How To Solve Maths Equations

Ever wondered how to solve maths equations? How on earth does the smartest guy seem to get all the answers? How do they achieve success in maths so effortlessly?

In this article, I’ll show you how to approach most, if not any maths question successfully. In a previous article I wrote for ExamsSolutions, I compared how to solve maths equations, to baking a cake.

]I spoke about using definitions and set methods as ingredients to come up with a tasty solution! I admit, at times it might be harder than baking a cake, but I promise you, there is always a method to the madness of maths!

I’ll show you exactly how I do it.

Ready? Set… 


Algorithms are by definition a set of rules or processes to be used to solve a problem. This would, therefore, involve a pattern and applying the algorithm. Algorithms are often used in computer programming to create functions. There are many uses for algorithms with maths equations being a great example of these.

Search engines, like Google, also use these to display the most relevant results to our online searches.

Although an algorithm ensures an accurate answer, it may not always be practical as it can be a very time-consuming process.

How to approach a Maths Question

1. Know your stuff

In maths, you will often encounter questions where the finish line looks blurry at the start. How do you get there then you might wonder. My initial focus is always to make sure that I know the foundations for every single topic.

These foundations are:

  1. Definitions eg: Moments = Force x perpendicular distance
  2. Theorems: Circle theorems eg ‘The angle at the centre of a circle is twice the angle at the circumference’.
  3. Key Statements and results: e.g. the domain of a function f(x) = the range of f^-1(x) if it exists.

A function is increasing if f’(x)>0 for all x on its domain.

2. Keywords

In statistics, the word ‘given that’ is a word usually associated with conditional probability.

In calculus, the word ‘turning point, maximum or vertex’ is usually associated with differentiation or completing the square.

Methods-which includes things like:

Without knowing these, you simply can’t be confident. When you need to solve maths equations, confidence is key. Confidence can only be developed by constant practice and subsequent success.

So if you don’t know your stuff, or need a confidence boost, feel free to contact us so we can help you out!

3. Connect the dots

After you have made the effort to learn the ‘how-to’s’, definitions keywords and results, from there on, it’s a case of how well you’re able to connect the dots and reach the finish line.

How to solve this maths equation for AQA & OCR A-level maths

for example :

‘When the polynomial f(x) is divided by x-2, the quotient is the same as the remainder. Prove that f(x) is divisible by x-1’

At first glance, I have absolutely no idea/ foresight on how I’m going to prove this.

At least make an effort and underline the keywords 1st and then try and think of a method to use.

Ermmm …. I’m not a quitter, so I’ll go for 2.

My Keywords

In order to remind myself of what a quotient is, I would do a very basic example using numbers (because I know how numbers work more than polynomials) which have a remainder when you divide them e.g. 7/2 = 3r1

So, what’s the relationship between them all?

Well 7=2*3 + 1If 2 is the divisor and 1 is the remainder, I now remember that 3 must be the quotient!

Comparing this to polynomials, I can now say that

Polynomial = Divisor*Quotient + Remainder




***Never be afraid to use a basic example to try and solve harder problems[/vc_column_text]

[vc_column_text]In the question, we are told that Quotient = Remainder

Because we don’t know what this is, we can just call it some function say g(x) (This is the CREATIVE bit)

(x-2) is clearly the Divisor and f(x) is clearly my Polynomial

If we sub in the expressions, then:

f(x) = (x-2)g(x) + g(x)

I see 2 common expressions g(x) so let’s factorise and see what we get:

f(x) = g(x)(x-2+1)f(x) = g(x)(x-1)

This shows that x-1 is indeed a factor of f(x). Proven! Done!

This is an example showing you how I could solve a maths equation by using what I know to get me to the unknown.

Therefore I get to solve the maths equation successfully.

It’s not easy at the start, but that’s where we step in as teachers and tutors to guide you along the way.

‘ 10,000 hours of deliberate practise are needed to become world-class in any field ‘ – Malcolm Gladwell’s 10 000 hour rule

So how do you solve maths equations?

You really don’t need to be a rocket scientist to get a 9 or an A in GCSE and A-level Maths.

You need to know your stuff. This means lots of practice.

The essential element is time. There is really no hard and fast rule to being a successful mathematician. Even those that are so-called ‘smart’, spend hours and hours in learning new concepts and developing muscle memory by using different techniques to solve problems.

If I can do it, so can you.

You have to be willing to spend time to learn and practice! If you want to know how to approach any maths question you need some kind of starting point. These are the basics.

Once you have a starting point you can navigate to the end result.

Why not invest in online maths tuition with us today. The benefits will amaze you and the results will show in your grades.