problems.  If you have trouble with these, practice the non-word problem worksheet first.

Assignments – Integrated Math 3

27 March 2013

Complex numbers as solutions to polynomials

You have to create polynomials with certain characteristics in this assignment.  There are an infinite number of possible correct answers for every question.  You can work with partners in coming up with answers, but no two people should use the same polynomials.

• Come up with two different quadratic polynomials that have complex roots, and show both roots for each one.  Also find the vertex of the parabola that is described by the polynomial.  Is there any relationship between the complex roots and the parabola?  (Hint:  Using the quadratic formula, and especially the discriminant, could help you in finding an equation with the right type of solutions.)
• Repeat the process you just did with complex roots, but this time find two different polynomials that have irrational real roots.  Write the exact values of your roots – don’t round off square roots.  You should find the vertex of the parabola and compare it to your roots again.
• Create three different cubic polynomials that have integer coefficients: one with three rational root; one with one rational root and two irrational roots; and one with one real solution and two complex solutions.  Hint: Remember how the factored form of a polynomial is related to its roots.  Be sure to give both the standard form of your polynomial, and list all the roots.
• What, if anything, can you say about the irrational or complex roots of your cubic polynomial?
• Do you think you can make a cubic polynomial with three complex roots?  Explain.
• If you have not already completed all the Khan Academy exercises on imaginary and complex numbers (they are listed in yesterday’s assignment) you can work on those at any time.

Advanced Functions – Logarithm Practice

We are continuing on into logs – remember that “log of” is the inverse operation for “raised to the power.”  The main use of logs in practical problems is to solve an equation with a variable in the exponent.

Assignments:

• Check Your Understanding on p.562 (purple book).  On (a) you should not use the calculator.  On (b) you can use the calculator to “guess and check” with powers of 10, but don’t use the log function.
• p.563, #1-4.  On 1, using logs should tell you the power of 10 you need.  On 2, start by writing the given number  (without an exponent) as “10^k” and raise both sides to the x power; you’ll need to find the value of k to get the final answer.  Number 3 uses the same ideas – simplify the equation to isolate the exponential part (move everything else to the right), and then write both sides as powers of 10.  On number 4, write an exponential growth or decay problem first.
• If you finish, or at any time are lost about how to finish, complete the Khan Academy assignments from yesterday (it includes two videos on logs), as well as the exercises Simplifying Logarithms and Simplifying Logarithms 2.

Assignments During DC Trip

For those who are not in DC, you have your assignments, but here is a reminder:

• English – you have a reading (Gilgamesh) and set of questions to answer from the Literature book.  There is a movie proposal to make as well.  If you finish, work on CIS homework or get a book to read.  Please remember to return the books to Ms. Pickering’s room at the end of first period.
• Social Studies – reading from the textbook (Chapter 20, sections 1-4) and definitions, then work on the semester portfolio entries.  Remember that you must have seven entries completed by April 2.  (This is the day we come back from the 4-day Easter Weekend.)

Math assignments – we have two different classes, obviously.

• Advanced functions – Khan Academy exercises to review exponents – Negative Exponents, Exponent Rules, Simplifying Expressions with Exponents  (Note: You may have completed these before, but not recently.  Do it for review.  And BE SURE YOU ARE LOGGED IN for credit). Khan Academy videos: introduction to logarithms (really a review, since we did these last semester as well.)  Log Properties 1.
• Integrated Math 3 – Continue practice with imaginary and complex numbers (note: you may have completed some of these exercises already.)  Powers of i;  Complex Plane; Adding & Subtracting Complex Numbers; Absolute Value of Complex Numbers;  Multiplying Complex Numbers; Dividing Complex Numbers.  These are listed in rough order of how difficult they are; all of them except dividing should be fairly straightforward.  After these are done, watch this video to remind you about discriminant of a quadratic equation and this one on Complex Roots for Quadratic Equations.

