From my house to the street,

slight uphill driveway -> stop/wait for the gate to open -> slowly approach the street (uphill) -> stop, look both left and right, slowly turn left into the street (uphill) -> start accelerating (downhill)

when accelerating, the street is downhill and I am having trouble upshifting at this stage.
as soon as I am on the street I shift to second and if I just leave the car in second, the car is too slow. I need to upshift to 3rd.
However, when I push clutch in, the rpms drops so fast, by the time I shift to 3rd and let the clutch out, the rpm need goes up instead of down. and this results in an unpleasant jerking motion.

How do I smoothly shift from 2nd to 3rd? Stepping on the throttle with the clutch in is the proper way? for upshifting?

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2012 Audi A3 S-Line Titanium 6MT

Yes. Step on the accelerator a little bit to help your engine speed better match the speed that the transmission wants it to go.

In older cars you have to do it for almost every shift.

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1980 Buick LeSabre 4.1L 5MT

Put your car in your sig!

Learn to launch/FAQs/lugging/misused terms: meta-sig

this, I have to do it almost everytime when I am taking my time..sometimes I can just drop the clutch and I manage to get it somewhat close to where it needs to be.

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1991 Honda Civic DX 308k
2000 Honda Civic EX 82k

a few more options

-shift faster. double clutch if you necessary to synch up the gears.

-skip 2nd, wait a little longer than you would shifting out of 1st

-skip 3rd, assuming 4th is not too fast

I figured it out... kinda.
The rpm drops really fast only when the car is cold.
to minimize roughness and jerking, i shift to 2nd as soon as possible, and blip the throttle when shifting to 3rd.
on flat ground, i wait till the engine rev up little higher than usual so I have enough time to complete my shift before rpm drops below the 'ideal' range.

thanks guys for your help!

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2012 Audi A3 S-Line Titanium 6MT