This Week's Work : Week 14 - for Inquisitive Young Mathletes

Venn Diagram explained from AoPS : learn the two set and three set examples

Principle of Inclusion-Exclusion from AoPS: again, two set and three set examples

Video on Venn Diagrams with Two categories from AoPS

Video on Venn Diagrams with Three categories from AoPS

Word problems on Venn diagrams medium level (instant feedback)

Word problems on Venn diagrams medium hard level (instant feedback)

The common error for most students (especially boys, oh oh) is arithmetic error.

Make sure you line the category with specific number given right and check your math.

Chicken, rabbit algebra speed test : aim for less than 5 minutes. No calculator, please !!

Motivation, Not IQ, Matters Most For Learning New Math Skills from Time Magazine

Power of Ten Video

This Week's Work : Week 13 - for Inquisitive Young Mathletes

First, review target level questions you got wrong last week and practice counting systematically.

Right triangle inscribed in a circle proof from Khan Academy

Review 30-60-90 special right triangle from AOPS and practice getting the two legs/hypotenuse fast.

Review 45-45-90 special right triangle from AOPS

The harder questions are the ones when given the length to the 60 degree of the 30-60-90 special right triangle or
the length to the 90 degree of the 45-45-90 special right triangle so make sure you can get them fast and right.

practice here  (instant feedback)

more practices (instant feedback)

See if you can solve all these questions as they are countdown problems.
(hint : lots of Pythagorean triples or applicable special right triangle ratio concept)

from Regents prep (high school level)

Videos/articles on math for this week:

Fractals: Hunting the Hidden Dimension

 

Nature by numbers

 

What Is It About Bees And Hexagons?

This Week's Work : Week 12 -- for Inquisitive Young Mathletes

Link to the online timed test on questions you mostly got wrong or not fast enough. 
(sent through e-mail)

Common Pythagorean Triples: 
3, 4, 5 and its derivatives 
5, 12, 13 
8, 15, 17 
7, 24, 25 (at least these for SAT I and II) 

9, 40, 41, (the rest for state and Nationals, so we'll learn them later)
11, 60, 61
12, 35, 37
13, 84, 85
20, 21, 29

Shoe string method in finding the area of any polygon

Heron's formula in finding the area of a triangle.

Don't mix up the "s" with the other "S" of finding

the area of an equilateral triangle -- proof and formula (You can also use 30-60-90 special right
triangle to get that.)
or
the area of a regular hexagon

In Heron's case, "s" stands for half of the perimeter.

Besides, I've noticed most of the questions, when given the sides, are best solved by using Pythagorean triples, especially in sprint round questions, so make sure to actively evaluate the question(s) at hand and use the most efficient strategy.

Here is the link to 2003 chapter #29 that most of you got wrong:

You don't need to use complementary counting for that specific question since it's equal cases either way. Make sure you understand why you need to times 3. (AA_, A_A, and _AA for team A to be chosen two out of three days).

From Mathcounts Mini: Area of irregular polygon

See if you can use shoestring method to get the same answer.
Second half is again on similar triangles, dimensional change and sometimes
Pythagorean triples.

From NOVA : Fractals - Hunting the Hidden Dimension

This Week's Work : Week 11 -- for Inquisitive Young Mathletes

Area of an equilateral triangle

You can also use angle ratio 30-60-90 to prove that; besides, if you times that by 6, you'll get the area of a regular hexagon.

More links on Pascal's Triangle from Art of Problem Solving:

Introducing Pascal's Triangle

Patterns in Pascal's Triangle

Other review links:

From Math is Fun

Pascal's Triangle and Its Patterns

Triangular numbers

Science link :

From NOVA : How Smart Can We Get ?

This Week's Work : Week 10 -- for Inquisitive Young Mathletes

Learn or review : How many zeros?

Learn or review : Special Right Trianlges

From Art of Problem Solving of some triangles:

Isosceles and Equilateral Triangles

Isosceles Right Triangles (45-45-90 degree special right triangles)

30-60-90 Degree Special Right Triangles

Math and Science go hand in hand so watch this fascinating video from NOVA just for inspiration. 

From NOVA: What Will the Future Be Like? 

Have fun problem soling and exploring !!