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What country are you in
What's your credit card number?
Just about any topic can appear on any paper. A few things tend to appear on non calculator papers, e.g. Simple %, Surds, Indices, Arithmetic with integers, decimals and fractions, Exact trigonometry values, Trigonometry graphs and transformations. A few things like iteration, reverse %, compound growth/decay, quadratic formula, trigonometry with any angle, tend to appear on a calculator paper.
They also didn't mention if they're talking about foundation or higher but it's most likely higher. Whole most of what you are saying is quite true, even quadratic formula could come up on non calculator but you would leave answer in simplest surd form, as you said exact trigonometric values however you could be asked to use them with trigonometry but to find a side on non calculator.