Paper 3 isn't a math test — it's an investigation. Learn how to bridge the gap between syllabus knowledge and unfamiliar problem-solving, and keep the marks flowing even when the context is brand new.
Paper 1 and 2 test what you know. Paper 3 tests how you think when you encounter a context you've never seen before.
The examiners deliberately pick unfamiliar contexts to see if you can reason on your feet. Don't panic when the first page looks foreign — the marks aren't in the final answer, they're in the journey from the known to the unknown.
A typical Paper 3 investigation lasts 5+ pages. The biggest mistake students make is losing the thread by page 3.
Use clear link-phrases like "Using the result from part (a)…" and keep your notation consistent throughout. If your calculation hits a snag, describe the logic you would use — reasoning marks keep flowing even when the arithmetic stalls.
Every Paper 3 begins with a simple "show that" or a numerical case. That's your foothold — use it to spot the pattern.
If the question later asks for a general rule for $n$ terms, look back at your results for $n=1$ and $n=2$. The comfort-zone cases are the clues for the general proof.