IBHL Mathematics 2005-2006
Note:  The IBHL Math exams will be given on three days in May.     Paper 1 on May 3, Paper 2 on May 4, Paper 3 on May 15.  Note:  The AP Calc BC exam will be given on May 3.

Welcome to our web page. 

The IBHL curriculum can be found at:
http://www.mrsantowski.com/IBHLY1.htm
HERE IS A GREAT WEBPAGE WITH LOTS OF LINKS FOR EXTRA HELP: [cursor down to click on a link] http://mrsantowski.tripod.com/Linksb.htm#top
Here are Jonathan Hsu's IBHL notes:  http://homepage.mac.com/stray/ib/maths/index.html
You can contact Ms. McCleary via e-mail
denise.mccleary at  bvsd.org (sorry, due to SPAM, I prefer to not have actual email addresses on these pages. You'll have to type this email address manually - replace " at " with @. )

Ms. McCleary’s office is located at the back of Room 222.   She is available for help during 3rd, 4th,  and 8th period and during the common lunches on Block days.   Please be sure to let her know you are coming since there are other classes that meet in Room 222.  Ms. McCleary may be available after school.

DATE
TOPIC OR ASSIGNMENT
STATSTest 2.4 stats:  mean = 103%, median = 105%  Enough said.
REVIEWLines and plane review
Click here for my notes
REVIEWVector review
Click here for notes
Here is another set of notes:   http://homepage.mac.com/stray/ib/maths/vectors.pdf
3/24We finished Discrete Math.  Please do the odds in the first Discrete Review.
For more on the Chinese Postman Program see:  http://people.bath.ac.uk/tjs20/introduction.htm
For more on TSP see:  http://www.tsp.gatech.edu/index.html
3/23Weighted graphs
Click HERE for the notes
3/21Trees, Spanning Trees, Minimum Spanning Trees
Here is a nice website for spanning trees:  http://www.people.vcu.edu/~gasmerom/MAT131/mst.html
3/20Planar graphs and introduction to trees [thank you, Arthur for your great scupture]
Here is a great website for planar graphs:  http://www.math.lsa.umich.edu/mmss/coursesONLINE/graph/graph5/index.html
Daniel, is this your solution?

image

3/17Hamiltonian graphs
TEST 2.4 is due next FRIDAY!
3/16Eulerian graphs [circuits, traversable]
3/14Happy Pi Day!  To see the giant Pi drop:  http://mathematicianspictures.com/PI/PI-DAY.htm
3/13adjacency matrices for mutli-graphs, Konisberg Bridge Problem, Euler stuff [paths, trails, walks, circuits]
3/10isomorphisms and adjacency matrices
3/9Good Calc Review!
3/8Even more graph theory - must be a theme here!  Handshaking Lemma, Pigeonhole Principle, Graph Isomorphism
3/6More graph theory - bipartite graphs
3/2introduction to graph theory  
Here's a great website with graph theory info:  http://mathworld.wolfram.com/topics/GraphTheory.html
2/28divisibility and Fermat's Little theorem - here is  another look at Fermat's little theorem:  http://mathworld.wolfram.com/FermatsLittleTheorem.html
2/27divisibility - here are some nice "American" explanation of the divisibility rules:  http://mathforum.org/k12/mathtips/ward.html
http://mathforum.org/k12/mathtips/division.tips.html
http://www.learner.org/channel/courses/learningmath/number/session5/part_b/eleven.html
2/24Test 2.2  results:  
mean = 89.5%; Q = 85%; median = 94%; Q3 = 96%  Good job!
2/23The non-Chinese remainder way to solve [the parametric way]
2/21 The Chinese Remainder theorem  Here is a nice website with more info:
http://www.math.hawaii.edu/~lee/courses/Chinese.ps
Test on Friday!  Natasha, thanks for your Asian pride!  Trevor, you are now an honorary member of Team Asia!
2/16solving linear congruence equations - Test alert - test next Friday
2/14lots of congruent modulo problems   Please have your homework as well as your review work for the next class.   Thank you
Here is an okay webpage on modular arithmetic:  http://www.math.rutgers.edu/~erowland/modulararithmetic.html
2/13linear congruences [congruent modulo]
2/10
quiz results to be posted later
Congratulations to Sarah and Joe who are at All State Orchestra
2/9
primes; review assignments = 11A,12A?  quiz tomorrow
2/7
quiz on Friday over Euclid's division algorithm, linear diophantine equations, logarithmic stuff 
finished lde and started primes
2/6
more linear diophantine equations - moo!
Hey, I found a linear diophantine equation solver on-line. Check it out:  http://www.math.uwaterloo.ca/~snburris/htdocs/linear.html
2/3
linear diophantine equations - Happy Birthday, Sarah!  Nothing like a good birthday skip!
2/2
gcd, lcm, Euclidian Division Algorithm
1/31
different bases -binary, ternary, etc.
1/30
divisibility stuff - Euclid's division algorithm
A plethora of proofs:
Here is a link for Euclid's division algorithm:  http://www.cut-the-knot.org/blue/Euclid.shtml
Here is a totally awesome website that has some of the IBHL Discrete topics nicely written out.  You should give it a whirl:  http://en.wikibooks.org/wiki/Discrete_mathematics:Number_theory
Here are some more proofs to ponder:  http://en.wikibooks.org/wiki/High_School_Mathematics_Extensions/Mathematical_proofs
1/27
the Fibonacci Sequence and more proofs  Here is a link to the Fibonacci Quarterly:  http://www.engineering.sdstate.edu/~fib/
1/26
Proofs and lots of them.  Here is a webpage with my favorite proof by contradiction:  http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html
review assignment 4A

