For many, math is a subject that is shrouded in mystery.
You take one look at a question and there’s just an unknown language staring back at you.
Well, math is another language, but just like a language, it has rules.
Rules that can be learnt and followed.
After all, math is a science. The purest science in fact. It is governed by rules that (at least at high school level) cannot be broken.
There is no subjectivity.
Just like a Rubik’s Cube, the solution is 100% possible, you just need to follow certain steps to get there.
You follow the rules of math, you get the marks.
This is the beauty of math, and why it can be a really satisfying subject once you ‘get it’. Once you know the rules and how to apply them, that’s really all there is to it.
There are three types of math questions. Easy, medium, and hard.
Forgive us for perhaps oversimplifying here for a second and bear with me.
An easy question will generally give you the relevant equation or formula and the relevant values.
For instance: “Expand and simplify (x + 3)(x + 2)”
And that’s it. You’re spoon-fed all of the information you need. You just need to know the steps required to, in this case, ‘expand and simply’ a quadratic. (For the teens reading this, you’ll know you should apply the FOIL method to expand this quadratic.)
A medium question will often give you the relevant values and relevant equation or formula, but will ‘hide’ the relevant values. The relevant values are often hidden amongst the words in a word question.
For instance: “If Sarah walks for 2 miles in a north-westerly direction, and then walks for 3 miles in south-westerly direction, how many miles does she need to walk to get back to her starting point, assuming she walks in a straight line?”
This, as you have probably picked up, is a question that requires us to use Pythagoras’ theorem. For those of you that need a refresher, when dealing with a right-angled triangle, a2 +b2 ALWAYS = c2. Where ‘a’ and ‘b’ are the two shorter sides of the triangle, and ‘c’ is the hypotenuse.
This question is harder than our first example, because it requires you to know, on your own, that the formula to use is Pythagoras’ theorem, and it requires you to enter the relevant values into the formula on your own.
So yes, this question is clearly one up on the hardness scale from the first example, BUT — it’s actually not that scary.
You are still GIVEN the relevant values! They are right there in the question, in plain sight. They’re just contained in a sentence rather than spoon-fed to you.
The only thing you would have to recognise on your own in answering this question, is that you are dealing with a right-angled triangle, and therefore Pythagoras is the relevant formula. Sometimes a question like this will even be accompanied by a diagram representing Sarah’s path (ie, a right-angled triangle).
So even though this medium question might look a lot more complicated than the ‘easy question’, you’re still given all of the information you need, and you still apply the exact same rules you’ve learnt in class.
Now, a hard question.
A really tough math question is, well, they can be incredibly challenging.
Often, you’re not explicitly given the relevant values or relevant equation or formula. Like a medium question, the values will be there, but they will probably be hidden in the form of a word question, or veiled in some other way, and it’s up to you to figure out what to do with them.
And further – it’s up to you to figure out what equations or formulae are required to solve the problem. I say equations and formulae — plural — because a hard question may very well require multiple equations and/or formulae to find the solution.
Hard math questions might also throw in irrelevant information into the question (‘red herrings’), and it’s up to you to know what information is required to solve the problem and what is extraneous.
BUT — and AGAIN — a hard math question will still only be based on the rules that you’ve learnt in class.
The question is just dressed up to appear a lot more complicated, and requires you to think on your own more.
I’m not saying this means every student should be able to answer every hard math question. Exams are purposefully written so that not everyone should get 100%. That’s just the game we’re dealing with.
The point of us trying to un-shroud some of the mystery surrounding math questions, is to help you see that math is not as scary as you might think.
Every question thrown at you will be based on what you’ve learnt in class. You will never be expected to have gone away and buried your nose in a math book pitched at a higher year level than you, and you’ll never be expected to have read a biography on Isaac Newton.
Remember, math is based on the rules that you learn in class. Apply the rules, and you’ll get the marks.
Photo credit: William Warby