Lumosity

Free (IAPs) NEEDS iOS 11.2 or later

Lumosity includes tests that cover several aspects of mental performance, but it does allow you to focus on specific areas, such as memory, if you prefer. The app starts with some quick tests to assess your performance, and then plans a training course. It’s free for the first 14 days, but then requires a subscription of £11.99 a month or £54.99 a year.