# Blog

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• The Golomb Sequence
In previous blogs, we’ve looked at some interesting integer sequences. We started with the daddy of all integer sequences, the Fibonacci sequence. Then, the Look and Say sequence. Today’s sequence is the Golomb sequence. The sequence is named after its founder, American mathematician Solomon Golomb. Golomb was not only an… Continue reading The Golomb Sequence
• How to fix a calculator that is in the wrong mode
If you’re studying GCSE or A Level maths, you will be spending a lot of time using a calculator. Sometimes by accident (or by a friend getting hold of it!) the mode of a calculator is changed and the results don’t display in the way you want it to. You… Continue reading How to fix a calculator that is in the wrong mode
• Perfect numbers
“If you look for perfection, you’ll never be content” There are very few things that are perfect in the world. But in maths, there are perfect numbers. What is a perfect number? To describe what a perfect number is, we first need to know what a factor is. The factors… Continue reading Perfect numbers
• The Capture-Recapture Method – how to estimate the number of fish in a lake
In the previous blog, I explained the Difference of Two Squares, as this mentioned in the Advance Information. Another topic that is mentioned specifically in the Edexcel Advance Information for the Summer 2022 GCSE exams is the Capture-Recapture Method. This will be very easy to prepare for as the questions… Continue reading The Capture-Recapture Method – how to estimate the number of fish in a lake
• The Difference of Two Squares
Mentioned specifically in the Edexcel Advance Information for the 2022 GCSE exams is something called the Difference of Two Squares. So I decided to write a blog about it. I’ve already touched on factorising quadratics in these two blogs – Factorising Quadratics (Foundation) and Factorising Quadratics (Higher). In those two… Continue reading The Difference of Two Squares
• Advance Information for Summer 2022 GCSE Exams
Due to the disruption to schooling caused by the Coronavirus pandemic, exam boards have provided advance information for the upcoming Summer 2022 GCSE exams. This consists of: a list of topics that will come up in the exams, allowing students to focus their revision on fewer topics a formula booklet… Continue reading Advance Information for Summer 2022 GCSE Exams
• Times Tables App Review – Math Ninja
For a child in primary school, there is nothing more important in maths than knowing your times tables. It will make everything you learn in the subject so much easier. If a child needs to write out their times tables every time they need to work out something like 6×4… Continue reading Times Tables App Review – Math Ninja
• How to use triangles to remember exact sin, cos and tan values
If you’re taking the higher maths GCSE, there are certain values of sin, cos and tan that you need to know off by heart. Luckily in two of the three exams you will be allowed to use a calculator, but in the non-calculator exam you will need to know the… Continue reading How to use triangles to remember exact sin, cos and tan values
• A more efficient method for listing the factors of a number
In this blog I will show you the most efficient way to list factors, and explain why this is a good method. What is a factor? The factors of a number are numbers that you can divide the number by and get a whole number result. For example, 5 is… Continue reading A more efficient method for listing the factors of a number
• GCSE and A-Level Results 2021
Unfortunately due to the pandemic, GCSE and A-Level exams were cancelled again in 2021. Grades were awarded based on teacher assessments. 746,880 students were entered for GCSE mathematics and 97,960 for A-Level mathematics in 2021. The GCSE results were very similar to the previous two years, with a slight increase… Continue reading GCSE and A-Level Results 2021
• The Look-and-Say Sequence
In a previous blog I looked in more detail into “the daddy of all integer sequences” – the Fibonacci sequence. While the Fibonacci sequence is an impossible sequence to match up to, there are plenty of other intriguing integer sequences out there. So if you can deal with the disappointment… Continue reading The Look-and-Say Sequence
• How to represent a recurring decimal as a fraction
What is a recurring decimal? Some decimal numbers are easy to deal with – 0.5, 0.3, 0.25 etc. These are easy because they do not have recurring digits. Converting between these numbers and fractions is easy. Recurring decimals are numbers which have a repeated digit or sequence of digits –… Continue reading How to represent a recurring decimal as a fraction
• Divisibility rules for numbers 7-12
Following on from the previous blog, which showed you a series of tricks you can use to determine if a number is divisible by the numbers 2 to 6, this blog will build on this for the numbers 7, 8, 9, 10, 11 and 12. Rule for 7 This is… Continue reading Divisibility rules for numbers 7-12
• Divisibility rules for numbers 2-6
In this blog I will show you how you can easily check any number is divisible by the numbers 2-6. So simple that should your mental arithmetic be strong enough, you will be able to just take a glance at the number and know immediately whether it is divisible by… Continue reading Divisibility rules for numbers 2-6
• The Fibonacci Sequence and the Golden Ratio
We have previously touched upon Fibonacci sequences when discussing different types of sequences for GCSE maths so you may already be familiar with them. This blog will go into more detail and show you some more uses of the Fibonacci sequence that you probably wouldn’t expect! What is the Fibonacci… Continue reading The Fibonacci Sequence and the Golden Ratio
• The Problem with Solving Inequalities in GCSE Maths
In this blog, I will explain one of the most common mistakes I see made by GCSE maths students. We have already seen how to solve equations, but you also need to be able to solve inequalities in GCSE maths. What is an inequality? There are two inequality signs you… Continue reading The Problem with Solving Inequalities in GCSE Maths
• 5 things that make a good maths tutor
Following on from our previous blog on why university students make excellent maths tutors, in this blog I will list 5 traits that every good maths tutor has. Having hired over 30 tutors since starting Metatutor, I know a good maths tutor when I see one. I am leaving out… Continue reading 5 things that make a good maths tutor
• Triangles in GCSE Maths
