This Week's Work : Week 9 -- for Inquisitive Young Mathletes

Part 1:
See below for links:
They are all related to dimensional change and similar polygons.

Dimensional change questions I 

Dimensional change questions II 
 
Dimensional change questions III : Similar Triangles 

Par II:
Tangent Segments and Similar Triangles from Mathcounts Mini 

If you have more time, download the extra word problems to see if you can solve them at
reasonable speed and accuracy.

Online timed test and problem of the week will be sent out through e-mail.
Time: 40  minutes without a calculator.

The Monty Hall Problem explained

This Week's Work : Week 8 -- for Inquisitive Young Mathletes

Assignment 1:
Using Algebra and Number Sense as Shortcuts from Mathcounts Mini

Watch the video and work on the activity sheet below the video on the same link for more practices.

 Also, review the following:
\(x^{2}-y^{2}=\left( x+y\right) \left( x-y\right)\) \(\left( x+y\right) ^{2}=x^{2}+2xy+y^{2}\) \(\left( x-y\right) ^{2}=x^{2}-2xy+y^{2}\) \(\left( x+y\right) ^{2}-2xy =x^{2}+ y^{2}\)
\(\left( x-y\right) ^{2}+ 2xy =x^{2}+y^{2}\)
\(\left( x+y\right) ^{2}-4xy =\left( x-y\right) ^{2}\)

Assignment 2:

Pascal's Triangle  from Math is Fun

Pascal's Triangle and Its Patterns

Assignment 3:
It'll be sent through e-mail.
Happy problem solving !!

This Week's Work : Week 6 and 7 Review -- for Inquisitive Young Mathletes

Watch Joint Proportion from Art of Problem Solving 

Spend some time pondering on "Work" word problems from Purple Math. 
These are some very standard word problems you'll encounter in competition math.  

Review --
dimensional change and probability links from previous weeks.  

More practices on inverse and direct relation 

From Regents Exam Prep 
Link I 

Link II

New concepts:

Height to the hypotenuse
How many ways to arrange the word "banana"? (with elements repeating)
Probability that two of the 3 friends were born on the same week day.

Question : If you can earn 0, 1, 3, 7 or 10 points with each shot and each person has three chances, how many scores can't be made? 

Note:
Percentage increase (don't forget to minus the original 100% or 1) is very different from at what percent will it return to the original size or what is the size compared to the original.

This Week's Work : Week 5 -- for Inquisitive Young Mathletes

Evan (a 5th grader in PA) 's Problem of the Week: 
A man notices a sign in Shop-a-Lot that says: "All prices are marked 25% off today only!" He decides to buy a shirt that costs $65.12 before the discount. He then uses a $16 gift certificate and the clerk applies 12% sales tax. What is the final cost of the shirt after all the steps are applied? Express your answer to the nearest hundredth. 
 
Solution: 
When there is a discount that is 25% off, the original price is going to be 75% times the original price. Therefore, 75% of $65.12 is $48.84. Next, subtracting $16, we obtain $32.84. Finally, applying 12% sales tax, we get $32.84 x 112% (since original price is added to the sales tax "price") which is $36.7808. This rounded to the nearest hundredth is $36.78.

Assignment 1: 

Painted Cube Problems

Visualization of the Painted Cube Problems 

It's more fun if you dig out Legos or Unit Cubes and just build some cubes (and later rectangular prism) 
and spend some time observing how it works. 

Assignment 2:

Review special right triangle, Pythagorean triples, theorem :

30-60-90 , 45-45-90 special right triangle angle ratios

Dimensional Change

Inscribed and Circumscribed Circle Radius of an Equilateral Triangle

This Week's Work : Week 4 -- for Inquisitive Young Mathleges

First of all, problem of the week from Evan, a 5th grader:
A man notices a sign in Shop-a-Lot that says: "All prices are marked 25% off today only!" He decides to buy a shirt that costs $65.12 before the discount. He then uses a $16 gift certificate and the clerk applies 12% sales tax. What is the final cost of the shirt after all the steps are applied? Express your answer to the nearest hundredth. 

This week, we'll learn two very common sequences : arithmetic and geometric sequences.
There are quite a few similarities between these two types and they are closely linked to ratio, proportion
so just watch the videos and play around/generate a few/ponder on those sequences. I don't expect you to learn them in just one week.

Notes from Regents Exam Prep: Arithmetic and Geometric Sequences and Series

From Mthcounts Mini:

Easier concepts:

Sequences

Arithmetic sequence/determine the nth term

Arithmetic and geometric sequences

Harder concepts:

Relationship between arithmetic sequences, mean and median

Sequences, series and patterns

From my blog : 
Some special arithmetic sequences and the easier way to find their sum

Write some notes of the most important features of the arithmetic sequence.
The best note will be posted here to share with other students.
Be creative !!