LETS DISCUSS....

TODAY WE CAN DISCUSS WHY IS SO IMPORTANT TO US...(IN MY OPINION)

SINCE IN PRIMARY SCHOOL..WE HAD LEARN MATHE...UNTILL NOW IN UNIVERSITY,WE ALSO HAVE TO STUDY MATHE(PRE CALCULUS)... AFTER LEARN MATHE FOR MANY YEARS...I CAN CONCLUDED THAT MATHE IS VERY IMPORTANT TO US...

THERE ARE MANY REASONS WHY MATHE IS SO IMPORTANT..IN MY OPINION..

THESE ARE SOME OPINION WHY MATHE IS SO IMPORTANT....

The reason to study math is that it gives you a different perspective on things. I think that most people hate math because it is taught just as an exercise in memorization. You get the impression that all there is to math is just a bunch of formulas that you can look up in a book. I think of math as something totally different. Check out these two links: What is Mathematics?

http://www.mathforum.org/dr.math/problems/erum.09.22.00.html

The way to be good at math is not to memorize a whole lot of different things, it's just to memorize a few small things and then play around with them and see what else you get.For example, what is algebra? Well, you already know about multiplication, division, addition, and subtraction. One day (a long, long time ago) somebody who knew all of those things was sitting around and thinking.

Moreover mathe isvery useful in our daily life likes example....mathematical problems abound in our daily life...we often to use simlple calculation when we buy or sell somethings.. and mathematical proficiency is also required for many jobs..if we dont have mathe knowledge..of course we cannot get oa good job.. and last mathe is essential for science,engeering,and research..

so,we as engeneering student must take this oppurtunity to study mathe because it is very useful to us....

POLYNOMIALS

POLYNOMIALS

PolynomialsA polynomial looks like this:
example of a polynomialthis one has 3 terms
It can be made of:
constants (like 3, -20, or ½)
variables (like x and y)
exponents (like the 2 in y2) but they can only be 0, 1, 2, 3, ... etc
That can be combined using:
+ - ×
addition, subtraction and multiplication, ...

... but not division!

Those rules keeps polynomials simple, so they are easy to work with!
Polynomials or Not?

These are polynomials:
3x
x - 2
3xyz + 3xy2z - 0.1xz - 200y + 0.5
And these are not polynomials
2/(x+2) is not, because dividing is not allowed
3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
But this is allowed:
x/2 is allowed, because it is also (½)x (the constant is ½, or 0.5)
also 3x/8 for the same reason (the constant is 3/8, or 0.375

FUNCTION

FUNCTION

A function is a relation (usually an equation) in which no two ordered pairs have the same x-coordinate when graphed. One way to tell if a graph is a function is the vertical line test, which says if it is possible for a vertical line to meet a graph more than once, the graph is not a function. The figure below is an example of a function. Functions are usually denoted by letters such as f or g. If the first coordinate of an ordered pair is represented by x, the second coordinate (the y coordinate) can be represented by f(x). In the figure below, f(1) = -1 and f(3) = 2. When a function is an equation, the domain is the set of numbers that are replacements for x that give a value for f(x) that is on the graph. Sometimes, certain replacements do not work, such as 0 in the following function: f(x) = 4/x (you cannot divide by 0). In that case, the domain is said to be x <> 0. There are a couple of special functions whose graphs you should have memorized because they are sometimes hard to graph. They are the absolute value function (below) and the greatest integer function (below). The greatest integer function, y = [x] is defined as follows: [x] is the greatest integer that is less than or equal to x.
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If nonvertical lines have the same slope but different y-intercepts, they are parallel. 1. Problem: Determine whether the graphs
of y = -3x + 5
and 4y = -12x + 20 are
parallel lines.

Solution: Use the Multiplication Principle
to get the second equation in
slope-intercept form.

y = -3x + 5
y = -3x + 5

The slope-intercept equations
are the same. The two
equations have the same graph.

2. Problem: Determine whether the graphs of
3x - y = -5 and
y - 3x = -2 are
parallel.

Solution: By solving each equation for y,
you get the equations in
slope-intercept form.

