It depends what type and board - I am doing OCR Maths B (MEI). For paper 1, which is next Tuesday, we did it last year before GCSEs and are redoing it for a better grade, a C is around 35% and an A* around 80%, for Maths 2 on the 15th June, which is much harder, a C is around 15% and A* around 75%.
Trigonometry can come up in the non-calculator, I remember seeing a pyramid question in a past paper and your answer had to be a fraction x square root
Differentiation should not occur in Maths, well for OCR anyway, but it will be in the Additional Maths syllabus.