We have covered on simplifiying and factorisation in th previous post, so for this post, we are doing solving equations. It is difficult to type out the explanations, hence, I have added this video:
Solving equations would require both factorisation and simplification, so before you 'confuse' yourself with this solving chapter, you should review the previous post and refresh your memory. Also, when you expand, do be careful and do not make any mistake. Once there is a mistake, the whole thing from then on will be wrong. So, do be careful and also, use the few algebraic rules.
Thankyou!
{C.Weishi -- P.S If you have any queries, feel free to email me @ c.weishi-@hotmail.com
Sunday, April 12, 2009 - [ Mathematics : MYE Topics ]
These are the topics that will be tested in the Mid Year Examinations, if you want to study them beforehand... Of course I will try my best to post all the details on this blog before mid year, but I may not finish everything, so STUDY BEFOREHAND!
= Similarity & Congruency = Percentage, ratio & rate = Direct & Indirect proportion
= Construction of triangles & Quadrileterals - Perpendiculor Bisectors - Parallel Lines - Angles Bisectors
= Algebra - Simplification / Expansion (Refer to April 6,2009) - Factorisation - Fractions ('+', '-', '/', 'x') - Changing of Subject of Formula
= Prime factorisation - Highest common factors - Lowest common multiple
So, these are the topics that will be tested for mid year, so do study! And dont say you didnt know the topic, they are all here! =P All the best! Jiayous!
Before we begin, let us first recap on the basic information of algebra... i) Integer = number (Example: 4a)Variable = the alphabet (Example: 4a) ii) Index = the small number on the top right hand corner (Example: 4a2 ) iii) Like terms: 3ab + 2ab (Example)Unlike terms: 2a + 3b (Example)
Now, since we have recalled on the different terms in algebra, we shall move on to Algebraic Expansion... There are a variety of ways to expand the algebraic expressions. I shall only include those that are usually used in examinations.
i) Product of single terms Example: (ab)(b2c) - Group the product of b together. Then, express the product in index form.
(ab)(b2c) = (a x b) x (b x b x c) = a x (b x b x b) x c = ab3c
ii) Product of Two Expressions Example: a(x+y)
a(x + y) = ax + ay
This is called multiplying in the number in front ONE BY ONE into the brackets.The 'a' in the expression is multiplied step by step into the bracketed numbers, first, a x x and a x y, which gives us ax and ay respectively.
To give you a better idea, watch the short clip on Algebraic expansion:
iii) Using the THREE golden rules of Algebraic Expansion - Saves time - Easier method
(a + b)2 = (a)2 + 2(a)(b) + (b)2 (a - b)2 = (a)2 - 2(a)(b) + (b)2 (a + b)(a - b) = (a)2 - (b)2
So, just replace the 'a' and the 'b' with the actual numbers or expressions, and then voila! We have the answer! To have a better understanding, just watch the video, it is actually very useful!
If you have any questions or queries after reading this, feel free to approach me in school or email me at merlion0512@hotmail.com Thankyou! And credits to Aravind who spotted some of my typos, kudos! =)
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