Making Hard Questions Easy: General Approach

4.3 General question approach

With that covered, we can now look at my generalized recommended question approach, with reasonings for each step. This approach applies to all questions each question type will have a specific topic question approach too.

Set up the problem

This first step you can do no matter what question it is, you will always be successful at this step and it will always be the first thing you do. Why is this important? It means, no matter how hard a question may be, you already know the first thing you are going to do and you know you are going to achieve it. This immediately takes some of the instant panic reaction away from seeing a hard question because instead of thinking I have no idea what to do! you know exactly what you are going to do, at least at first. And by the time you ve done this bit, it is often much easier to make progress

It also standardizes a lot of questions if you are applying the same approach every time, to every type of question, you get very good at it and a lot of questions are actually solved just by doing the standard easy set up parts.

What exactly does setting up the problem consist of? This consists of everything you can possibly do for any question before actually worrying about what it s actually asking you to do or how you will do it. It often consists of:

Drawing an accurate, large diagram with all information labelled on it

Going slowly through the question and underlining/numbering each bit of information that is given to you

Translating said information explicitly into its most useful form and extracting all possible use from it

Some information may not have an immediately clear use make sure to circle it or otherwise label it to show it has not yet been used

Defining all unknowns and writing down any equations you already know that will likely come in useful If possible, writing down a vague plan of the question and what different tasks the question is likely to involve

Make sure to extract all information from a problem and have everything clearly defined, written down and explained (don t be scared of using words and short sentences). Take the time to actually set up problems and write out what you are doing in a way that you would understand if you came back to the problem in a week s time with it half solved. This happens to also be a way such that it is extremely easy for an examiner to follow your working and give you maximum credit. Work out as much information as you can in as simple a form as possible before even worrying about how to solve the question. Often this can make even seemingly difficult questions completely trivial.

If you manage to get into the habit of mastering that first step, good news, you re 50+% done with essentially every question you come across. This step is that important. This step should also be done slowly, carefully and thoroughly. The set up is the key part of every question. A good set up makes harder questions much, much easier. Also, time spent on setup is saved twice over in reducing time confused/looking for how to complete a question and time looking for errors. This is the part in which you are careful to define everything properly and note down/take care of things that would be likely to cause errors later on if not accounted for properly.

There are numerous benefits to approaching problems in this way, not least that you will have usually netted yourself a large chunk of the marks just by doing routine things and labelling diagrams, which is already far better than 0.

However, the main benefit is that this is always your first step and you can always do it. So you never have to worry about how to solve a question until you have done this step. At which point, solving the problem is often far easier/more obvious. Additionally, you will find that this method automatically provides a structure and path that is often missing from the harder questions it should make (12) mark questions feel no different really to a question split into 4x(3) mark parts.

This method of setting up questions first also encourages something else which is important to get into the habit of doing: slowing down and considering which approach will be best or where various approaches are likely to lead. One major common cause of both unsolved exam questions and massive amounts of wasted time is due to students jumping in to questions far too quickly and not considering whether a certain step is likely to be helpful/quick or if there is a better option available. Students are often very quick to, for example, expand out all brackets in an answer, without first considering whether or not that will actually simplify things or just lead to a horrible algebraic mess.

Before embarking down a path, it is worth quickly running through in your head where it may lead and whether there are alternative options that might be a better idea. See a tan squared in the question? Before immediately converting it to sin squared over cos squared, consider whether sec squared minus one might be more useful. See a product of two functions in an integration question? Consider whether one is the differential of the other before diving into integration by parts.

By taking just a moment to consider what you re about to do before diving into the algebra, you can often avoid questions turning into hopeless timewasting algebraic messes that lead nowhere.

2. What can I possibly do? / What s in my toolbox?

At this stage, if it is not obvious what to do, ask yourself a different question. Forget about what the question is asking you for, just look at what is on the page and ask the extremely basic question What can I possibly do?

You might not know what the right choice is, but there are a very limited number of paths you can go down for most questions write out your possible toolbox in a list if necessary and look through it to figure out if any tools might come in helpful/allow you to make progress. The question What can I try/what can I possibly do? is the most powerful question you can ask yourself in solving questions in which you are not sure what to do. You will often find that there are only 2-3 possible choices of what you could possibly do with the information you have and by simply testing them the answer drops out.

After you have done this, or to help guide you with this approach, you can also sometimes find it helpful to ask yourself

3. What do I need? in order to finish this problem, and write that down explicitly. Then you can think about how you might get an equation with that piece of information in it.

At this point, your next step is to ask:

4. What haven t I used? and try to figure out how you might use the remaining information

Finally, if the route is still not clear at this point:

5. Use the answer/work backwards This is often the last thing to try, but can come in handy for certain questions, and can often help answer the question What do I need?

In summary, the method is as follows:

Set up: TAKE YOUR TIME - MOST IMPORTANT STEP

a) Diagram

b) Translate all info given fully, keeping track of what has/hasn t been used

c) Write down and define everything you will be working with: unknowns etc.

d) Complete all routine steps possible

e) If possible, write down a vague question plan and split tasks into labelled parts

What can I do?

What do I need?

What haven t I used? Use the answer - work backwards and play around

4.4 Partial answers

An additional final point is that maths questions are very much not all or nothing marks wise. It is usually possible to pick up roughly half the marks to a question just by working out the easy things and writing down the obvious . If you get stuck on a part, you can often still do later parts or do some more working as if you had solved earlier parts.

The grade boundary for an A in 2019 for Edexcel Maths was 55.0% __ that does not mean you had to get 55% of questions fully correct. It actually means, if you were clever and maximised your partial marks, that you could probably get an A without even being able to finish the vast majority of the questions. Partial answer maximising is very useful, especially on harder papers with low grade boundaries!