y = 3x + 5
y = 3x - 2

The slopes are the same, and
the y-intercepts are different,
so the lines are parallel.
Sometimes, you will be asked to find the equation of a line parallel to another line. Not all the information to put the equation in slope-intercept form will always be given. Example: 3. Problem: Write an equation of the line
parallel to the line 2x + y - 10 = 0
and containing the point (-1, 3).
Solution: First, rewrite the given equation
in slope-intercept form.
y = -2x + 10
This tells us the parallel line
must have a slope of -2.
Plug the given point and the
slope into the slope-intercept
formula to find the y
intercept of the parallel line.
3 = -2(-1) + b
Solve for b.
1 = b
The parallel line's equation is
y = -2x + 1.
If two nonvertical lines have slopes whose product is -1, the lines are perpendicular. Example:
1. Problem: Determine whether the lines
5y = 4x + 10 and 4y = -5x + 4
are perpendicular.
Solution: Find the slope-intercept equations
by solving for y.
y = (4/5)x + 2
y = -(5/4)x + 1
The product of the slopes is -1, so the
lines are perpendicular.
Sometimes, you will be asked to find the equation of a line perpendicular to another line. Not all the information to put the equation in slope-intercept form will always be given. Example:
2. Problem: Write an equation of the line
perpendicular to 4y - x = 20 and
containing the point (2, -3).
Solution: Rewrite the equation in
slope-intercept form.
y = .25x + 5
We know the slope of the
perpendicular line is -4
because .25 * -4 = -1. (Notice
that the slope of the
perpendicular line is the re-
ciprocal of the other line's
slope.)
Now plug the given point and
the slope into a slope-intercept
equation to find the y
intercept.
-3 = (-4)2 + b
Solve for b.
b = 5
Now, you have the information
you need to write an equation
for a line perpendicular to
4y - x = 20. The answer
is the following equation:
y = -4x + 5.

JOM BLAJAR MATH.....

LETS STUDY THE CALCULUS...

CALCULUS IS FUN........

HOW TO GET AN A IN MATH(CALCULUS)

How to Get an A+ on every math test you take

Just as with everything in life you need to put in effort in order to succeed. Math is the same, if you give your time and effort you will be able to get an A+ for your tests.
Understand the subject
Before you even begin to study for tests or exams make sure you understand what you are going to study. Do some research, or take time to study the text book. It will do you no good to walk into the exam room without proper preparation. Understanding your subject is vital to success.
Color Coding
Use color coded stick-on's to mark your books. This way it will be easier to identify where you are and what you are busy with. You can make an index to know what color you are using for what problem or project. This way your study time will be a bit more organized.
Finding your niche
Get a place where you can study alone and regularly. It should be quiet, comfortable and without any traffic. Concentration can easily be distracted by others. Make sure you have a desk or table and a comfortable chair. Enough fresh air will ensure that you will not get tired too quickly.
Conquer the mountain first
Start your study time with the difficult subjects. It will be no good to study when you are tired or have been busy with other subjects for an hour. Your brain will be exhausted and you won't be able to concentrate. Give yourself a fresh start.
Making notes
Make notes of difficult problems with their solutions and stick them where you can see them. The bathroom mirror or the fridge, this way you will be able to read them with regular intervals and they will start to sink into your long term memory.
Take time to exercise
Exercise helps the blood flow to release more oxygen and it will give you the mental ability you need. Your mind will be sharp and you will absorb more when your brain is alert. You will also sleep better and feel rested.
Study breaks
Take a break when you start to feel tired. It will do you no good trying to study when your brain is exhausted. Take regular intervals, eat something and go for a walk. Then come back and study again. This way you can observe more.
Diet
Most people crave foods like hamburgers, hot dogs or any other take-away. It's more convenient and easy to get without taking time to prepare it yourself. This will do you no good as your body needs fuel to perform. Invest in healthy foods when you study. A lot of fruits and vegetables will increase alertness and help you to concentrate better, try eating some nuts as well. Avoid too much sugar as it will tire you.
Get Organized
Having a lot of papers lying around will just confuse you. Take time before you study to organize your desk. Get rid of all clutter and organize everything you need so that when you start to study you can be focused and nothing needs to distract you from the subject at hand. Nothing can be as debilitating as to look for a highlighter or notes.
Don't cram your brain
Have you ever experienced blankness during a test? This is because you try to cram your brain in a short period of time. Your short term memory gets overloaded and stops in its tracks. Take time to study beforehand, and get a good nights rest before the test.

