Mathematics: Structure of Answers

afrocod

I'm self studying the course to sit in 2012 and I was just wondering is there any technical details I might not be aware of such as:

If your answer is in decimal form show the answer to five places before rounding to the specified detail in the question 3.14159... (round to two places) 3.14

Can I leave my answer in surd form or rational form to avoid decimals unless specifically asked to do something different?

Do I have to indicate where a calculator was used? Defining some notation at the start of the paper? e.g. "Cal" and placing that wherever a calculator was used.

I like to skip steps in my head. Will I lose marks if I don't list every painstaking detail (assuming my answers are correct)

Or anything else of this nature that had I not been to a teacher training day, I would not be privy to these technical details that are not mathematically defined standards, just SEC or NCCA standards.

Any help would be much appreciated,

Deuces.

**Timbuk2**

Leaving your answer in surd form, or in terms of pi, e, etc. is perfectly acceptable unless it is stated to do otherwise - in fact, it is usually preferred, as it's neater.

You don't have to indicate where a calculator is used, it is implied as you are doing the Maths exam, a lot of things are very difficult to do without a calculator.

Sometimes you can write out the sum you will do on one line, then on the next line you can write (using calculator ) = <answer>, but there is no need to do it!

If you don't list every step but have the right answer, then you will get full marks. However, if you don't list every step and don't get the right answer, the examiner will try and give you marks for what you have written down. If you have left a lot of things out, he or she may have no choice but to give you no marks, or more likely, attempt marks.

My advice would be to get into the habit of writing down the steps you are taking. It makes it a lot easier to read. Something that is obvious to you, may not be obvious to somebody else when they are reading over your answer - you ideally don't want the examiner reading the paper going "Where did he/she get this line from?"

Also, I would recommend starting a new page for a new question, and listing your sums in vertical format - i.e. instead of
[latex]\displaystyle{\frac{a^3-b^3}{a-b} = \frac{(a-b)(a^2+ab+b^2)}{a-b} = a^2 + ab + b^2}[/latex]

It is neater to write, and easier to read
[latex]\displaystyle{\frac{a^3-b^3}{a-b}}[/latex]
[latex] = \displaystyle{\frac{(a-b)(a^2+ab+b^2)}{a-b}}[/latex]
[latex] = a^2 + ab + b^2[/latex]

afrocod

Perfect answer. Thanks a million.

The only thing that's left is if I'm specifically asked to round to 2 places, do I have to list five or some other number before I round or can I just put the answer straight down.

Chuchoter

Two decimal places is usually the safest option, or surds if they're available. If you happen to be doing physics or chemistry though by yourself, try keep as many decimals as possible at least when you're doing the sum on the calculator, because rounding up too soon affects your final answer.

afrocod

Thanks for that, I am taking all the sciences.

What I'm really asking is, is there an official procedure of writing a certain number of decimal places before rounding if specifically asked to round.

Technical details that I would have no way of knowing because I don't attend a class or grinds or anything. Defined procedures that will lose me marks if not followed.

**Timbuk2**

I don't think there is any defined procedure in relation to decimal places. General advice is, and although it's more relevant to science subjects, would be to not round too early as you will lose accuracy.

Sometimes it's possible to keep the number in your calculator, so if this is possible try to do so to avoid unnecessarily having to type everything back into your calculator.

E.g. get [latex]\sqrt{1+x^2}[/latex] where [latex]x = e^{-2}[/latex] (this is a ridiculous example I just made up!).

You could type the following on your calculator
e^[-2]
Square it
Add 1
Square root it

then put down answer = ... on the paper, without losing any accuracy.
You could can write down individual steps if you want to (e.g. what [latex]1+x^2[/latex] is, to maybe 4 or 5 decimal places, but keeping the actual value on your calculator)

If you have a scientific calculator, another option is to store values in memory. E.g. if I work out something I will use later, I might often press the STO button, then the button which has A written above it - this stores that value in memory location A. To get it back I'd press RCL then A.

And I could use this directly in calculations on my calculator - e.g. SquareRoot(1 + (RCL A)^2) (which will just display as SquareRoot(1 + A^2) on my calculator).

I don't have knowledge of any of the science subjects apart from Physics, but for physics, often the amount of decimal places you use is determined by the context.
For example, if you are doing a question on an experiement of focal lengths of mirrors/lenses, and if the readings are only taken to two decimal places, it doesn't make a huge amount of sense to be quoting answers in terms of 6 decimal places - you are giving it an accuracy it doesn't deserve. It isn't wrong to do so, as such, but for example when using the formula to calculate vocal length -
if u = 0.34 and v = 0.6
then 1/u = 2.941176 and 1/v = 0.666667

So f = 0.2771739

It doesn't really make sense to leave f in this form, since all our readings were taken in terms of 2 decimal places, so even if not asked, I would tend to round and say
f [latex]\approx [/latex]0.28

finality

You should leave it in surd/fraction form unless it's specified that you should round to a certain number of decimal places.

afrocod

Grand, my mind is at ease.