Can I just make a couple of comments - speaking from past experience as well.
The C1 course may very well ask you to give answers that require a calculator and ask you to give your answers to so many sig figures, But I would imagine that if the exam is supposed to be done without a calculator, then that exam is simply testing your mathematical skills rather than your computational skills in using a calculator. In the exam, results will be (numerically) simple answers (otherwise a calculator would be needed) - perhaps in surd form as mentioned. Or you may be given a result and then asked to prove it.
So, even though the C1 course needs you to use a calcultor, the exam questions will be designed to not require one.