How to answer complex unfamiliar questions

[Delis101]

Hi all, how can I answer math methods questions that are complex unfamiliar or the A standard questions? Thanks. Is it with practice? Because I doubt practicing will help because the questions are unfamiliar. Thanks

[RuiAce]

It's unfamiliar in the sense that you're not meant to have seen the question type at all, unless you've been quite familiar.

But it's examinable, because it uses techniques that you've been taught throughout the course.

In the exam, you can usually single out the complex unfamiliar questions, by either
- noticing an absurdly high mark allocation,
- seeing a significantly large wall of text without much guidance, or
- looking at the question and realising that the method/technique to solve it is not immediately obvious.

According to the syllabus, this is the main difference between complex familiar and complex unfamiliar.

all the information to solve the problem is not immediately identifiable; that is
­- the required procedure is not clear from the way the problem is posed, and
­- in a context in which students have had limited prior experience.

all of the information to solve the problem is identifiable; that is
-­ the required procedure is clear from the way the problem is posed, or
­- in a context that has been a focus of prior learning.

Seeing as though the useful information in the problem is not made obvious for you, somehow you need to find it along the way. A good scaffold on how you can approach these problems is the following:

1. Start by at least singling out what little information you have been given. Be able to understand and interpret information off any given diagrams. Identify what goes with what (for example, which variables are presented in the table of values, what is the equation of the graph, etc.).

2. Make it very clear what your final aim is. What is the goal in the question? Are you trying to find some maximum/minimum value? Are you trying to solve some kind of equation?

3. With both what you know and what your target is in mind, consider what little things you can do to help yourself. For example, can you draw any more diagrams? Can you annotate diagrams? Does the information you have right now lead you to some equation or formula that you feel is appropriate for use? (E.g. binomial distribution results, cosine rule, area under curve etc.)

4. Go a step further and consider if there's any useful techniques. For example, in exam 2 is there anything that your calculator would make trivial for you? Or is now a good time to start solving an optimisation problem?

5. Start heading towards the goal. Wrestle through as much of the computation as you can, and try to now derive something useful. If you find you reach your goal, is awesome. If not, you may have just made a few more steps. (You can begin to suspect that you're straying too far when for example, the numbers get needlessly ugly, you probably filled up too much writing space, or when you realise you've attempted to answer something you suspect is 100% unrelated to the goal.)

6. Rinse and repeat, until you reach the goal.

Many of the later questions in both sample exams 1 and 2 provide questions that I would argue are similar to the complex unfamiliar calibre.

Note that practice is perhaps unlikely to directly contribute to your abilities in solving the complex unfamiliar. But it does indirectly contribute a little, in the sense that you should become more accustomed to actually using specific techniques. What's not-so-easily learnt is knowing when to use what.

[Bri MT]

If you want to practice this style of question, the last question of exam 1 in each VCE methods exam are known for requiring more problem solving application skills and not being "plug and solve". Even though your questions won't be exactly the same, I do still think it's useful to practice working with this style of question.