iamemerlynf-blog

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Yesterday we had the discussion about Factoring and today we tackled about Completing the Squares and it’s easy at the beginning but as we go along and after Sir Bargo gave as an activity I realized that it is not only knowing the formula to get the right answer but also you need to analyse the equation for to easily solve and get the final answer.

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This day we continue on solving Quadratic Equations by using Factoring and yeahh thinking of the term “factoring” is quite easy but when the time comes that we need to solve several Quadratic Equations with higher values I’ve met some difficulties but still I answered them correctly.

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Buffering....

This morning, we discussed about the Solutions of Quadratic Equations. Of course, the solution of an equation or root of an equation refers to a particular value/s of the unknown which satisfy/s the mathematical condition being expressed by a mathematical equation. And in addition, we can identify the number of solutions of an equation in terms of its degree.

There are two kinds of solution, the Distinctive and Multiplicity Solutions. And also, there are four cases for Incomplete Quadratics.

Case #1: ax2 =0 wherein x=0 w/multiplicity of 2

Case #2: ax2 + bx=0 wherein x1=0 x2=-b/a

Case #3: ax2 + c=0 wherein    ax2= -c

                         x2= -c/a

                         x= ± √-c/a

                         x=± √c/a i

 Case #4: ax2 - c=0 wherein    ax2= c

                           x2= c/a

                           x= √c/a

 After the discussion, Sir Bargo gave us activities regarding the topic and at first I’ve met some difficulties in answering but happily I got the correct answers and aimed a perfect score.

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Better luck next time...

First, we checked our last assignment wich is about quadratic equation and thankfully I got 36 out of 37. After that, Sir Bargo asked us if we truly understand now the lesson about QE then we answered YES. He gave us a quiz regarding the said topic and at first, I’m quite confident on my answers but when it comes to the last number I just freak out cause I don’t know what to do anymore! Sir Bargo gave us clues but I keep asking on my mind on what should I need to distribute?! In the end, I didn’t got the right answer, well, most of us, but some got it right. I am soooo disappointed to myself because why on Earth did I forgot that the “a” and “b” are the ones that should be distributed too, so that it is easy for me to find the right answer and their specific value also. Argghhhh!!!

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Quadratic Equation

If there is Linear Equation, of course, there is Quadratic Equation also. This equation also known as 2nd Degree Equation has a

General Form of ax+bx+c=0 but

a, b and c  ∈ R

a ≠ 0 

if b=0, then, ax2+c=0        

          if c=0, then, ax2+b=0

          if b=0, c=0, then, ax2 =0

ax2=quadratic part

b=linear part

c=constant part

So, we called ax2 =0 as Pure Quadratic Equation

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NCAE yeah!

We just finish taking our exam for National Career Assessment Examination (NCAE) and I am telling you guys that it is not easy as what you think. Even though the result of the exam will not affect our grades still we should take it seriously because with this we can already think of the jobs we wanted to or jobs which is/are suited for us.

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Grades...Grades...Grades...

Today, we’re very nervous because we already computed our grades by our own and there is a possibility that most of us will get low grades. Sir Bargo help us in computing our grades and in time he also told us that we’ll be using the new grading system and most of us were shocked regarding the results. So he told us that our grades which were low will get lower because for the past 8 or 7 years the teachers used in computing of the grades with the base of 60 but this time it will be zero. We’re happy that he said he will find ways just to help us not to get grades with line-of-7. So in mean time, he said that we should not worry about our grades and just focus on the today’s lessons.

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This day, Sir Bargo came from an educational tour. We haven’t do lessons for the past week but he gave us back our various quizzes, chapter tests, and periodical test for us to compute for our grades. He presented us on what we are going to do and told us to write our computation in a ½ index card, place them in a short brown envelop and submit them tomorrow.

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Wish me Luck!

Yeahhh, this day we took our periodical test in Mathematics and at first I’m expecting for a nice result. “Expect the unexpected” I remember this quote during our examination because I know that our teacher will not give us an easy test but I didn’t expected that the exam will be that hard. I reviewed my notes before our exam but I know that my review was not enough and thinking about my result give me a headache! 

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Everything is connected to everything else...

