The 2nd pattern A Major scale uses the A shape open chord (Big surprise). When looking at the open A chord, the root notes are on the open A string and the 2nd fret G string.
A
Important: The notes used in the A Major scale are A B C# D E F# G#, there are three sharps in the A Major scale.
If we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X and the thick black double lines represent the nut.
| $1.0.$4.0.$5.X.$6.0 || $3.1 | $1.2.$2.2.$3.X.$4.2.$5.2.$6.2 | $2.3 | $1.4.$3.4.$4.4.$5.4.$6.4 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing this scale on the guitar, I normally start on the lowest pitch root note, the open A string, and play up to the highest pitch note of the scale, 1st string 4th fret, which is a G#.
| $5.0 2 4 $4.0 2 4 $3.1 2 $2.0 2 3 $1.0 2 4 |
Descending back to the lowest pitch note of the scale, the E on the open bottom E string.
| $1.4 2 0 $2.3 2 0 $3.2 1 $4.4 2 0 $5.4 2 0 $6.4 2 0 |
Then back up in pitch to the A root note on the open 5th string.
| $6.0 2 4 $5.0 |