1. HELPFUL LEARNING TOOLS FOR YOUNG MATHEMATICIANS tutorials and problems kirsten young

2. 1A. PREALGEBRA TOPICS http://www.aaamath.com/fra.html Find out how to do basically anything with fractions. Very easy to understand and a wide range of topics to explore. http://www.math.umn.edu/~garrett/crypto/a01/Euclid.html Will use Euclidean algorithm and show all the steps involved in solving for the GCD. http://www.math.sc.edu/~sumner/numbertheory/euclidean/euclidean.html Enter anything you know into the blanks (there are spaces for two numbers, the GCD, and the LCM) and it will compute the missing ones, with a mathematical explanation for how the conclusion was reached. However, it is important to already know HOW the Euclidean algorithm already works.

3. 1B. MEASURING ANGLES http://mathworld.wolfram.com/30-60-90Triangle.html Shows what a 30-60-90 triangle is and has formulas to determine the area, side lengths, inradius, and circumradius. Fairly straightforward and easy to understand. http://www.mathsisfun.com/geometry/complementary-angles.html Extremely easy site to understand complementary angles, with a link to view supplementary angles. http://www.regentsprep.org/Regents/math/angles/Lparallel.htm Easy to understand how angles formed by parallel lines are related.

4. 1C. ELEMENTARY TRIG http://www.sosmath.com/trig/Trig5/trig5/trig5.html A fantastic table of any sort of trig identity one could possibly need, including sum-to- product formulas and product-to-sum formulas. http://people.hofstra.edu/Stefan_Waner/trig/trig2.html This site shows how to get the 6 basic trig functions, whether in a circle, triangle, or as a function of the other ones.

5. 1D. ROOTS OF QUADRATICS AND POLYNOMIALS http://www.sosmath.com/algebra/quadraticeq/root/root.html Very easy to understand the basics of what roots of quadratic equations are. http://www.purplemath.com/modules/synthdiv.htm In-depth explanation of synthetic division with some examples. However, the explanation is a little long-winded and somewhat confusing if the student has no prior knowledge of dividing polynomials. http://www.purplemath.com/modules/fcnnot.htm Short little tutorial about function notation, then lets the student try their hand at a problem.

6. 2A. LINEAR EQUATIONS IN ONE UNKOWN http://www.webmath.com/solver2.html This site is AMAZING! It shows how to solve linear equations. You can have it just solve the equation OR show all the steps involved. http://www.analyzemath.com/Linear_Inequalities/Linear_Inequalities_Tutor.html Shows how to solve linear inequalities, and has practice problems as it teaches. Easy to understand

7. 2B. FAMILIAR GEOMETRIC FIGURES, CONGRUENCE, AND SIMILARITY http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Altitudes-Medians-and-Angle- Bisectors.topicArticleId-18851,articleId-18787.html Even though it IS Cliffsnotes, it explains the topic of medians, altitudes, and angle bisectors well. Plus, there are some practice problems. http://www.arcytech.org/java/pythagoras/ This is a really cool site that lets the student figure out Pythagoras’s Theorem. http://www.mathleague.com/help/ratio/ratio.htm This is the Math League’s site for learning about ratios, rates, and proportion. It’s built for the student so it’s very straightforward and easy to understand. http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut18_ineq.htm This is an amazing learning tool for inequalities

8. 2C. TRIGONOMETRY http://www.ping.be/~ping1339/gonio.htm This is a great site for ANYTHING trig related. Click on the links and they explain the topic well. http://en.wikipedia.org/wiki/Trigonometric_identity#Power-reduction_formulae YES, it’s Wikipedia. However, it shows all the power reduction formulas, plus a lot of other useful trig functions.

9. 2D. ANALYTIC GEOMETRY OF STRAIGHT LINES AND CIRCLES http://www.tpub.com/math2/6.htm Good tool for learning about line forms. http://mathworld.wolfram.com/Circle-LineIntersection.html Extremely in-depth explanation about circle/line intersections. Also provides links to circle/circle intersections. This site is more difficult to understand, so it’s better used by older and more knowledgeable students.

10. 3A. SYSTEMS OF LINEAR EQUATIONS IN 2 OR 3 VARIABLES http://www.sosmath.com/soe/SE2001/SE2001.html Shows how to solve systems of equations with two variables. It gives examples of substitution, elimination, matrices, and graphing. It’s a fairly straightforward sight and is good for younger learners who aren’t sure of themselves yet. http://www.ping.be/~ping1339/determ.htm Extremely in-depth and effective tool for learning about any sort of determinant. This site has links to all sorts of topics on determinants, from the determinant of a 1 x 1 matrix to theories and transposition of matrices.

11. 3B. QUADRILATERALS AND POLYGONS http://planetmath.org/encyclopedia/PtolemysTheorem.html This site provides and easy-to-understand look at Ptolemy’s Theorem. It includes the formulas for a cyclic and non-cyclic polygon. http://www.mathleague.com/help/geometry/polygons.htm This is a very basic site for understanding all sorts of polygons. I recommend it for younger learners

12. 3C. TRIGONOMETRY http://mathforum.org/library/drmath/sets/select/dm_demoivre.html This site explains and has problems about De Moivre’s theorem. It’s a little more complex to understand, so it’s recommended for more advanced students. http://www.acts.tinet.ie/inversetrig.functions_668.html Very basic explanation of the inverse trig functions and what they mean. Good tool for young learners

13. 3D. EXPONENTS AND LOGARITHMS http://abacus.bates.edu/acad/acad_support/msw/exps_and_logs.pdf Basic properties of exponents and logs. Good, easy to understand. http://www.ccrnp.ncifcrf.gov/~toms/paper/primer/latex/node2.html Very in-depth site about changing the base of logs. It starts with the basics of logarithms then goes into base changing. Very informative, and good for most older learners.