Exam Statistics:  IBHL Mathematics
Mean = 96%; Q1 = 90%; Median = 92%; Q3 = 105% Great Job!
1/10
differential equations
1/9
integration by parts
1/6
the rest of special substitutions
1/5
more "special" substitutions
1/4
integrating with trig substitution
for the great calculus review website see:  http://www.frapanthers.com/teachers/zab/
There is BC content
1/3/06
all of the IAs that I have are graded. They were very impressive except for the "ghost" part!  Here is a link to similar data for Boulder:  http://bcn.boulder.co.us/basin/
12/19
IA due today ;  Review Assignment
12/13& 12/15
IA workday   The statistics on our test on Statistics - median = 100%  Enough said.
12/12
Internal assessment #2  Here's a link about the Nolichucky River:  http://www.usaraft.com/nolichucky.htm
 For an explanation on r^2 and what it means, go to http://www.physics.csbsju.edu/stats/least_squares.html
12/9
Does Elvis know calculus? [worksheet]   Here's a link about Elvis:  http://www.sciencenews.org/articles/20030607/mathtrek.asp
12/8
Stat Test plus 
review assignment 15B page 397
12/5&6
stat review - test on block day
12/2
z distribution and  more cool stuff on our TIs - test next Thursday
12/1
Normal pdf - cool stuff on our TIs    Test next Thursday
11/29
More continuous PDF  -a good chance to review your basic calculus
11/28
Poisson distribution and continuous probability density function
11/25
After five grueling days, your internal assessments are graded.  Overall, they were impressive.
11/17
more statistical fun!   Special E(X) and Var(x) properties  - MARSUPIAL, MARSUPIAL, MARSUPIAL!  Your I.A.  looks great so far.  I will endeavor to grade them all next week.  IA party tomorrow!
11/15
Internal assessment work day - it is due on THURSDAY
11/14
Expected value and the mean and standard deviation for a population  Here is another on-line graphing calculator:
http://www.coolmath.com/graphit/
and another:  http://graphingcalc.hmco.com:8080/calculator/calc.html
11/10
Internal assessment - Type I   DUE NOVEMBER 17th 
Here is a website with a TI emulator
To download the emulator, create a folder called TI83. Then download each of the following files into the folder.

http://www.bigskies.com/TI83/TI83.HLP
http://www.bigskies.com/TI83/TICALC.EXE
http://www.bigskies.com/TI83/TICALCLG.FON
http://www.bigskies.com/TI83/TICALCSM.FON

To run the Windows emulator, just click on the EXE file in the folder.  If you have any problems, please drop me a note.