Mathematics only result to many problems and an headache but what about when it is added with Science?! Then just double or triple the result of Math!. Since from our last lessons our minds are still “unconscious” *just saying but not too OA* and just this day, we discussed Math with a combination of Science. Variation. one word but consist of lots of meanings.

Variation

It is a function that relates the values of one variable to those of other variables or the manner in which two or more quantities change relative to one another.

Types of Variation

Direct or Proportional Variation - y varies directly with x y = kx

Inverse or Indirect Variation - y varies inversely with x y = k/x

Joint Variation - y varies jointly with a and b y = kab

Combined Variation - y varies directly with x and inversely with z y=kx/z - y varies jointly with a and b and inversely with z y=kab/z - y varies direct with x and inversely with a and b y=kx/ab

Types of Law

Boyle’s Law - In this law, the pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system. P = 1/V or PV = k P is the pressure of gas V is the volume of gas k is constant

Charles’s Law - This law states, when the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly related. V = T or V/T = k V is the volume of gas T is the temperature of a gas (measured in kelvin) k is constant

Gay-Lussac’s Law - In this law, there are two connected values and when one increases, the other also increases. P/T = k The pressure-temperature fraction will always be the same value if the volume and amount remain constant.

Combined Gas Law - This is the law that combines Charles’s Law, Boyle’s Law and Gay-Lussac’s Law. This law states, the volume and temperature are directly proportional to each other as long as pressure is held constant. PV/T = k P is the pressure V is the volume T is the temperature (measured in kelvin) k is constant (with units of energy divided by temperature)

Avogadro’s Law - This law states, equal volumes of all gases at the same temperature and pressure have the same number of molecule. V/n = k V is the volume of gas n is the amount of substance of the gas who’s measured in moles k is proportionally constant

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IMAGINARY AND COMPLEX NUMBERS

New day, new learning. After our previous lessons, today, we discussed about imaginary and complex numbers. We know that complex means many or different, so I thought of many and different numbers! HAHAHAHA and I just realized that we are in Math Subject so it is not just a simple meaning of “complex” added with “numbers”. Our teacher start and continue in discussing about complex numbers and I was like (・。・) *oohhhhhh okay!* and being a “diligent” student *HAHAHA PROUD HERE* I list down notes that were important.

Imaginary number is a complex number whose squared gives a negative result. Imaginary unit defined as i √-1.

The first 4 powers of i are: i 0 = 1 i1 = i  i2 = -1 i3 = -i 

Complex number - can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

The real number is called the real part of the complex number a + bi and  the real number b is called the imaginary part of a + bi.

Complex Conjugate of a complex number - is the number with equally real part and imaginary equal in magnitude but opposite in sign. Example: a+bi = a-bi

Operations on Complex number

·         Addition of Complex number -  Add the real parts and add the imaginary parts.  Example: (4 + 7i) + (2 + 3i) = 4 + 7i + 2 + 3i  = 4 + 2 + 7i + 3i  = 6 + 10i 

·         Subtraction of Complex number -  Subtract the real parts and subtract the imaginary parts.  Example: (5 + 6i) − (7 − 3i)  = 5 + 6i − 7 + 3i  = 5 − 7 + 6i + 3i  = −2 + 9i 

·         Multiplication of Complex number -  In multiplying two complex numbers is accomplished in a manner similar to multiplying two binomials. Use the FOIL process of multiplication and distributive multiplication. Example: (2 + 3i) • (4 + 5i)  = 2(4 + 5i) + 3i(4 + 5i) = 8 + 10i + 12i + 15i2 = 8 + 22i + 15(-1) = 8 + 22i -15 = -7 + 22i

·         Division of Complex number -  Rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.  Example: [ (8 + 4 i)(1 + i) ] / [ (1 - i)(1 + i) ]  = [ 8 + 4 i + 8 i + 4 i 2 ] / [ 1 - i + i - i 2 ]  = (4 + 12 i ) / (2)  = 2 + 6 i

So that’s it! Hoping that these lessons will stay put in my mind and wait for my next post :D

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Newbie ^_^

Hi! I created this blog because it is our project in Mathematics. I am a Grade 9 student. So, this blog will be all about Math. Feel free to leave comments about my posts and you can help me to improve this blog. Thank you!