Hello, XXXXXXXXXX
Given her age I would get her a check up to be safe. Things like kidney problems, diabetes, and thyroid issues can cause a cat to pee outside the litter box. At 11 years old any of these are possible.
Spraying is typically a territorial behavior.This is common in all cats male/female fixed or not. Females are far less likely to do it, but are more than capable of it. There may be some new cats in the neighborhood and she feels the need to mark her house to tell them "this is mine" "stay away."
Try some of these tips to stop the behavior.
You should add a second litter box.
Many times cats do not like to urinate in the same box they defecate in. Nor do cats like to share litter boxes either sometimes. It always a good rule of thumb to follow this formula (n+1= number of litter boxes) N= number of cats in house.
You can use a litter called cat attract. Attract Litter is designed to make it easier to get cats of all ages trained or re-trained to use the litter box. You can get this a petsmart, petco, and larger pet supply stores.
Very important to clean the areas that has been marked. You need to use a enzyme odor eliminating cleaner such as nature's miracle. Regular cleaner such as Lysol will not work as good. She will keep going to the same spots because she smells her scent there. You must get rid of the scent. Nature's miracle also makes a cat only formula now.
You can also use a product called feliway. This is a pheromone spray that helps cats with aggression, territorial issues, and anxiety. You can spray it on surfaces she has previously urinated on. You can also get it in an electric plug in that puts the pheromone into the air called Comfort Zone. You can get this at Pet Smart or most larger pet supply stores.
When you do catch her using the litter box appropriately reward her with a yummy little kitty treat. Cats learn very fast a reward method of training.
Do get her a vet check up though to be safe.
Sincerely, XXXXX
Expert in cat behavior and health
Expert in cat medical and behavior issues.
Fantastic!!
Sorry I can't see your additional information added until after I post to your question. I see it now however. Just try the additional tips you haven't yet. There is also prescription medications you can get from a vet for this too if she is very stubborn about it.