Math+Experts

General Formulas that you need to know for Scholastic Bowl: Area of a Square= S^2 Area of a Parallelogram and Rhombus= b * h Area of a Triangle= b * h / 2 Area of a Circle= πr^2 Circumference of a Circle= 2πr

Area of a Trapezoid=

Volume of Cube= 6S^2 Volume of a Prism= l * h * w Volume of a Cylinder= πr^2 * h Volume of a Pyramid= b * h * 1/3 Volume of a Cone= 1/3 * πr^2 * h Volume of a Sphere= 4/3 * πr^3
 * The Letters || What they represent ||
 * l || Length ||
 * w || Width ||
 * S || Length of one of the sides ||
 * b || Base ||
 * h || Height ||
 * r || Radius ||

__//**--Perry Lim**//__

Tau - This is a mathematical constant that is equal to 2pi. Many mathematicians think that we should use tau instead of pi. Here is a great video saying why we should use Tau: @http://www.youtube.com/watch?v=jG7vhMMXagQ

__//**Roman Numerals**//__ __//**--Perry**//__
 * I || 1 ||
 * II || 2 ||
 * III || 3 ||
 * IV || 4 ||
 * V || 5 ||
 * VI || 6 ||
 * VII || 7 ||
 * VIII || 8 ||
 * IX || 9 ||
 * X || 10 ||
 * XI || 11 ||
 * XII || 12 ||
 * XIII || 13 ||
 * XIV || 14 ||
 * XV || 15 ||
 * XVI || 16 ||
 * XVII || 17 ||
 * XVIII || 18 ||
 * XIX || 19 ||
 * XX || 20 ||
 * XXX || 30 ||
 * XL || 40 ||
 * L || 50 ||
 * LX || 60 ||
 * LXX || 70 ||
 * LXXX || 80 ||
 * XC || 90 ||
 * C || 100 ||
 * CC || 200 ||
 * CD || 400 ||
 * D || 500 ||
 * DC || 600 ||
 * DCC || 700 ||
 * DCCC || 800 ||
 * CM || 900 ||
 * M || 1000 ||
 * MM || 2000 ||
 * MMI || 2001 ||
 * V || 5,000 ||
 * X || 10,000 ||
 * L || 50,000 ||
 * C || 100,000 ||
 * D || 500,000 ||
 * M || 1,000,000 ||

