Advice for worded problems?

[Liam Hernon]

Hello everyone,
I am interested to know if any of the members of the Atar Notes community has any valuable advice regarding a general approach to tackling the worded problems that are regularly seen in Mathematical Methods exams and SACS, and, if possible, how to strengthen this area of mathematics that many people struggle to improve on, let alone grasp from the beginning.
Cheers

[Alwin]

Hello everyone,
I am interested to know if any of the members of the Atar Notes community has any valuable advice regarding a general approach to tackling the worded problems that are regularly seen in Mathematical Methods exams and SACS, and, if possible, how to strengthen this area of mathematics that many people struggle to improve on, let alone grasp from the beginning.
Cheers

Buy a highlighter.

[b^3]

1. Read the question through as a whole, get an idea of the situation.
2. Read it again, pick out the key information and what is the question asking for? Note this down at the start of the question or underline/highlight it (or both).
3. Draw a diagram of the situation. Picturing it can help a lot, and can let you see when something will be restricted to fit real life (e.g. we can't have negative lengths, so if you had a side of something of length , which say implied something else was length , then you know that .
3. What tools do you have that you can use to manipulate the key information.
e.g. Knowing that if you're given the gradient at a point, that you can pull two pieces of information from it. You can get an equation substituting it back into the original function, and you can get another equation from differentiating the function, then substituting in the value and gradient. They could say, map the height of a roller coaster by a function, and ask you to find the equation for the function give two points, and a gradient at that point.
Otherwise think back to what you can manipulate to get what you're required to get in the end. E.g. For related rates problems, work out what rates you have (the key information), what you want to know, and what other variables you have that are related to what you currently know.
4. Do the working for the question, once you've come to an answer, check whether it makes sense and is reasonable.
5. Conclude and check that you've answered everything that you're asked for.

The other thing is, just getting used to problems, doing past questions, the overall approach is normally quite similar for certain types of questions, it's just a different 'situation'.

Also getting back to 'what tools you have', if you know the formulas and concepts you need to manipulate things, rather than relying on your bound reference, when you get to a problem you'll know what you can apply straight away, rather than having to flick through your reference and not knowing what you're looking for. There's an exercise in the early chapter of the essentials maths book that has a nice summary of relevant formulas that you should know off by heart, and how to apply them (e.g. distance between two points, tangent lines, normal lines e.t.c)

There's probably a little bit more to it than just all of that, but it doesn't come to mind at the moment, I'll add it later if it does. Anyways, hope that helps, and just remember, keep persisting

[Alwin]

I'm sorry for my first reply, allow me to expand a bit more if you would be so courteous and to add to b^3's suggestions.

1. Don't go blindly rushing into a question without reading it in its entirety.
Okay, so you've got your highlighter, now you want to actually not touch it. During the first reading of question, have nothing in your hands. I mean nothing.. I've personally done this too many times, half read the question and start factorising or solving or something fancy then realising the question was actually asking something else.. such as the domain rather than the range

2. Once you've read the question, underline or highlight important words or numbers
I don't mean mark everything as important. For graphs, always highlight the domain, it's so easy to miss in later parts of the question or when sketching. Other important things (but not limited to) are units and the accuracy of your answers, such as 3 significant figures or 2 decimal places. Make sure you get these correct!

3. Now you're nearly ready to start the question!
So look at the action words, like show, or prove, or find, or differentiate. These point you into the direction of the question.

You'll go flying into the question rather than bumbling around!

4. The most important part, double check your answers!
If you found, say the price of apples in the question was $350 a kilo, possibly check your working

Hope it helps!
EDIT: beaten by b^3 again.. well sort of

[Liam Hernon]

Thank you Alwin and b^3 for a thorough, step by step procedure of a good approach to tackling worded problems . I suppose repetition is a very powerful tool in terms of learning. I appreciate both your advice and will try to get use to these processes before exams.
Cheers