When you upgrade your kernel the old one will still exist and you can revert back to that kernel if you have any trouble with the new kernel. If you boot to the new kernel, you should still have all the new tools that were installed with the upgrade and the only difference is that you're running the old kernel.
If you'd like to uninstall the old kernel you can run:
you will see a line that looks like this:
dpkg -l | grep kernel
or something similar but with your kernel version instead of 3.2.9
rc linux-image-3.2.9 3.2.9-1 Linux kernel, version 3.2.9
In your terminal run the following:
and of course remember to replace 3.2.9 with your kernel version that you are removing. Next time you boot the machine you will not see the old kernel in your grub menu.
dpkg -r linux-image-3.2.9 && update-grub2
Keep in mind that this should not be necessary and if you accidentally uninstall the wrong kernel you may not be able to boot anymore and need to start from a fresh install.
I believe this is accurate information but if anything needs correcting or if there's anything to add hopefully someone else will chime in.