Some do's and don't's:
Do NOT hit the cat. Ever. He won't understand why, and you'll just make him afraid of you.
Do NOT dump the cat outside if he isn't used to it. He can become disoriented, run away, eat something he shouldn't, or get hurt/killed by another animal/human.
Do NOT rub his nose in the urine. That doesn't work. He already knows what it smells like, and doesn't share your notion of what smells "good/normal" and what smells "bad."
DO talk to your vet. It's possible this could be a medical issue related to diet or digestion. The cat could have a kidney problem. He could have some psychological issue. This is likelier if the cat is over 10 years old.
DO try the cat with clumping cat litter. Yes, it's pricier than the cheaper stuff. But it doesn't lead to a smelly, horrible litter box and it's much easier to clean up. The cat will be more apt to use the litter if it doesn't stink.
DO feed your cat at regular times and keep a diary of when he does this carpet peeing. If there is a pattern, you may need to adjust his feeding schedule or food.
DO learn the cat's body language. As with puppies, the moment he squats down, pick him up and put him in the litter box. If/when he pees in the litter box, praise him.
DO clean the carpet, thoroughly. Pet stores carry a wide range of products that can help eliminate the urine odor after the carpet is clean so the cat will (hopefully) not return to that spot.
DO make sure the cat isn't acting up out of boredom or loneliness. It's probably unrealistic to get him a companion cat, but older cats love to play too. They just don't do it the same way that a kitten does.
You might need to start over with a brand-new litter box and litter. Yes, it costs $$. But that's better than the cost of new carpeting and/or your mother committing murder.
Patience is essential. Don't hit your cat. Don't yell at him. A firm "No!" is okay when you see him squatting on the floor, but no violence.
You really need to talk to your vet. I can't stress how important this is, as there may be a medical reason for this behavior. I had an older cat that started to pee on the floor, and it turned out that she was stressed over the new cat I'd introduced to the household. I gave her to my dad, and she was okay there (just one other cat, who was usually outside).