Integrated Math 3 Assignments – Mar. 12

• There is a short page about when a product is positive, and when it is negative.  Do this at the start of class.
• There are four more advanced problems and people have been assigned to four groups to complete these.  Each group only has to complete one paper (you can put the sticky note with your group members on top) but you need to have a very complete answer.  Show all your work, explain (with sentences) what you did, and draw diagrams or figures when important.  Turn in your work at the end of class.
• After that is finished, you should work on the Pi-Day assignment (see below.)  Be sure to let the teacher know what your planned Pi-Day activity is, even if you don’t get a chance to do it in class.  Everyone has to do something for Thursday.

Advanced Functions Work – Mar 12

The main assignment is a chance to earn extra points for the probability test.  You should try to finish this problem set and turn it in before class is over.

After that is finished, you should work on the Pi-Day assignment (see below.)  Be sure to let the teacher know what your planned Pi-Day activity is, even if you don’t get a chance to do it in class.

Pi-Day Assignments

You must choose one of the following topics.  You must turn in a description of your choice at the end of class Tuesday, and the work will be presented during the last 40 minutes of class on π-Day (Thursday, March 14):

• Prepare a poster about π.  The poster could be about the history of π (how it was calculated, when it was discovered, etc); different places in math and science where π is used; the primary geometric definitions of π, with diagrams to demonstrate; or another idea of your choice.
• Write a paper about π.  The topics discussed above are all good choices.  Another idea would be explaining how π is calculated, both ancient methods and modern methods that allow the computation of millions of digits (or more).  A good poster or paper will earn the maximum number of points.
• Write a piem.  Making it personal, and tasteful, will be the best way to prove you didn’t copy it from somewhere.  Memorizing a previously published piem, and using it to compete in the π-memorizing contest, would also count.  You could come up with multiple different examples, or even use them to make a poster or paper.
• memorize π to as many digits as possible (minimum of 20).  This is a minimal credit assignment, but the winner will get extra credit.  I recommend choosing another topic as well, especially since you have time in class to work on this.
  

These assignments are required, but successful efforts will count as extra-credit (not just regular assignments) on the third nine-weeks grade.

Int. Math 3 – Feb 26 – Practicing Linear Programming

Follow the linear programming steps as listed in class Monday – list your results from each step:

1. Define the variables
2. Write constraint inequalities
3. Graph the constraint inequalities and find the feasible region
4. Find the corner points of the feasible region
5. Write the objective function equation
6. Determine which of the points from step 4 optimizes the objective

Which problems to do (note: the first two for each group are closely related):

• Brooke, Ethan, Leila – #6 (p.146) & #9 (p.148); #13, p.149
• Michaela, Lauren, Laiken – #7 (p.146) & #10 (p.148); #14, p.149
• Jacob, Molesh, Victoria- #8 (p.147) & #11 (p.148); #13, p.149
• Marisol, Savanna, Britney, Hannah- #6 (p.146) & #9 (p.148); #14, p.149
• Casey, Lindsey, Sendi, Yesenia – #7 (p.146) & #10 (p.148); #13, p.149

Homework:  Check Your Understanding on page 136-137 and page 142-143.

Advanced Functions – Feb 26 – Standard Deviations

In the purple books, we are doing the lesson on Normal Distribuitions (begins on p.236).  You may want to read pp.236-237.  The assignment for today is questions 1-5, on pages 238-241.  Working in your current groups, you should take turns reading the questions so and making sure everyone understands the task.

Question 1 asks you to estimate the mean and standard deviation based on histogram.  It is very easy and should be completed very quickly.  Question 2 asks you to estimate median and standard deviation (the mean is given).  It also asks you to mark important points above and below the mean on a copy of the graph.  

It is important to realize that with the exception of the scale on each axis, every normal distribution could have exactly the same probability distribution graph.  We have made a sample of this graph in class and it is still on the board.  Use this in answering questions 3-5.

Homework:  Complete Check Your Understanding on page 242.  Also do the Khan Academy exercise Exploring Standard Deviation.  This exercise involves moving points around to change the standard deviation of a data set.