What kind of mathematics do I need to know for the TSA?

The TSA does not test for advanced mathematical knowledge. You certainly do not need to have taken Further Mathematics at A-level to answer any of the mathematical questions on the TSA. For example, there will be no questions that require you to take a derivative or use trigonometry. Instead, the TSA tests for your computational and problem-solving skills. As long as you have a solid grasp of algebra and a knack for problem solving you will be fine.