Mathematics Is Difficult Or Is It Not?

We all know it. Everyone talks about it. MATHEMATICS IS DIFFICULT. Others even spelled out an acronym for it as "Mental Abuse To Humans". A subject filled with numerous problems that are supposed to be solved at the end of the day, and yet, as funny as it may sound, the one figuring out a way to give solutions to the problems becomes PROBLEMATIC before the day ends. This, undoubtedly, brings FRUSTRATION to the students, to YOU. 

Are you one of those students who tremble in fear or lose their sanity when the word “Mathematics” suddenly comes in? Are you one of those students who can’t help it but scratch their heads when they have to deal with the subject? Do you belong to those students who haven’t dwelt in trying and yet, they give up already and whine about how difficult Mathematics is? Or do you consider yourself among those students who tried already and yet, understanding seems to be far away from reach?

           
Mathematics doesn’t always have to be that hard. Most especially in junior high school. All things, may it be a situation, a problem, a crisis or a subject, can always be dealt in two ways; the hard way or the easy way. Just because everyone seems to be doing it that way doesn’t mean you have to do it the way they do as well. There’s always an alternative, simpler way. You can always encourage or find yourself settling in a path to easiness. Below are some useful and easy processes or solutions about solving specific topics or lessons in the field of Mathematics which are not being often introduced or taught in some schools or universities but can become quite handy when faced with such. There's only one thing you must do; UNDERSTAND AND YOU SHALL ESCAPE THE COMPLEX.

Square Root of a Number

Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself.

The perfect squares are the squares of the whole numbers.

The square root of a number, n, written below is the number that gives n when multiplied by itself.

Here are other examples of square roots of all perfect squares from 1 to 100.

Getting the square roots of perfect squares is so much easy, but using a calculator makes the work easier including those numbers that do not belong to the category of perfect ones.

Here's a MATHEMATIP on how to get the square roots of ANY NUMBER in just a matter of seconds without the aid of a calculator. Remember, ESCAPE THE COMPLEX. 

SQUARE ROOT OF PERFECT SQUARES 

If the video cannot be viewed, kindly click the link below:

https://www.youtube.com/watch?v=nUyLnjgGumg

SQUARE ROOT OF ANY NUMBER 

If the video cannot be viewed, kindly click the link below:

https://www.youtube.com/watch?v=PJHtqMjrStk

Double Synthetic Division: Dividing a Polynomial by a Trinomial

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient.  The simplest polynomials have one variable. 

Polynomials in one variable are algebraic expressions that consist of terms in the form axn where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term.  The degree of a polynomial in one variable is the largest exponent in the polynomial.

Note that we will often drop the “in one variable” part and just say polynomial.

Here are examples of polynomials and their degrees.

There are two cases for dividing polynomials: either the "division" is really just a simplification and you're just reducing a fraction or else you need to do long polynomial division. However, synthetic division is a shorthand, or shortcut, method of polynomial division (long method of division) in the special case of dividing by a linear factor. Here is an example.

 -- and it only works in this case. Or so we thought?

What if you are asked to divide a polynomial in one variable and it isn't by a linear factor, but by a TRINOMIAL where the leading coefficient can either be 1 or not? Are you still up for that challenge? Before you say no, here's a MATHEMATIP by the name of DOUBLE SYNTHETIC DIVISION. Remember, ESCAPE THE COMPLEX.

DIVIDING A POLYNOMIAL BY A TRINOMIAL USING SYNTHETIC DIVISION (a = 1)

If the video cannot be viewed, kindly click the link below:
https://www.youtube.com/watch?v=mdgWnxohHNg

DIVIDING A POLYNOMIAL BY A TRINOMIAL USING SYNTHETIC DIVISION (a is not 1)

If the video cannot be viewed, kindly click the link below:
https://www.youtube.com/watch?v=T7YOSJcNXfE

Trigonometric Ratios: Hand Trick

The six trigonometric ratios relate the sides of a right triangle to its angles. Specifically, they are ratios of two sides of a right triangle and a related angle. Here are the formulas for these six trig ratios:

  

All the trigonometric ratios for angle with measures 0°, 30°, 45°, 60° and 90° are provided in the following table:

Having a hard a time memorizing the trigonometric ratios table? Well, no more. Say goodbye to memorization and say hello to your HAND. Here are two MATHEMATIPs on how to get the trigonometric ratios of special triangles without having to use a calculator or cracking every neuron that your brain has. Remember, ESCAPE THE COMPLEX.

TRIGONOMETRIC RATIOS: HAND TRICK

If the video cannot be viewed, kindly click the link below:
https://www.youtube.com/watch?v=jI81WXyFrL0

If the angles are in radian measures, this is how you do it.

Writing Non - Terminating Recurring Decimal to Fraction

A decimal is a number expressed in the scale of tens. Commonly speaking we talk about decimals when numbers include a decimal point to represent a whole number plus a fraction of a whole number (tenths, hundredths, etc.). It is probably the most commonly used number system. The decimal number system consists of ten single- digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number after 9 is 10. The number after 19 is 20 and so forth. Additional powers of 10 require the addition of another positional digit.

A decimal point is a point or dot used to separate the whole part of a number from the fractional part of a number.

There are three different types of decimal number

• exact,
• recurring
• other decimals.

An exact or terminating decimal is one which does not go on forever, so you can write down all its digits. For example: 0.15

A recurring decimal is a decimal number which does go on forever, but where some of the digits are repeated over and over again. For example: 7.3333333333

Sometimes recurring decimals are written with a bar over the digits which are repeated, or with dots over the first and last digits that are repeated.

Other decimals are those which go on forever and don't have digits which repeat. For example pi = 3.141592653589793238462643...

Converting exact decimals to fraction is very simple. But writing non - terminating recurring decimals in the form p over q (fraction form) takes so much time. Here's a MATHEMATIP on how you can make the work done in a correct and convenient way. Remember, ESCAPE THE COMPLEX.

CONVERTING NON - TERMINATING RECURRING DECIMAL TO FRACTION

If the video cannot be viewed, kindly click the link below:

https://www.youtube.com/watch?v=UfMOqaxgUAg