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#### RuiAce

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##### Verbs and Maths
« on: September 04, 2016, 11:08:05 am »
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In the world of mathematics, the directive term you're given is slightly different to every other subject. This is due to the absence of long response questions. Sometimes, you're asked to give a numeric answer, whereas at other times you need to generate some kind of expression.

This post is intended to be a mini-guide on what words you should expect in a typical mathematics exam.

Deduce: Use anything that you're given to you (except the final result), and try to draw out something useful. Many 'deduce' questions overlap onto other key verbs, however you should be able to provide a concluding statement.
Evaluate: Giving a judgement can be seen as giving a value. Except in maths, we give an actual numeric value. So most likely you are intended to perform a computation which results in your final answer being a number. You may have to do some algebraic manipulation though (e.g. computing an antiderivative for a definite integral)
Explain: Can be treated as a "prove" question, but even in maths you can still relate cause and effect to this word. You don't have to write a huge paragraph of reasoning but use sentences to communicate your answer if it's more convenient to do so.
Find: This is the most arbitrary word. As a standalone, it wants you to do some kind of computation. If it's used more subjectively (e,g, find an expression), then it's self explanatory
Given: Usually comes with "DO NOT PROVE THIS". And don't, because you won't get marks for it. Just take the result for granted.
Justify: A bit more uncommon; basically asking you to further your explanation on something you have proven. This may be related to why a result you proved is unsurprising.
Prove: You are given the final answer. Instead of figuring out the answer yourself, you need to generate a logical series of steps that get to this final result. Under normal circumstances, you should not work backwards (except to check your answer or get some help).
Show that: In practice, means the same thing as 'prove' or 'verify'. However, you should always vouch for 'prove' BEFORE you vouch for 'verify', that is, assuming the result
Simplify: You are given something that's not in its most tidiest form. All you have to do is tidy it up
Solve: You are given an equation of some sort. (Remember, the difference between an equation and an expression is that equal (or inequality) sign.) You need to find the value of the unknown (say, x).
Write down: The weirdest of the lot. You can give an answer without ANY working out if you're capable of doing so.
Verify: Assume what you're trying to prove. Take what you're trying to prove as granted (and anything else you know), and feel free to backtrack to an appropriate result.

And there's also a family of self explanatory words:
Factorise
Differentiate
Integrate
Sketch
Use
« Last Edit: September 16, 2016, 07:01:34 am by RuiAce »

#### Jakeybaby

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##### Re: Verbs and Maths
« Reply #1 on: September 04, 2016, 09:35:17 pm »
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Hence: Implies that you need to use the result from the previous question throughout this question.
Hence or otherwise: Shows that there is more than one way around the question, although, using your answer from the previous question should provide the easiest method of solving.
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#### jakesilove

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##### Re: Verbs and Maths
« Reply #2 on: September 04, 2016, 09:47:14 pm »
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Hence: Implies that you need to use the result from the previous question throughout this question.
Hence or otherwise: Shows that there is more than one way around the question, although, using your answer from the previous question should provide the easiest method of solving.

I have rarely seen a 'hence or otherwise' question in which you should even attempt the 'otherwise'; the only exception being to use 4U methods (De Moivre's theorum) to prove

$cos(A\theta)=Bcos^4(\theta)+Dcos^2(\theta)....$

etc. etc.
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