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Improve your Maths skills

Welcome to the web page for the book “How to Improve your Maths Skills”. On this page you can find fully-worked solutions to all the exercises in the book, and some further, more practical questions for you to try. You can also contact me with any comments, suggestions or queries, and there are a few extra links and things for you to do as well. Please click on one of the links to get started!

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Further things of interest

Further things of interest

Graph paper

No graph paper? Don’t worry, you can download a printable sheet (pdf format) here

The largest prime number known

Although there must be infinitely many prime numbers, the largest prime number we know at the time of writing is the number 243112609 – 1 which is almost 13 million digits long. To try to put this into context, the number of atoms in the known universe is only around 1080, which when written is just 81 digits long (1 followed by 80 zeros). You can help the search for even larger ones! GIMPS is a project allowing ordinary people to run searches on their computer - if you are interested check out their website here

How to remember pi

In the book, we mentioned that a phrase like “hey I want a pizza” can be used to help remember the special mathematical number

π

(pi), as it consists of words of length 3, 1, 4, 1, 5, so

π

is approximated to 3.1415. This is called piphology. Look at

π

to 1000 decimal places in the book – can you create something longer? The longest I know is “how I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics” which gives 3.14159265358979. If you think you have something really good, feel free to send it to me via the contact page!

Tricks for checking factors

There are quick ways to check if a small number divides into a big number. You might not have known all of the following:

  • 2 divides into a number if it ends in 2, 4, 6, 8, or 0. For example, 2 divides into 3456
  • 3 divides into a number if, when you add up all the digits in the number, 3 divides into that. For example, with the number 924, the sum of the digits is 9 + 2 + 4 = 15, and 3 divides into 15, so 3 divides into 924
  • 4 divides into a number if it divides into the last two digits. So for example 4 divides into 5616 because 4 divides into 16 (the last two digits)
  • 5 divides into a number if the last digit is either 5 or 0. So, for example, 5 divides into 5785.
  • 6 divides into a number if both 2 and 3 divide into it (use the checks above)
  • 9 divides into a number if, when you add up all the digits in the number, 9 divides into that. For example, with the number 846, the sum of the digits is 8 + 4 + 6 = 18, and 9 divides into 18, so 9 divides into 846
  • 10 divides into a number if it ends in 0, so for example 10 divides into 3560

 

Learning these sort of rules can make things fast for you (and impress people as well!)

 

Maths can be fun!

I know you probably never thought it, but maths can be fun! There are lots of interesting questions that you can find. If you come across any maths-related questions that you think are particularly interesting, feel free to send them to via the contact link page.



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Contact the author

Thanks for showing an interest in contacting me! Just to give you a little information about me, I'm a Senior Lecturer in Mathematics at Greenwich University in London, having formerly worked at the University of Glamorgan, near Cardiff in South Wales. Although this a varied job, a lot of my work involves teaching mathematics to non-specialists, and this is my main interest, and sparked the idea for this book.

Please click here to contact me.

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