RPM's really worrying me!

I have a 2005 Chevy Aveo LS Hatchback and it has a manual transmission.

I know this will be a lot to read but please try and help if you can. I would greatly appreciate it if i could figure out why my car keeps doing this!

Lately when i drive my car will get into this habit at any random time. I will be slowing down from any speed, from 10-55 mph, to a stop sign and take my foot off the gas and i depress the clutch to put the car into neutral and press on the brake to stop. Well, when i press in the clutch or even just pop the car into neutral without the clutch, my RPM's jump up to 3000 RPM's. Sometimes it will jump anywhere from 2000-3500 but every time i stop it jumps to the same RPM's as before. So it is consistent on how many RPM's it is jumping up to. When i say this i mean it will jump to a certain RPM every time i stop while the car is running on a certain trip to the store or even to another city. I could be driving for 10 miles in a stop and go situation and it never do any RPM jumping but sometimes it will just randomly start to jump RPM's in the middle of my trip and keep doing it until i get to where I'm going or it might stop after a couple miles.

This is greatly impacting my gas mileage and i really need to know what is wrong!

Thank you so much for reading and i hope to hear any ideas of what it could be no matter what they are!

Last night on my way home from work I was going about 55 mph and i pressed in the clutch and put it into neutral to slow down and my RPM's jumped from 2500 to 3100 RPM's. After being at 3100 RPM's for about two seconds it would drop straight down to 2000 RPM's, then after being there for about two seconds, it would jump back up to 3100 RPM's and start all over again.

One possibility might be the throttle position sensor. Have you ever cleaned the throttle body? The TB will collect a pile of gunk over time, and the TPS can get trashed out along with it. The TPS on the 2005 can be removed and cleaned without removing the TB.

I have cleaned the throttle body with throttle body cleaner and just replaced the TPS tonight but the problem is still present. When i am wanting to coast in neutral to come to a stop, i put it in neutral and i apply the brake, and the RPM's stay at the place it was before i put it into neutral. Sometimes it will jump up and stay at 3000 or 2500 RPM's but when it doesn't jump it just doesn't drop the RPM's until i come to a complete stop. Could it be a leak in voltage to something or a vacuum leak?..

Checking vacuum would definitely be a good next step. Some of the parts shops will loan or rent the testing equipment, and it's not too difficult to run the basic testing to check vacuum. But finding the actual leak can be a PITA, and may require a smoke test to locate it.

Okay, thank you! I will post any results if i find them!

I belive that the 05 has an all manual throttle body aka cable from the go pedal to the throttle body, I wonder if it's as simple as something along the cable routing has come loose and under the right conditions when you press in the clutch it catches the cable and actuate the throttle body causing the jump in rpm.

I can see your point but it happens continuously and consistently while in a single trip. Sometimes if i turn off the car for a minute and start it back up then it runs normally...

Do you have cruise control?

No, i wish i did though lol The car is a manual transmission and doesn't come with cruise control, the only way to get cruise control is by getting a cruise control actuator kit for it and running all the wires and cables and hooking it all up to the throttle cable and so on