Modulus Algebra (FP2 Complex Numbers)

Modulus algebra is something that is not taught in any of edexcel’s textbooks but is rather assumed knowledge so here’s a little example if you get stuck like me when the mark scheme doesn’t explain the working step by step!

3 = [2i/w -3i]

3 = [(2i – 3iw)/w]

3 = [2i – 3iw]/[w] This means exactly the same as the line above except now you can move [w] to the other side

3[w] = [2i – 3iw]

3[w] = [2 – 3w][i] By looking at an Argand diagram it’s easy to see that [i] = 1

3[w] = [2 – 3w]

3[w] = [3w – 2][-1]

3[w] = [3w – 2]

3[w] = [w – 2/3][3] You could combine this step and the previous step and simply take out [-3] but I did both steps for clarity!

[w] = [w – 2/3] The solution of this is obviously a bisector of the points (0,0) and (0, 2/3) with the equation of the line being u= 1/3

I hope this has helped! If there’s any other maths questions you are stuck on please leave a comment and I’ll do a post on it 🙂

Disney to the rescue!

Thanks to my classmates I’ve found the best way to learn german vocab (or vocab for any language for that matter) – Disney songs! My current favourite is ‘When will my life begin’ from Tangled, and ‘Zero to Hero’ from Hercules actually sounds even better in German – the lyrics are hilarious, but you really need to watch it to know what I mean! So if you’re struggling to learn words or are bored to death of memorising lists give it a try – for pretty much every decent Disney song you can find the foreign language version with subs and translation 🙂

How To Write A Personal Statement: Top Tips

Having just gone through the UCAS application process I thought I should share what I learnt from the experience:

  • Plan it with as much vigour as you would an essay: Before you even begin to write your personal statement, it helps to first draw a mind map (or make a list if you’re like me and can’t stand mind maps!) including a summary of everything you might include in your personal statement, such as why you want to study *insert your subject*, wider reading, relevant activities and hobbies. If you have a fairly long list it may be a good idea to ask your reference writer to include some parts of your list in their reference, so you have more characters to write in depth in your statement.
  • Don’t worry about the opening and closing paragraphs:These two paragraphs are arguably the most important and so are notoriously difficult to get just right straight away, so I would advise you to initially concentrate on the main body of text, and then it will become clearer what would work at the beginning and the end.
  • The majority should not be what you do outside of school: although these are important to include, about 60-70% should be about why you want to study the subject(s) you’ve applied for. The admission tutors are looking for enthusiasm for their subject and will want to know what specific topics you enjoy/ are interested in.
  • Include wider reading/relevant academic activities: It is often a good idea to find one book relevant to the subject you wish to study (or two if you’re applying for a Joint Honours/Natural Sciences) that interests you, and that you would be comfortable talking about if you were interviewed. It shows that you don’t just learn what’s given to you in the textbook, but have a genuine interest in the subject (it can also create an interesting introduction if you’re stuck for original ideas). By academic activities I mean Model United Nations (MUN) for students studying subjects such as Politics or Economics. For mathematicians there is the UK Senior Maths Challenge, and for chemists there is the C3L6 online challenge and year 12 paper. There is also national Olympiads in many subjects you could take part in; ask your teacher for more details. Also mention any relevant (field) trips you’ve been on, and any relevant school clubs, for example at my school there is an after school club to build a cosmic ray detector. Perhaps you could start a club or society one lunchtime a week if there are not many clubs at your school – it looks very good on your UCAS application.
  • Use a Thesaurus! :Once you have most of what you want to say on paper (or on a screen), use a thesaurus reword parts to make it sound more impressive/sophisticated. Phrasing is important – the person reading your statement will get bored if it’s not interestingly worded and it will be quickly forgotten amongst other applications. It will also show how good you are at essay writing – an important skill in every subject, as most students will need to write an essay of some sort – be it a write up of an experiment or a dissertation – at some point.
  • Ask teachers/friends/parents etc to proof read it and make suggestions: You and your reference writer will have gone over your statement so many times that neither of you will are likely to notice small spelling mistakes or grammatical errors, so it’s a good idea to get someone who has not seen your statement before to check it over. Also, give copies to your family/teachers etc – they will be more than happy to take a look and will give you constructive feedback, such as if you’ve missed something out – this is particularly helpful if you’re stuck and have no idea which direction to go with your statement.
  • Read the statements of previous successful applicants for your subject: Take note of how they have structured it, what they have included it, and how they have worded it to turn what could be a whole paragraph into a single sentence. However, don’t read too many and don’t keep re-reading any of them as you may accidently copy too much and your statement may be flagged by UCAS’s checking software as somebody else’s work.
  • Remember that a new paragraph on UCAS = 2 characters: I was caught out by this; Word said my statement was exactly 4000 characters, but UCAS wouldn’t let me upload it as it was apparently 12 characters too long. It’s actually quite easy with some clever rewording in a few places to cut characters out, but to save yourself hassle, make sure your 2 characters under the limit per paragraph you wish to have. Don’t stop using paragraphs because of this though – one large block of writing is difficult to read and appears unstructured – not the impression you want to give.