Thursday, November 4, 2010

Mathematics in Taglish

Dahil wala man lamang pumapasyal sa site na ito (maliban sa akin), minabuti kong isalin na lang sa wikang Filipino o Tagalog sa abot ng aking makakaya ang mga aralin sa Matematika. Alam kong may mga termino sa English ang walang katumbas sa Filipino pero sapat na sigurong gamitin ang terminong iyon sa wikang Ingles kung nauunawaan naman ng mga mag-aaral/mambabasa ang konsepto nito.

Tuesday, October 19, 2010

How to find vertices, edges and faces of a prism given the sides or base?

1) To find the number of vertices, edges and faces of any prism given the number of sides (or) base, use this formula:

a) vertices of a prism = 2n
b) edges of a prism = 3n
c) faces of a prism = n + 2
where n is the number of sides of a prism

Examples:
Find the number of vertices, edges and faces of a hexagonal prism.

We know that a hexagon has 6 sides (n), therefore
vertices = 2n ==> 2 * 6 = 12
edges = 3n ==> 3 * 6 = 18
faces = n + 2 ==> 6 + 2 = 8

INVERSE OF A FUNCTION

To find the inverse ( f^-1)(x) of a function f(x); follow the following steps:
Example: Find the inverse of
y = 1-2x

1) Write the original equation.
y = 1-2x

2) Solve it in terms of x.
y = 1 -2x
-2x = -1 + y
x = (1-y)/2

3) Interchange y and x in the result of step 2.

x = (1-y)/2 ==> y = (1-x)/2

4) The inverse function f^-1(x) of f(x) = 1 -2x
is therefore f^-1(x) = (1-x)/2


Saturday, May 29, 2010

Convert Radians to Degrees and Vice Versa

A) To convert radians to degrees

Multiply radians by 180 degrees/pi
Example:

3pi/4 ==> degrees

3pi/4 x 180 degrees/pi (pi will cancel out)

540/4 = 135 degrees

B) To convert degrees to radians

Multiply degrees by pi/180 degrees
Example:
60 degrees ==> radians

60 degrees x pi/180 degrees ( degrees will cancel out)

60pi/180 = pi/3

Tuesday, May 25, 2010

Quadratic Equation: Completing the Square

One way of solving for x in a quadratic equation is by completing the square. Here's how:

x^2 + 6x - 7 = 0 ===> ax^2 +bx + c = 0
==================
1) Move the constant to the right side. In the equation above, the constant is 7. You can do this by adding the negative value of the constant on both sides of the equation;

x^2 + 6x -7 + (+7) = 0 + (+7)

x^2 + 6x = 7

2) Take half the value of the x-term or b ( 6).

6/2 = 3

3) Square it.

3^2 = 9

4) Add the result to both sides.

x^2 + 6x + 9 = 7 + 9

5) Convert the left side to squared form and simplify the right side.

( x + 3)^2 = 16

6) Take the square root of both sides.

x + 3 = +/- 4

7) Solve for x

x + 3 = 4
x = 4 - 3
x = 1
========
x + 3 = -4
x = -4 - 3
x = -7
=========
Answers:
x = 1 and -7