What’s Integrity for?
It’s a home for all the maths questions I’ve created, guides I’ve written, and various other mathematical adventures. You can find out more in Synopsis.
Who wrote these questions?
Me!
All of these questions were hand-crafted from scratch. A few will no doubt have been inspired by ideas or tricks from other questions I’ve seen before. And of course, this is maths, so there’s no such thing as an ‘original question’ anyway.
What are these questions for?
Some, such as the Addvent questions, I created for events and competitions at school.
The rest I just come up with for fun, whether to experiment myself or challenge my friends.
Writing questions is a pretty unique and fun way of deeply delving into a topic – you really learn a lot. You come to appreciate a lot of things you otherwise wouldn’t know, and start thinking about the process in a different way.
How did you write these questions?
Honestly, I don’t even know. I just gave it a shot, and it turned out I quite enjoyed writing maths problems! It’s a creative and problem-solving process that is satisfying in a similar way to software development or music production.1
A lot of questions are simply the results of permuting different functions – throwing stuff together and seeing what works. Some are built from the ground up with an intended method or track in mind.2 A rare few come to me in dreams.3 Others take hours of painstaking engineering.3
Why are there so many questions?
Oh my days, I actually love creating questions (especially integrals) too much. I came up with like 16 on a coach journey once. They just keep on coming, y’know. You’d think I’m approaching a point where I’ve tried most of the common combinations of the functions in maths, but nope!
It’s just fun, what can I say.
Why are the questions so difficult?
Well, the vast majority of integrals on Integrity are made to be nontrivial. I want this site to be a source of high-quality, thought-provoking, handcrafted integrals that aren’t just a test of speed.
Some questions are only tough because they have a very specific and obscure trick.
This is less true for the Completing the Square questions, but how hard can completing the square get…
Why are the questions so easy?
Okayy, can’t fault you for being too good at maths! The integrals are definitely above A-level level, but I wouldn’t say anything above A-level Further Maths knowledge. (Can confirm: my A-level maths friends could solve most of them.)
And Addvent was for Addvent, there’s a reason the questions were accessible.
I’ve finished all the questions, do you have any more?
Hello!! Congratulations on solving so many, and tysm for using Integrity!
I’m regularly adding more questions (because I can’t seem to stop writing more), so just check back in a bit and there’ll almost certainly be more waiting for you.
Can I use these questions?
Absolutely, you’re more than welcome to! For more details, see Licence.
Why would I want to practise integration?
See Why Integrate?
Why would I want to practise graph drawing?
See Why Draw Graphs?
Why would I want to practise completing the square?
How was the site built?
See Synopsis.
How are the questions stored?
See decoded.
What are the question codes?
They’re unique identifiers for each question which encode its topic, purpose, year etc. You can find out more in Docs.
Is dark mode available?
Yep! The site is synced with your local system’s theme, so just enable dark mode on your device.
I decided against allowing different themes on this site, since the focus is on maths :v
I’d like to request a feature please!
Just drop an Issue on Github, and if I like the feature, I’ll get round to implementing it!
Are the questions checked?
All integrals are checked with Desmos before being added to Integrity, if possible. For those where the solution is difficult to plot, or are just generally horrific, solutions have been verified with either WolframAlpha↗ or my mathematically inclined friend iTechnical.
Uhh, a question has an incorrect solution?
Ohhh dear, I’ve done it again. Definitely drop an issue on GitHub and I’ll fix it as soon as I can.
Uh, there’s a LaTeX rendering error?
Oh dear, the parsing engine’s flopped again. Or more likely, I’ve made some typo in the source LaTeX. Drop an issue on GitHub and I’ll be right on fixing it.
Uhhh, the site’s broken?
If the loading overlay’s taking a while, it almost certainly means JavaScript’s broken or crashed. This seems to happen very easily on Safari, but rarely on Chrome. I do check the site after each deployment, so if it’s immediately unusable I will go and fix it.