Sometimes a question will be clear about what you have to do. It might not be easy, requiring some precise manipulation or application of a complicated method, but you at least know what you are meant to do.
Often, though, this is not the case. These are some tips for those points when you simply don’t know where to start with a question.
The main point I would like to make is that you should not be afraid to ty things. Be open to exploring avenues which might turn out to be dead ends, but also might not. Be willing to try the first part, without knowing what you will do after that.
Most STEP questions are not direct applications of a method, and there are usually many possible ways of doing something. Most questions will also require multiple steps which won’t seem obvious from the start. Your thought process must be:
- What does the question want?
- What is something I can try?
- Am I closer to a solution?
The main ways to improve at this are to have more things you can try, and being quicker to recognise whether what you have tried is helpful. This requires a strong knowledge and understanding of the underlying A Level content, as well as a familiarity with STEP questions.
Try the obvious
Time can easily be wasted in the exam by searching for a trick or shortcut which makes the question trivial. This is not a good idea, as you probably won’t be able to think of such a trick by just staring at the question.
Instead, get stuck in as soon as possible doing the ‘obvious’ things, even if it seems inefficient. While doing this, be thinking about alternative ways you can do the question. This is a much more effective method, as you are more likely to think of a better way to do the question while actively attempting the problem. Also, the method which looked like it might take a long time might unexpectedly simplify a few lines in.
Try a simpler problem
If you don’t know where to start with a quite general problem, try a simpler one. This can mean tackling one specific case, or a simpler version of the same problem using smaller numbers or coefficients set equal to 1.
This will help you understand intuitively why something is true or what method you need to use, without getting bogged down with arithmetic and algebra. It can often be relatively easy at that point to generalise any solutions to the more complex problem.
If it seems that the result you are trying to show has come from nowhere and you have no idea at all what route to take, just try anything, especially if you have time left to spare. If you have a function, sketch it, differentiate it, and integrate it. If you have a geometry problem, work out every angle, side, tangent, and radius you can find. If you have a vectors question, calculate dot products, find directions, see which things are perpendicular to each other.
Doing these things gets you actively thinking about the question, making you more likely to think of a method or see something which might lead to a solution.
Working some things out may also get some marks if they could have led to a solution.
Try methods from similar questions
This is where practising lots of questions and past papers is very important. Questions are not often repeated in STEP, but often they do rhyme. Methods which you use in some questions can be used in a variety of other places, especially with topics like integration questions and vectors.
Look forward in the question
Looking ahead in the question can often help you see the route the examiner wants you to take. It can also help you understand the overall structure of the question. If you have spent a lot of the time on the first part of a very long question it might be a sign that you have missed something in the question, or have chosen a poor method. When trying to show something to be true, you can also work backwards, perhaps aiming to meet in the middle.
Leaving and coming back to a question can be very helpful. When you look back at the question, you might see it with a new perspective. Also, some questions are much harder than others, and you may have just chosen one of the more difficult questions when there are easier ones available.
This may seem incongruous to the previous piece of advice, but sometimes you simply have to work through a fiddly bit of algebra or difficult calculation. It may seem as though you are going nowhere, and not getting any nearer to a solution, but then it suddenly works out. You have to practise finding that balance, and knowing when to stop and when to keep going.
I found that with mechanics questions it is easy to get lost in algebra with many different equations flying about, often missing terms or minus signs. This is best stopped by taking a very slow and methodical approach. For instance, write out Newton’s Second Law or the Conservation of Energy equation fully, labelling each term as you write it. And then step-by-step, cancel and simplify, doing as little as possible in your head. Not only does this help you keep track of the algebra, it also helps the examiner find marks even if you made algebraic slips.
STEP questions can often seem daunting, but the most important thing to keep in mind is that the questions are written to be solved in the amount of time you have, with the knowledge you have, and the skill level you have. They can be done, just stay focused and use some of the techniques described above.