Non-calculator papers are unnecessary in the current world and so students should be allowed to use them in exams. It is very rare that you would have to use mental arithmetic in many jobs, and even if you did, important maths can usually be double checked using software anyway.
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The point of school is to prepare people for the working world and should therefore teach essentials that most people will use in their working life. Now that difficult mental arithmetic (like doing trigonometry in your head) can often be carried out by computers in the workplace, it should also be phased out of the education system. We must keep our education system up to date with current times and not teach unnecessary information to students.