Alternative to INDEX MATCH Array Formula to Populate Teaching Groups?

The attached workbook contains dummy data, but is the actual one that I use to sort out language teaching groups from option choices made in the early spring each year: the teaching groups are shown on the second tab, and they use an array formula to draw names from the master list on the first tab:

{=IFERROR(INDEX('Y7 Language Options 2016'!$A:$A,SMALL(IF(LEFT('Y7 Language Options 2016'!$K:$K,1)=MID(B$2,3,1),ROW('Y7 Language Options 2016'!$A:$A)),ROWS($A$1:$A1))),"")}

This works well, but rather slowly, and I have to switch to manual calculation when filling in the choices on the master sheet. What I am wondering is whether there is a non-array formula that I can use that will do the same thing, but quicker? I do not want to change the layout of the workbook and I would much prefer not to have to use helper columns (personal preferences).

Can anyone help?

I didn't download your file.

Reduce the references to entire columns to smaller specific ranges where highlighted:

=IFERROR(INDEX('Y7 Language Options 2016'!$A:$A,SMALL(IF(LEFT('Y7 Language Options 2016'!$K2:$K100)=MID(B$2,3,1),ROW('Y7 Language Options 2016'!$A2:$A100)),ROWS($A$1:$A1))),"")

Also, if you don't know how much data you might have use dynamic ranges.

Thanks, Pete. So, what in this case would you use as a helper column? The formula I'm using is adapted from various things I've learnt here, and whilst I fully understand the INDEX MATCH element, my comprehension of the rest of the formula is somewhat hazy, which makes it difficult at my stage in learning to see alternatives. Thanks for the help!

Thanks again, Pete - I will have a look, however Tony's comment about limiting the ranges (a stupid oversight on my part) has eradicated any slowness in calculation, so the issue is resolved. I'll certainly study the other thread out of academic interest, however.

Good deal. Thanks for the feedback!