Sesuai yang dijanjikan sebelumnya, saya bakal post tentang
contoh soal H2 Math.
Apa sih H2
Math?
Jadi, H2
Math itu Matematika yang diajarkan di Junior College Singapura (setara SMA di
Indonesia). Kok namanya bukan A-Level? Iya, sebenarnya ini memang setara dengan
A-Level, hanya saja Ministry of Education-nya Singapura memodifikasi soalnya
lagi supaya lebih berbobot. Jadilah H2 Math. H2 Math sendiri adalah lanjutan
dari H1 Math, jadi anggapannya H2 Math lebih advanced dari H1 Math.
Materinya banyak yang berbeda dari
materi di SMA Indonesia, misalkan saja di sana sudah diajarkan complex number, sedangkan kita belum.
Cara pengerjaannya juga berbeda. Di Indonesia, matematikanya tentang hafal
rumus. Di Singapura, kebanyakan soal matematika pertanyaannya hanya: “Show that … equals to ….” Murid dituntut
untuk menggunakan logika, bukan sekadar hafal rumus. Apa ini menunjukkan
kurikulum Indonesia tertinggal dengan kurikulum luar negeri? Bisa saja. Mungkin
hal ini bisa jadi bahan introspeksi bagi pemerintah, tidak hanya menjadikan
kurikulum sebagai alat politik. *no
offense*
Jadi, begitulah pengantarnya.
Sekarang saya bahas beberapa soal. Lumayan, bisa jadi soal latihan UEE NTU dan
NUS. From now on, I’m using English,
since you have to do the test, i.e. NTU and/or NUS’s UEE, in English, too. Well, you have to be used to it, otherwise
you would struggle in doing the test.
PS:
I DO NOT own the question. All credit
goes to mathdistinction.com. However,
I worked on the solution by myself. I did it on Microsoft Word and used
snipping tool.
Question 1
You can see that you are going to
be told about the marks of each question.
Let’s go
straight to the problem.
Analysis Step
Look at the first inequality.
Well, how should I solve this problem? Do I have to multiply each side by x-2? Or
do I have to subtract x+1 from each side?
Be aware. I
said, BE AWARE.
On the
first glance, I know you would be tempted to multiply each side by x-2. But,
you don’t know whether x-2 is a negative number or not. If it is negative, then
you have to change the inequality sign. If it is not, then you do not have to.
Such a
gambling, isn’t it?
So, the
most righteous way to do this is to subtract x+1 from each side.
“Working on the problem” Step
As I told before.
Almost done, folks. Just add here
and subtract there.
The minus sign annoys me, so I
multiply each side by -1. The sign changes from “greater than or equal to” to “less
than or equal to”. Then, factorise.
From here on, use sign test. I’m
sure you’ve learned it in your Senior High.
Before advancing, I want you to
look at the denominator. The sign is a “less than or equal to”. But, since you
cannot have zero at the denominator, you have to change it a little bit. ONLY
for x-2, it has to be a strict inequality, not a weak inequality. By all means,
you do not include 2 in the sign test.
See? The circle for 2 is hollow
while the other circles are solid. I did this to distinct strict inequality and
weak inequality.
As we need the negative result, the
set of values of x are:
Let’s move to the
second part.
When you see “hence”,
then you do not have to think too far from your previous solution.
It seems like you have to work from
scratch, but don’t!
There is an easier way to solve
this.
Remember the first inequality?
Just replace x with 1/x.
Then, it is just algebra thing. We
get the second inequality.
From the first solution, replace x
with 1/x, again.
This is just a recriprocal
business. When you change 1/x to x again, keep in mind that the sign has to be
REVERSED.
Voila.
Ya, jadi itu soal tentang
pertidaksamaan. Untuk mengerjakan pertidaksamaan, kita hanya perlu berlatih dan
berlatih.