One thing to keep in mind about AppleCare, or any other extended warranty, is that it is insurance. As with any other insurance it is intended to cover catastrophic loss. In general it is good to have if you could not afford repair or replacement, but if you can afford to cover the repair or loss yourself ("self-insurance") then you are better off without. Don't forget that AppleCare is a source of profit and not a charity!
According to recent news articles. Consumers Reports states that the MacBook Air has a 7% failure rate in the first three years. With a purchase price of about $1000, if you were to simply toss out a failed MBA without considering repairing it would be a loss of an average of $70/each. Considering they can be fixed free in the first year, if you were to do so, the loss would be even less. AppleCare only provides coverage in the second and third year of ownership.
Since you would pay at least twice that for AppleCare if you can use the Education Store, or over three times that retail, AppleCare is a poor return on investment. Go ahead and take the risk.
Here's my Mac repair history (*-bought refurbished). Not all of these are used by me, but I know their status.
2014 27" Retina iMac -- 15 months, no repairs
2012 i7 Mac mini* -- 16 months, no repairs
2012 i5 Mac mini* -- 25 months, no repairs
2012 15" MacBookPro* -- 48 months, keyboard failed at 1 month, no other repairs (an aftermarket hard drive failed, but would not be covered by AppleCare)
2010 11" MacBook Air -- 62 months, no repairs
2009 27" iMac -- 77 months, display card replaced at 5 years.
2009 base Mac mini* -- 69 months, no repairs
2009 Aluminum MacBook* -- 81 months, no repairs.
2008 24" iMac -- 92 months. Hard drive failed and replaced at 4 years, 4 months.
Remaining systems either sold or given away so I don't know if they are still being used or their repair history.
2009 Mac mini with Snow Leopard Server* -- 56 months. Hard drive replaced at 22 months (would be covered under AppleCare) second hard drive replaced at 54 months.
2009 base Mac mini -- 72 months, hard drive failed and replaced at 3.5 years.
2009 24" iMac -- 66 months. Hard drive replaced under recall. No repairs.
2007 MacBook* -- 50 months until given away. Water damage (would not be covered under AppleCare) at 17 months.
2006 20" iMac -- 39 months. Display card replaced at 2.5 years (would be covered under AppleCare).
2005 12" iBook G4 -- 50 months. No repairs
2004 17" iMac G5 -- 66 months. No repairs
So that's 16 Macs purchased with 3 less than 36 months old. Two required repairs that would be covered by AppleCare. But even there the cost of AppleCare would exceed the cost of the repair.