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 🙂

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The Square Puzzle

Start with an 8 x 8 grid:

Next, enter the number 1 into any box in the grid of your own choice.

You have now got to move around the grid as a knight piece does in chess; you can only move 2 squares up/down then 1 square left/right or vice versa.

Number consecutively each box you land on.

Here’s an example;

From this you can see I placed the 22 in the wrong box – if I had chosen one of the other 3 possibilities I could have continued.

So, can you fill all 64 boxes?

Hexaflexagons!

 From the Daily Post: You have three hundred words to justify the existence of your favorite person, place, or thing. Failure to convince will result in it vanishing without a trace. Go!

For anybody who hasn’t seen any of youtuber Vihart’s videos before, she recently created a series of interesting videos about hexaflexagons; essentially a thin strip of paper folded into a hexagon by first folding it into a line of equilateral triangles, then following the folds in the triangles to make a hexagon.

 

So what? Well, they’re not just any old hexagon, you can turn them inside out (or flexing) to find different sides, and doing this in a certain way means you disocver new sides. Logic would tell you that it would have two sides, but you can make ones with 3 or even 6 sides.

 

This feature is why they should exist – they’re a fun way of teaching maths to children because it’s visual and interactive – you can see for yourself the effects of maths in real-time in your hands, instead of on a whiteboard or screen.

 

Even more useful is their unusual property, with the six sided hexaflexagon, of having the same sides in different states – to understand better what I mean by this video. This allows children to be introduced to diagrams, in this case a Feynman diagram, and helps them to develop their lateral thinking.

Still not convinced hexaflexagons are worth saving? They can also be used to help exaplin A2 Chemistry, in particular the topic of chirality, because depending on how you twisted the original piece of paper, you get a non-superimposable mirror image hexaflexagon – one way the flaps face clockwise, and in the other they face antoclockwise.

 

Above all, they are fun and can be used to improve artistic ability – what you draw on one face will appear different on another so there begins the challenge of a pattern that looks good on all the faces.

You can even make hexaflexagons out of tortillas for a delicious yet mathematical combination!

 

I hope I’ve convinced you that hexaflexagons are worth saving, and don’t forget to cast your vote in the poll below to protect the humble hexaflexagon!

Stopping Distances

 

Instead of learning them off by heart for your theory test, remember that the thinking distance is always the speed (mph) in feet, the braking distance is the speed in feet times a constant, where the constant is 1 plus 0.5 for every 10 mph over 20 mph, then the stopping distance is those two numbers added together – simple really! The method is summarised in the table below: