ID QR question type

[nikki21]

Hi!

I'm having trouble identifying what the following question is testing you on. Is it related fractions, ratios, powers (I know area is tested)?

The question is:
The A series is a set of paper sizes that begin at A0 and continue to A1, A2, A3, A4 and so on. Each size is half the previous size and so each size has a consistent height to width ratio of 1:1.41. An A4 paper has dimensions 297 x 241
1)  What is the area of the A3 and A2 paper put together
2) What is the area of the A10 paper
3) How many A0 papers would it take to make 150 A3 papers.
4) An A5 book has 350 pages. What is the total area of all the pages laid.

Specifically, I didn't recognise that I had to raise 2 to powers and then divide/multiply accordingly (at least that's the fastest way of doing 2). What skill am I lacking? Or what can I search up on google to find questions that test the same skill (lol). 

Thankyou!


Thankyou

[fun_jirachi]

Hey there!

Seems like there's a typo (A4 paper has dimensions 297mm x 210mm). It would also help to note that since the ratio of the sides is the square root of two, each successive size of paper has area half of the previous (as noted by the question!) - this is very important! This is what should clue you in to using powers of two, as you say.

A more simplistic way to start would be just to make an exhaustive list of all areas involved with the question - 11 numbers isn't too bad, particularly if you have a calculator (which you do!) and note them down. A quicker method of course is to recognise and realise that this sentence here ('Each size is half the previous size and so each size has a consistent height to width ratio of 1:1.41.') almost tells you that for some size of paper \(A_n\) has area \(A_0 \times 2^{-n}\). In fact, for each part of the whole question, this is probably one of the easiest methods. If you have trouble reading into this, it might help to try wordier math questions that might appear in your schoolwork - these are very similar! Improving with this sort of thing isn't really maths-related since I'm sure that part sounds okay from what you say - it's more about synthesising the info given and turning it into 'math language', so to speak.

Hope this helps