A New Year For Math

A new school year typically means a new teacher, new schedule, or new classmates. For me it typically involves raising difficulty in math. So, I'm just going to share some miscellaneous math stuff I've been thinking about all summer!

Pi, 3.14159265… is the ratio of the circumference to the diameter of a circle. Pi is used to find the volume of cones and spheres. It is also used for the area of a circle, but who has time for all that beginner stuff? So, let's skip to the advanced stuff.

The volume of a sphere is 4/3πr³. This formula may confuse you, but it's actually very simple. If the radius is 2, we then solve the exponent, so 2³=8. This now gives us 4/3π(8), then you multiply 8 by pi which gives you about 25.13. Then it gives you 4/3(25.13), or (4 × 25.13) / 3. If you calculate this, you'll find the volume is about 33.51 cubic units.

Algebra, Algebra, Algebra, Algebra, Algeb… It sounds like a nightmare waiting to be put to rest, but it really isn't that bad. Let's do some equations; the first few are going to be easy, but they are going to progress. Now let me get the math started.

4x=12+x, this equation is quite simple. For the new 6th Graders (Welcome to CCMS), I'm going to teach you the simplest thing to know for this. Read the problem as words: "4 times something is equal to 12 plus something." This really helps you soak in the meaning of the equation. Another thing you need to know, especially for this kind of question, is substitution. Let's try substituting numbers in: 4(1)≠(12+1), 4(2)≠(12+2), 4(3)≠(12+3), 4(4)=(12+4), or 16=16.

5x+3y=4 given x=4y+2 and y=4x-6. (Just a reminder, headaches do occur during hard mathematical situations, so don't worry or give up). So there are two ways you could solve this: solve using x or solve using y. Let's substitute y into 5x+3y=4 first: 5x+3(4x-6)=4. Simplify to get 5x+12x-18=4, or 17x-18=4. First add 18 to both sides: 17x=22, so x = 22/17 ≈ 1.29. Now we can solve for y using y = 4x - 6: y = 4(22/17) - 6 = 88/17 - 102/17 = -14/17 ≈ -0.82. Alternatively, substituting x into the first equation yields 5(4y+2)+3y=4, leading to 20y+10+3y=4 or 23y+10=4. Subtracting 10 from both sides gives 23y=-6, so y = -6/23 ≈ -0.26. Last year I only scratched the surface of algebra; this year I'm making a math return, so be prepared for some systems of equations and my biggest fear… Scientific Notation :(.