10 Reasons Why It is Important to understand Mathematical Patterns?

10 Reasons Why It is Important to understand Mathematical Patterns?

Wouldn't it be great if you could predict the future? Well, some people believe that predicting the future is impossible but it would be more accurate to say that making outlandish predictions not based in logic leads to low accuracy. However, looking at the relationship of a series of patterns over time can lead to making accurate predictions of particular results. This is a common method of mathematical pattern analysis and such an analysis is important for the following reasons:
Understanding mathematical patterns allows someone to identify such patterns when they first appear. After all, you can not gain the benefit of patterns if you can't see them and you can only see them if you understand them.
Patterns provide a sense of order in what might otherwise appear chaotic. When you notice that things happen in a certain pattern - even something as mundane as a bus always stopping at a certain corner at 5pm - order is provided.
Patterns allow someone to make educated guesses. Much science is based on making a hypothesis and hypothoses are often based on understanding patterns. Similarly, we make many common assumptions based on recurring patterns.
Understanding patterns aid in developing mental skills. In order to recognize patterns one need to have an understanding of critical thinking and logic and these are clearly important skills to develop.
Patterns can provide a clear understanding of mathematical relationships. This can be seen in a very evident manner in the form of multiplication tables. 2 x2, 2 x 4, 2 x 6 are clearly examples of the relationship pattern found in multiplication.
Understanding patterns can provide the basis for understanding algebra. This is because a major component of solving algebra problems involves data analysis which is deeply related to the understanding of patterns. Without being able to recognize the appearance of patterns the ability to be proficient in algebra will be limited.
Understanding patterns provide a clear basis for problem solving skills. In a way, this is related to critical thinking but more directed towards mathematics specifically. Patterns essentially provide a means of recognizing the broader aspects that can be shored down in order to arrive at the specific answer to a particular problem.
Knowledge of patterns is transferred into science fields where they prove very helpful. Understanding animal patterns has been used to help endangered species. Understanding weather patterns not only allows one to predict the weather but also predict the common impact of weather which can aid in devising the appropriate response in an emergency situation.
One of the lesser known aspects of patterns is the fact that they often form the basis of music. For example, there are various patterns of notes that provide the basis for proper harmony on a piano. If you don't believe patterns are important when playing a piano simply walk up to the nearest piano and start banging away randomly at the keys. You probably won't hear any songs that you recognize!
Patterns provide clear insight into the natural world. While animals and certainly plants are far from thinking beings they do have certain habits that exist in patterns and understanding these behavioral patterns provides a clearer understanding of all living things.
It is safe to say that the benefits of understanding patterns open many doors where this knowledge can be applied. Of course, that is a commonality with all forms of learning mathematical logic: there is a deep application that can be provided that we often do not realize when we first study the material. With understanding patterns - and other forms of math - sometimes you really need to stick with it for the long term, but the great

COMPLEX NUMBER

LEARNING THE COMPLEX NUMBER

COMPLEX NUMBER ARE ONE OF THE TOPIC IN PRECALCULUS. LEARNING THIS TOPIC IS VERY INTERESTING TO THE STUDENT.

In mathematics, the complex numbers are an extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:[1]

Every complex number can be written in the form a + bi, where a and b are real numbers called the real part and the imaginary part of the complex number, respectively.
Complex numbers are a field, and thus have addition, subtraction, multiplication, and division operations. These operations extend the corresponding operations on real numbers, although with a number of additional elegant and useful properties, e.g., negative real numbers can be obtained by squaring complex (imaginary) numbers.

Complex numbers were first discovered by the Italian mathematician

Girolamo Cardano, who called them "fictitious", during his attempts to find solutions to cubic equations [2]. The solution of a general cubic equation may require intermediate calculations containing the square roots of negative numbers, even when the final solutions are real numbers, a situation known as casus irreducibilis. This ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, it is always possible to find solutions to polynomial equations of degree one or higher.

The rules for addition, subtraction, multiplication, and division of complex numbers were first developed by the Italian mathematician

Rafael Bombelli. A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions.

Complex numbers are used in many different fields including applications in engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory. When the underlying field of numbers for a mathematical construct is the field of complex numbers, the name usually reflects that fact. Examples are complex analysis, complex matrix, complex polynomial and complex Lie algebra.

MY FIRST EXPERIENCE ABOUT PRE CALCULUS

ALOHA.....

Thank you for viewing my blog.



This is my first time i learn to create a blog. I feel very excited to learn about it especially its about precalculus. PRECALCULUS is my favorite subject and by doing this blog, it help me more to learn about it......

The meaning of precalculus is..


In mathematics education, Precalculus, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is sometimes considered to be an honors course. Courses and textbooks in precalculus are intended to prepare students for the study of calculus. Precalculus typically includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric functions, vectors, complex numbers, conic sections, and analytic geometry. Equivalent college courses are college algebra and trigonometry.
In detail, precalculus deals with:
Sets
Real numbers
Complex numbers
Solving inequalities and equations
Properties of functions
Composite function
Polynomial functions
Rational functions
Trigonometry
Trigonometric functions and their inverses
Trigonometric identities
Conic sections
Exponential functions
Logarithmic functions
Sequences and series
Binomial theorem
Vectors
Parametric equations
Polar coordinates
Matrices
Mathematical induction
Limits