Miss Loi: This part is actually a test on your concept of Percentages - a very basic Sec 1 topic that sadly managed to caught many students out.

After correcting your careless mistake in Comment #2, you're right to list that:

• Original F = k/t^2
• New

So the change in F = New F − New F =
∴ % change
= (change in F/ original F) x 100%
= × 100%
≈ −88.9%

So when t is tripled, F will decrease by 88.9% → not 11.1%, or 800%, and most certainly NOT a Sadako Loi-induced 0.889%!!!!!!!!!!!!!!!

Miss Loi: Yes the question states that "F is inversely proportional to the square of x".

Putting this English statement in mathematical context
⇒ F↑, x²↓ ⇔ F↓, x²↑ (⇒ Graphs I & II are out!)
⇒ F ∝ (by definition)
⇒ F =

If you're an upper sec student who's already familiar with the various sketches of important graphs, you should straightaway be able to identify the graph of , jump up from your seat and scream "It's IV! It's IV! IT'S IV" excitedly like a siao cha/ta boh (to the chagrin of those around you).

Else you may follow mathslover's wisdom of elimination and/or her comment below to arrive at the same conclusion.

P.S. It's good to write out the F = expression coz it's easy to forget that we're dealing with a square of x here, as many of us may already have the image of F = from textbooks/formula sheets burnt deep deep in our minds.

New F = 9F
Percentage change = change / original × 100%
= 8F / F × 100% = 800%

*Puts up WRONG WORKING tape* Move along now ... see corrected workings below!

Part 3 is one of the two typically standard kinds of proportion/variations questions (the other kind being something like this that you can expect to see in your O-Level E-Maths Paper 1.

As shown by mathslover's workings above, one can see that it's important to read the statement in the question carefully (i.e. pick out the critical words like "inversely", "square of x", "F falls to half of this value" etc.) in order to obtain the expression () and subsequently the value of k correct from the start.

After which it's simply sub, sub, sub in the given values to find that Miss Loi has about half a minute to take corrective action to prevent irreversible damage to her skin!