Can’t believe I’ve had this website up and running for a full year now! With the help of Google Analytics, I’ve been looking at plots of different traffic data and I thought I would share with you two that are most telling.

This first shows a plot of unique website users since last November, while the second shows unique downloads (mostly of the .pdfs of my Number Sense practice materials) during the same time period. (Note: I only have been keeping track of *that* information since mid-July — shout-out to my buddy Jerod for helping me out with that.)

As you can see, the exponential growth is pretty evident which validates what I’ve thought all along: students and teachers are thirsty for free practice material to help their students succeed in STEM-fields.

Anyway, I plan on helping out where I can in the coming years and have some exciting things I want to put together! Here’s to another fruitful year!

Hi! I am a senior at Boerne High School, and I had a quick question about #49 on your Number Sense Exam 036, 8/17/2017. The question is : If x + y = −2 and xy = 5, then x^3 + y^3 = _____.

After messing with (x+y)(x^2 – 2xy + y^2) = x^3 + y^3, I came up with the following general solution:

x + y = a

xy = b

x^3 + y^3 = a(-3b + a^2)

This seems to work fine, but I’m wondering if you would go about solving the problem the same way. As a side note, many thanks for your willingness to distribute free and relevant NS materials! It is greatly appreciated.

Yep, that is how I would solve it // I would make similar relationships with x^4 + y^4; x^5+x^5; etc…

The “formulas” stem from the binomial expansion of (x+y)^3, (x+y)^4, etc…, so that will help you derive them more easily.

For example: (x+y)^3 = x^3+3x^2y+3xy^2+y^3 = x^3 + y^3 + 3xy(x+y)

After that, it’s just a memorization exercise.

Gotcha. Thanks again!

Thank you so much Bryan for generously sharing your amazing math knowledge and number sense tips and tricks! They are super helpful!