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Sergeant Loi’s Mid-Year Boot Camp 2008 – Obey The Rules of Indices!

Tuition given in the topic of A-Maths Tuition Notes & Tips from the desk of Sergeant Loi at 1:58 am (Singapore time)

Updated on 4 May 2008

No one messes around with Sergeant Loi!

The Mids are just around the corner. A time when students are put through grueling tests to realize how little they’ve actually learnt in a semester dominated by fun and laughter, peace and joy.

Unfortunately in this critical time, no word has yet been heard from Miss Loi – who is presumed to be still trapped in that fitting room since a few days ago.

And so to fill this void …

*Puts on helmet*

*SHOWS STERN & MEAN FACE*

Ok boys and girls, this is Sergeant Loi sent by The Temple to maintain discipline in Miss Loi’s absence!

In the coming days, you shall be subjected to a series of no-nonsense DRILLS and exercises on several ‘Hot Topics’ that you MUST complete in order to survive your Mids!

Rest assure that, with the menacing taskmaster Sergeant Loi around, there shall be no silly stories, lame content and fooling around on this blog, for ~~she is not as cheong hei as the Sexy Maths Tutor~~ there is no time to lose if you want to pass your Mids!

*Sounds bugle*

EVERYBODY FALL IN! Sergeant Loi’s first drill with you shall be on Indices!

*Cracks whip*

The Rules of Indices

A. SIMPLIFY THOSE WITH INDICES 1 OR 0

i.e. duuuuh!

B. FOR THE SAME BASE (`a`) WITH DIFFERENT INDICES (`m`,`n`): MULTIPLY IS TO PLUS, DIVIDE IS TO MINUS, POWER IS TO MULTIPLY

$a^m*a^n = a^{m+n}$
${a^m}/{a^n} = a^{m-n}$
$(a^m)^n = a^{mn}$

ONLY for the same base (i.e. a)! DON’T ever do this: $a^m*b^n = (ab)^{m+n}$ → WRONG!

C. THOSE WITH COMMON INDICES CAN BE MARRIED

${a^n}/{b^n} = (a/b)^n$

ONLY for those with same indices (i.e. n)! Couples with different indices cannot get along!

D. INDICES GET INVERTED WHEN TRANSFERRED TO THE OPPOSITE SIDE

e.g.

$a^{1/3} = b doubleright a = b^3$
$a^{-1/3} = b doubleright a = b^-3$
(The negative (-) sign follows across to the other side!)
$a^{-3/2} = b doubleright a = b^{-2/3}$
(The index gets inverted on the other side!)

SAMPLE PRACTICE QUESTION

If $(3^{x+2})(5^{x-1}) = 15^{2x}$ , find the value of .

Ans:

$doubleright (3^x * 3^2)({5^x}/{5^1}) = 15^{2x}$ → using B(1)+B(2) above
$doubleright (3^x * 5^x)(9/5) = 15^{2x}$
$doubleright {15^x}(9/5) = 15^{2x}$ → using C(1) above
$doubleright 9/5 = {15^{2x}}/{15^{x}} = 15^{2x-x} = 15^x$ → using B(2) above

Get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample question! Check out this question for further practice!

Print this out if necessary and obey the above rules strictly – for if you don’t and end up fumbling in your exams Sergeant Loi will throw you to the deepest dungeons beneath The Temple where unspeakable miseries shall be heaped upon you!

*Cracks whip!*

N.B. On the other hand, if you have any valuable input to add to the notes above, you might even get a medal from Sergeant Loi for your contributions!

頑張って!!!

Sergeant Loi