Guitar Exam - HELP !!!

I have a practcal exam on guitar for an English University application and I have been sent a spec of things I should do. Trouble is I don't fully understand it. It keeps referring to the number of shapes I have to play things in - what is meant by shapes? For example - here is my spec:

Major Scale - 5 shapes, any key
Pentatonic Scale - 5 shapes, major and minor, any key
Melodic minor scale - 2 shapes (r/6, i.e. root on the 6th string and r/5) any key.
Harmonic Minor - 2 shapes (r/6 and r/5) any key
Modes - Dorian, Aeolian, Mixolydian (r/6 and r/5) and key
Arpeggios - major 7, dominant 7, minor 7 b5, minor 7 (r/6 and r/) any key

I also don't understand what the modes are and what all this r/6 and r/ etc means.

Is there anybody out there can give me some advice or even better refer me to a book that has these things in?

I appreciate any advice anyone can give me.

Kind regards

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The whole music thing is a huge convoluted monster that turns more beginners away than anything else.

Most scales are learnt using 'shapes' (especially ones like the Pentatonic scale). Although the word 'penta' means five, this does not refer to the number of shapes but the notes in the scale, but your question is what are the 'shapes'?

Imagine trying to learn every note of a scale all over the fretboard in one big lump - to make this a lot easier, scales can be/are broken up into user friendly chunks and to use the pentatonic scale as an example, there are five shapes that all link together. The idea being, that you learn one shape, then the next and so on until you know them all. The good thing about this, is that the shapes remain identical no matter what key you decide to play in, so learn all five shapes and you know all 12(15) keys.
The other point is that the shapes remain true for both major and minor keys, the only difference being that the minor key is situated three frets lower - so if you are playing in C major, the relative minor key is 3 frets along at A.

This is highly simplified and apologies if it just makes the water even more muddy.

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