I am less familiar with the Mac emulator because I don't used Macs.  The emulator is contained in the archive file, ti83.sit.

http://www.bigskies.com/TI83/TI83.SIT

After the file is downloaded, double-click on the file to expand the archive. Macintosh users may need to use an additional tool, such as StuffIt(R) Expander, to expand the archive. StuffIt(R) Expander is available FREE from Aladdin Systems. A file named "readme" is included with the emulator. It contains system requirements and starting instructions.


11/8
probability with functions
11/7
Discrete Random Variables [chapter 30]
11/4
our second set of paper two problems
11/3
sigma and variance  REVIEW ASSIGNMENT 18A  Note:  "shape" means "positively skewed", etc.
11/1
the normal distribution
10/31
variance and standard deviation
10/28
finish paper two problems
10/27
matrices and our first paper two problems
10/25
box and whiskers plot, five item stat summary, and percentiles 
10/24
grouped data and cumulative frequency graph
10/21
ungrouped data
10/20
intro to statistics, review assignment = 14a
10/18
Quiz on probability
10/17
reviewed for tomorrow's quiz
10/14
Monty Hall Problem  Here is a webpage where you can simulate the problem:  http://math.ucsd.edu/~crypto/Monty/monty.html
10/13
Binomial [Bernoulli] trials  [binompdf (n, p, x)  Review Assignment 19A  Next quiz on Tuesday 10/18/05
Here is a netball webpage:  http://www.england-netball.co.uk/
10/11
Compound Probability, Independent events, and Bayes' Theorem
10/6
Many thanks to Jenni for bringing in her beads so that we could visualize circular permutations.  Review 9A for this week's review assignment.
10/4
permutations with and without repeats and circular permutations  [chapter nine in our new book]
10/3
A boatload of complex number problems
9/30
The conjugate root theorem and the end of complex numbers!  Yay!
9/29
The roots of unity [and how to graph a parametric function]  Great job on Test #2!
Our test statistics:  mean = 89.7%, Q1  = 82%, median = 93%, Q3 = 98%  
9/27
Our second IBHL test.  So far I have looked at the proofs and they look pretty darn good!
9/26
Review for tomorrow's test.  Please study
9/23
DeMoivre's Theorem  - Reminder: our next test will be on Tuesday, 9/27/05
9/22
Math induction and comples numbers - Reminder:  our next test will be on Tuesday, 9/27/05
9/20
More Complex number stuff - converting to polar and properties of mod(z) and arg(z)
Test One results are posted at Infinite Campus.  Here are the statistics for n = 30 [one person needs to take the test]
mean = 87%, Q1 = 77%, median = 93.5%, Q3 = 99%    18 out of 30 people earned A's  Nice job!
9/17
Ms. McCleary's father passed away this morning.  She will need to miss a few days of class.  Please respect the substitute teacher while she is gone.
9/20
In case I am gone:  pages 421-422  Review 16A  #1, 4, 5, 6 plus Review 16B #1, 2, 5, 6, 7, 9, 11
9/16
Complex numbers - arg(z), mod(z), "special" keys on our TI for complex numbers, z*, operations with complex numbers
9/15
Finished proof by mathematical induction.  Our first review assignment was page 228 -Review 10C
9/13/05
The pirates have relinquished our textbooks!  All hail, Dr. Wei and Ms. Dings!  Oh yeah, we had a quiz today.  I will post results once I have graded them.
9/12/05
More proof by Mathematical Induction  Reminder Quiz tomorrow
9/9/05
Proof by Mathematical Induction - hence, hence, hence, ...  Reminder:  Quiz next Tuesday on arithmetic and geometric sequences and series and the Binomial Theorem
9/8/05
Binomial Theorem  Reminder:  Quiz next Tuesday, 9/13/05
9/6/05
The end of arithmetic and geometric sequences and series.  Reminder: Quiz next Tuesday, 9/13/05
9/2/05
Koch Snowflake and geometric sequences and series
9/1/05
Happy September!   Finish arithmetic sequences and the Koch snowflake.  Here's a cool webpage where you can generate Koch snowflakes.  http://math.rice.edu/~lanius/frac/koch/koch.html
8/30/05
Arithmetic sequences and series on our TI calculators
8/29/05
Arithmetic sequences and series