Triangles come up a lot in GCSE mathematics. And there are a variety of different methods that can be applied to questions. If you are given a triangle with a missing side or angle, there are four different methods that you can use to find the missing information (bold means… Continue reading Triangles in GCSE Maths
• A guide to trigonometry (SOHCAHTOA) – Part 2
In the last blog, I introduced a method for using trigonometry to find the missing side in a right-angled triangle. This blog will build on that and show you how to find the missing angle in a right-angled triangle. I would recommend reading that before this one for an introduction… Continue reading A guide to trigonometry (SOHCAHTOA) – Part 2
• A guide to trigonometry (SOHCAHTOA) – Part 1
Following on from the previous blog on Pythagoras’ theorem, this blog will be a guide to solving trigonometry questions. This guide will show you how to use trigonometry to find a missing side in a right-angled triangle. The next blog will build on this idea and show you how to… Continue reading A guide to trigonometry (SOHCAHTOA) – Part 1
• Easy as Py – a guide to Pythagoras’ Theorem
a2 + b2 = c2. That’s Pythagoras’ theorem. What it says is that in a right-angled triangle, the sum of the squares of the two smaller sides equal the square of the longest side (or hypotenuse). From my experience, most GCSE students understand what Pythagoras’ theorem is, but when it… Continue reading Easy as Py – a guide to Pythagoras’ Theorem
• 5 more maths magic tricks
Following on from the previous blogs about the number 6174 and the (not-so) magic number 10, here are 5 more cool maths tricks that you can use to impress your friends. Trick 1 For this trick, pick a three digit number with repeating digits (eg. 222 or 999)Add up the… Continue reading 5 more maths magic tricks
• Distance, speed and time calculations
In this blog, we will look at distance, speed and time calculations and I will show you a handy trick that will help you to remember how to calculate them. First of all – distance, speed and time are all related. If you have two of them, you can use… Continue reading Distance, speed and time calculations
• GCSE Results 2020
Due to the Coronavirus pandemic, 2020 has not been an orthodox year for students taking their GCSEs and A-Levels. To many students’ disappointment, the exams were cancelled and grades were awarded based on a mixture of mock results and teacher assessment. Due to this, it was always inevitable that some… Continue reading GCSE Results 2020
• 5 reasons you should hire a home maths tutor
At Metatutor, we provide home one-to-one face-to-face maths tuition. In this blog, I will outline some of the many benefits this service can have on a student. I firmly believe that every student benefits from having some extra home support – it doesn’t matter whether you are a student targeting… Continue reading 5 reasons you should hire a home maths tutor
• A guide to solving linear equations
In this blog, I will show you a method for solving linear equations. Solving equations is the most useful aspect of algebra you will learn at school. Take the example below… Solve 3x + 1 = 13 The x is just a number that we don’t know yet. Solving an… Continue reading A guide to solving linear equations
• Hailstone Numbers
In our blog we’ve already covered Kaprekar’s constant, as well as the (not-so) magic number 10. Here’s another cool little trick to sink your teeth into… First, pick a positive integer (whole number). Now, we are going to generate a sequence of numbers, starting with our starting number. Each term… Continue reading Hailstone Numbers
• How to find the nth term of a quadratic sequence
Following on from our previous blogs on identifying different types of sequences and finding the nth term of a linear sequence, in this blog I will show you how to find the nth term of a quadratic sequence. It is important to note that this topic is only examinable on… Continue reading How to find the nth term of a quadratic sequence
• How to find the nth term of a linear sequence
Following on from the last blog on identifying different types of sequences, in this blog I will show you how to find the nth term of a linear sequence. This is a relatively simple process, but is incredibly useful. What is the nth term, and why is it useful? First… Continue reading How to find the nth term of a linear sequence
• Different Types of Sequences for GCSE Maths
If you’re studying for your maths GCSE, you will have encountered a lot of different sequences. For both foundation and higher GCSE mathematics, you need to be able to identify these different types of sequences: 1. Linear sequences Linear sequences are the most common and simplest type of sequence you… Continue reading Different Types of Sequences for GCSE Maths
• 5 reasons why university students make excellent maths tutors
At Metatutor, all of our tutors are university students at either the University of the West of England or University of Bristol. I purposely choose to only take on university students because I believe that they make excellent maths tutors, and our results certainly back that theory up. Here are… Continue reading 5 reasons why university students make excellent maths tutors
• Turning dragons into chihuahuas – why factorising is useful
Following on from the two previous blogs on factorising quadratic for foundation tier maths and higher tier maths factorising, in this blog I will use an example to explain why factorising is useful and how it will help you pass your maths GCSE. When you were first taught about putting… Continue reading Turning dragons into chihuahuas – why factorising is useful
• How to remember exact sin, cos and tan values
If you’re studying for your maths GCSE, there are certain values of sine, cosine and tangent that you need to know off by heart. Luckily, in two of the three mathematics exams, you will be allowed to use a calculator, but in the non-calculator exam you will need to know… Continue reading How to remember exact sin, cos and tan values
• The Magic Number 10 – A mathematical trick
Here’s another maths magic trick that you can use to impress your friends. This trick works for ANY number that you choose. Follow these instructions and you will always end up with 10. Pick a number. Multiply it by 3. Then add 30. Then multiply by 2. Then divide by… Continue reading The Magic Number 10 – A mathematical trick
• Factorising Quadratic Expressions for GCSE Maths – Higher Tier
Following on from the last blog on factorising quadratics, here is a guide to factorising quadratics of the form ax2 + bx + c, where a is greater than 1. This will only be tested on the higher tier GCSE maths exam, so if you’re studying foundation, this blog is… Continue reading Factorising Quadratic Expressions for GCSE Maths – Higher Tier