How to read the music staff with key signatures included?

Question

I am reading an introduction of music theory recently. From the first few chapters I learn the fundamental idea about notes, time signatures, music staff, treble & bass clef, interval and scale. But it is still quite confusing when I try to read the music sheet regarding major and relative minor. Let me break my question in pieces

The book states that the music stave is created with notes (pitches) arranged in major scale. The treble clef tells where the G note should be. Each line and space on the staff is then label each note on major scale one by one. Here is what I get from the book to identify the arrangment of notes for G major

The G clef locates the G note and according to major scale (C-D-E-F-G-A-B-C), I have each note landed as above. My first question is: is it sufficient to identify the above pattern to be a G major?

This question is not bothering me until I finish the chapter about the Circle of Fifths. With the help of the Circle, we could figure out how many sharp should be added to make a certain major key. To make a G major, we should add 1 sharp (i.e. F#) as the key signature as below (I copy that from the book)

If this is correct, I wonder what is the difference between the first and the second staff except for the key signature. The whole chapter of the Circle of Fifths tells that each stop on the circle counted from the top one (C note), and thus if I need a G major, shall I layout the notes on the staff with the key signature as below?

I add more detail on the question. I copy the following stave from the book

which is claimed as a F# minor (i.e. A major relative minor). I saw that there is a common # on the F line so the very last F will be sharped but the very first F is still a F (not F#), so in what sense should we call this F# minor instead of F minor. Thanks.

Answer 1

Firstly, the top stave is misleading. If it states that that is the G major scale, it's wrong. The scale goes from G to higher G, but they didn't include the fact that G major always has an F♯ note, not an F.

That fact can be shown in two ways. By putting the sharp sign (♯) on the F line at the top of the stave, at the beginning of each line, or by putting the same sign just before the F note. Note - the latter will only affect an F note in that bar, on that particular line, whereas at the beginning (called the key signature), it affects every F note in the piece.

This is where books and websites fall down - you can't ask questions, and sometimes there's erroneous information. That's where teachers come in handy.

So the second example is fine.The last example is confusing. There's an F♯ at the beginning, therefore it's the key sig., but the scale notes go C to C. C major has no sharps or flats in the key sig., so really what's written isn't the G major scale. it's not C major either. In fact, but don't worry about it, it's C Lydian...but that's for another day!