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Mental arithmetic practice
The NBT gives you no calculator. Pick your topics, set the number ranges, and drill until the arithmetic stops costing you time.
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Arithmetic speed is worth marks on the NBT
The NBT Mathematics paper gives you 60 questions in three hours with no calculator. That is three minutes a question — comfortable if the arithmetic is automatic, and very tight if it is not. Every second you spend working out 7 × 8 is a second not spent on the actual problem.
Short, regular sessions beat long ones. Five minutes a day on the two or three operations you are slowest at will do more than an hour once a week. Turn on sprint mode once accuracy is solid — not before, because practising fast and wrong just makes you quick at being wrong.
When the arithmetic feels automatic, move on to the NBT book, where the questions are the real thing.
Why arithmetic speed is worth practising
The NBT gives you three hours, sixty questions and no calculator. That works out at three minutes a question, and almost none of the marks are for arithmetic — they are for knowing what to do. Every second spent working out 7 × 8 is a second not spent on the part being examined, and worse, it is a second during which you are holding the rest of the problem in your head and hoping not to drop it.
This is the narrow, unglamorous skill that makes the rest possible. It is also the one that responds fastest to practice: a few minutes a day for a fortnight visibly changes how much of a question you can hold at once.
How to use it
Start narrower than feels sensible
Pick one or two topics and a range you can already do. The point of the first few sessions is to build speed on things you know, not to discover things you do not. Widen the range when the answers start arriving before you have finished reading the question.
Use the timer, but not every time
The one-minute sprint is where speed comes from, and it is also where a bad habit can set in: guessing to beat the clock. Alternate. Do a timed round for pace, then an untimed round where every answer has to be right, and the two together produce something better than either alone.
Let the mistakes tell you where to go
Wrong answers cluster. Almost nobody is uniformly weak — it is the seven and eight times tables, or subtraction across a ten, or dividing by a decimal. When a round goes badly, look at which questions caused it and set the next round to just those.
What it does not do
Getting quicker at arithmetic will not, by itself, raise an NBT score. It removes a tax you are paying on every other question, which is worth a great deal, but the reasoning still has to be learnt. That is what the NBT book and the SAT book are for. Use this to make the mechanics free, and spend the time you save on the parts that are actually being tested.