14. 4A. ALGEBRAIC MANIPULATION http://www.jamesbrennan.org/algebra/polynomials/factoring_polynomials.htm Basics of factoring, from simple cases to perfect squares. Good for younger students. http://rvgs.k12.va.us/faculty/elayne/SOL%20Prep%20Journal/2000- 2001%20SOL%20Prep%20Journal%20Files/2000-2001%20finished%20files/AII7.PDF Very interesting site about rational expressions and manipulations of them. It includes calculator keys to show how to use your graphing calculator in solving the problems.

15. 4B. CIRCLES http://mathrocks.thebernas.net/IntMath3/Circles/Pages/PropCrcl.htm This site is really good for explaining certain properties of circles. It includes diagrams for easier understanding. http://www.mathematicshelpcentral.com/lecture_notes/college_geometry_folder/circles.h tm Table of all sorts of definitions of circle related terms. It also has information on tangents and angle measurement.

16. 4C. MISCELLANEOUS TOPICS http://archives.math.utk.edu/visual.calculus/6/index.html This site is very informative on sequences and series. Word of caution: as the site is called “Visual Calculus”, it would benefit the student if he or she has some prior calculus background, as it is quite advanced. http://library.thinkquest.org/C0110248/algebra/apgpintro.htm This is a much easier-to-understand tutorial on sequences and series. http://www.purplemath.com/modules/binomial.htm This is a great, easy to understand site about the binomial theorem. It also contains a link to factorial notation.

17. 4D. ANALYTIC GEOMETRY OF CONIC SECTIONS http://math2.org/math/algebra/conics.htm Conic basics. It shows how the conics are derived (through a 3-D picture), defenitions of conics, and formulas for almost anything related to the conics. http://www.krellinst.org/UCES/archive/resources/conics/ Really cool learning tool for conics! You can learn the basics about the conics, then test how well you know them using exercises for each conic.

18. 5A. PUZZLE PROBLEMS http://www.syvum.com/teasers/ Some basic brain teasers and math puzzles. You can actually check your answer and ask for a hint as you solve them. It has different types of problems from easy to difficult. http://perplexus.info/ Interesting site that has different kinds of problems to test out, from logic problems to number problems to paradoxes. More advanced than the previous one.

19. 5B. AREAS, PERIMETERS, AND VOLUMES http://en.wikipedia.org/wiki/Heron's_formula Basic understanding of Heron’s formula. It has the history and a proof of the formula as well. http://math2.org/math/geometry/areasvols.htm Basic site for areas and volumes. Lots of formulas and diagrams.

20. 5C. COUNTING AND PROBABILITY http://www.regentsprep.org/Regents/math/permut/Lperm.htm Extremely bare-bones basics of permutations. Good for young students http://www.themathpage.com/aPreCalc/permutations-combinations.htm More in-depth explanation of permutations and combinations with good example problems.

21. BASIC PROBLEM SITES WITH LINKS TO SPECIALIZED SITES these sites are not necessarily math contest related, but they do provide a general idea of some sorts of problems http://www.svsu.edu/mathsci-center/?doc_id=4072 http://www.resourcehelp.com/edu_math.htm http://www.ashland.k12.ky.us/resources/math.htm http://edweb.tusd.k12.az.us/bowmang/stdntpg.html

22. http://www.internet4classrooms.com/eoc_algebra2.htm This site has interactive algebra problems and lets the student check his or her answer http://www.mathsnet.net/interactive.html Another interactive problem site, although it is a bit more confusing to navigate. http://www.wade.org/mathemat.htm Good site that links you up with other tutorials and problem sites. You can also do a search by topic. http://www.math.unb.ca/apics.papers/ This site has a lot of great math contest practice problems, but there are no answers www.math.uncc.edu/~hbreiter/problems/UNCC.html This is the University of North Carolina Charlotte’s High School Math Contest page, however, it’s only compatible with higher forms of Adobe Reader. http://www.mathleague.com/contests.htm The Math League’s website has a practice contest and solutions

23. http://www.artofproblemsolving.com/Resources/AoPS_R_Problems.php This cool site has links for beginner, intermediate, and advanced math problems. http://www.math.uiuc.edu/~hildebr/putnam/undergradproblems.html The UIUC’s undergrad math contest problem page, problems and solutions http://www.math.sc.edu/contest/problems.html The University of South Carolina’s high school math contest page with problems, answer keys, and solutions http://mathres.kevius.com/problem.html This site has a lot of cool problem links for more advanced topics.

24. http://www.webmath.com/ Great basic site, it has links to all sorts of topics or you can search for a topic http://olympiads.win.tue.nl/imo/books.html Recommended readings for math students http://staff.imsa.edu/math/journal/volume4/articles/NoahSheets.pdf The Noah Sheets http://mathworld.wolfram.com/ One of my favorite sites. Wolfram’s Mathworld has hundreds of topics ranging from easy algebra to calculus. It’s more challenging to understand than some of these sites, but it’s a great resource for advanced students and teachers. http://math.scranton.edu/monks/courses/ProblemSolving/HighSchoolPlaybook.pdf A wonderful packet for math preparation. High level of mathematics