Here's a list of square numbers and the square roots. NOTE: The square root is the square root of the original number!!!! -Sam Fansler []
 * **number** || **square** || **square root** ||
 * 1 || 1 || 1.000 ||
 * 2 || 4 || 1.414 ||
 * 3 || 9 || 1.732 ||
 * 4 || 16 || 2.000 ||
 * 5 || 25 || 2.236 ||
 * 6 || 36 || 2.449 ||
 * 7 || 49 || 2.646 ||
 * 8 || 64 || 2.828 ||
 * 9 || 81 || 3.000 ||
 * 10 || 100 || 3.162 ||
 * 11 || 121 || 3.317 ||
 * 12 || 144 || 3.464 ||
 * 13 || 169 || 3.606 ||
 * 14 || 196 || 3.742 ||
 * 15 || 225 || 3.873 ||
 * 16 || 256 || 4.000 ||
 * 17 || 289 || 4.123 ||
 * 18 || 324 || 4.243 ||
 * 19 || 361 || 4.359 ||
 * 20 || 400 || 4.472 ||
 * 21 || 441 || 4.583 ||
 * 22 || 484 || 4.690 ||
 * 23 || 529 || 4.796 ||
 * 24 || 576 || 4.899 ||
 * 25 || 625 || 5.000 ||
 * 26 || 676 || 5.099 ||
 * 27 || 729 || 5.196 ||
 * 28 || 784 || 5.292 ||
 * 29 || 841 || 5.385 ||
 * 30 || 900 || 5.477 ||
 * 31 || 961 || 5.568 ||
 * 32 || 1,024 || 5.657 ||
 * 33 || 1,089 || 5.745 ||
 * 34 || 1,156 || 5.831 ||
 * 35 || 1,225 || 5.916 ||
 * 36 || 1,296 || 6.000 ||
 * 37 || 1,369 || 6.083 ||
 * 38 || 1,444 || 6.164 ||
 * 39 || 1,521 || 6.245 ||
 * 40 || 1,600 || 6.325 ||
 * 41 || 1,681 || 6.403 ||
 * 42 || 1,764 || 6.481 ||
 * 43 || 1,849 || 6.557 ||
 * 44 || 1,936 || 6.633 ||
 * 45 || 2,025 || 6.708 ||
 * 46 || 2,116 || 6.782 ||
 * 47 || 2,209 || 6.856 ||
 * 48 || 2,304 || 6.928 ||
 * 49 || 2,401 || 7.000 ||
 * 50 || 2,500 || 7.071 ||
 * 51 || 2,601 || 7.141 ||
 * 52 || 2,704 || 7.211 ||
 * 53 || 2,809 || 7.280 ||
 * 54 || 2,916 || 7.348 ||
 * 55 || 3,025 || 7.416 ||
 * 56 || 3,136 || 7.483 ||
 * 57 || 3,249 || 7.550 ||
 * 58 || 3,364 || 7.616 ||
 * 59 || 3,481 || 7.681 ||
 * 60 || 3,600 || 7.746 ||
 * 61 || 3,721 || 7.810 ||
 * 62 || 3,844 || 7.874 ||
 * 63 || 3,969 || 7.937 ||
 * 64 || 4,096 || 8.000 ||
 * 65 || 4,225 || 8.062 ||
 * 66 || 4,356 || 8.124 ||
 * 67 || 4,489 || 8.185 ||
 * 68 || 4,624 || 8.246 ||
 * 69 || 4,761 || 8.307 ||
 * 70 || 4,900 || 8.367 ||
 * 71 || 5,041 || 8.426 ||
 * 72 || 5,184 || 8.485 ||
 * 73 || 5,329 || 8.544 ||
 * 74 || 5,476 || 8.602 ||
 * 75 || 5,625 || 8.660 ||
 * 76 || 5,776 || 8.718 ||
 * 77 || 5,929 || 8.775 ||
 * 78 || 6,084 || 8.832 ||
 * 79 || 6,241 || 8.888 ||
 * 80 || 6,400 || 8.944 ||
 * 81 || 6,561 || 9.000 ||
 * 82 || 6,724 || 9.055 ||
 * 83 || 6,889 || 9.110 ||
 * 84 || 7,056 || 9.165 ||
 * 85 || 7,225 || 9.220 ||
 * 86 || 7,396 || 9.274 ||
 * 87 || 7,569 || 9.327 ||
 * 88 || 7,744 || 9.381 ||
 * 89 || 7,921 || 9.434 ||
 * 90 || 8,100 || 9.487 ||
 * 91 || 8,281 || 9.539 ||
 * 92 || 8,464 || 9.592 ||
 * 93 || 8,649 || 9.644 ||
 * 94 || 8,836 || 9.695 ||
 * 95 || 9,025 || 9.747 ||
 * 96 || 9,216 || 9.798 ||
 * 97 || 9,409 || 9.849 ||
 * 98 || 9,604 || 9.899 ||
 * 99 || 9,801 || 9.950 ||
 * 100 || 10,000 || 10.000 ||

The Fibonacci Sequence
Most of you will ask "WHAT THE HECK IS THE FIBONACCI SEQUENCE??????" I have a solution. I found out what it was. Here are the first few numbers: =0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...= Do you see the pattern? Each number is the sum of the previous two.

0+1=1, 1+1=2, 1+2=3...
Well, now you know... -Montgomery The Fibonacci sequence is special because as you go on and on in the sequence, if you are to divide a number by the one that precedes it the number you get is close to the Golden Ratio, which is approximately 1.616161616161....... As you go on and on the number that you get by dividing the current number and the previous number gets increasingly closer to the Golden Ratio. James Han

=**Quadratic Formula**=


 * This is the quadratic formula. Notice: A, B, and C will be numbers, depending on the equation. There will be two answers.**

-Sam Fansler http://advancemaths.wordpress.com/2012/07/03/quadratic-formula/

Also you can use a method called completing the square. You make a = 1, subtract c from both sides, do (1/2b)^2, add that to both sides, square root both sides, take + or -, meaning split the equation into plus and minus variations. For example, if it was x=5+or-3, split it up into x=5+3 and x=5-3. Both answers will be x.

Solving Quadratics By Factoring (Basics) Let's say you have the problem x^2-2x-8=0 You need to factor, or find numbers that multiply together to make this. For example: (X+2) * (X-4) An algorithm is to find what two numbers add up to -2, and multiply to -8. X*X= X^2, x*2+x*-4=-2x, and -4*2=8. Now once you find the two numbers that fit the description, multiply them both by -1, and those are your answers. (Yes, two.) So X= -2 and 4. Plug in the numbers! Both will work! Please clear up anything that doesn't make sense. Montgomery