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What kind of bike? Are we talking a barely-legal 250 dirt bike, or something more adventure-capable?
What's the conditions like? Weather, bugs, critters, etc?
Honestly I'd roll with a sleeping pad and bag, don't even mess with the tent, but i'm up innamountains. Bring a tarp if you find yourself needing something. Might also consider a hammock. If you're set on a tent, check out some milsurp equipment.
Matches ... great, but bring something else. Lighters are better than matches in just about every way. Remember you've got fuel on the bike to get things going. I carry road flares too.
I find the folding camp saws to be more useful than an axe. Add some rope or mule tape to your pack - clothesline for drying out riding gear overnight.
I'm assuming you're carrying bike tools/parts and riding gear since you don't even mention it... spare master link or two, tube(s), air pump/CO2, extra nuts/bolts, sockets/wrenches/screwdrivers, zipties, etc.
