Well...
You obviously would not be able to maintain the same speed...
Its simple physics, The car needs to exert more force to climb the hill, so if you gave your care the same throttle, it would slow down (because it needs to do more work, but has the same amount of energy)
**loosing 15 mph climbing a hill sounds perfectly logical to me, (especially for a smaller car like the corolla,, which is designed for efficacy, not torque)
The shifting however should occur (shit to 3rd gear to help you climb it (lower gear= more torque/power to climb) *assuming you have a 4 speed
I would check your transmission fluid, it gets old and your transmission does not shift as good.
Hope this helps...
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