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Foundations before syllabus

Maths is not like your other subjects. In Biology you can learn Topic 7 without Topic 3 and still do well. In maths, almost everything sits on top of something older — every equation needs negative numbers, every rearrangement needs fractions, every graph needs both. When maths feels hard, it is very often not the new topic at all. It is a loose brick further down.

So we are not starting at Chapter 1 and marching forward. We find the loose bricks first, relay them, then build. That is slower for about three weeks and considerably faster after that.

This is also the opposite of how the science sections here work. Physics, Chemistry and Biology throw hard papers at you deliberately. Maths will not do that, not yet. Difficulty is only useful once the ground underneath is solid.

The thing that matters most about this course
From 2025 onwards, Paper 2 is non-calculator — two hours, 100 marks, half your entire grade, with no calculator on the desk. That makes arithmetic and algebra you can do unaided the highest-value thing you own in this subject. It is why almost every page here is non-calculator, and why the one page that is not says so loudly.
Paper 2Non-calculator · 2h · 100 marks · 50%
Paper 4Scientific calculator · 2h · 100 marks · 50%

The fading sequence

Every idea on every guide is taught the same way: a fully worked example, then the same kind of problem with the last step blank, then the last two blank, then one entirely on your own. You are never staring at a blank page, and never just watching someone else do it — which is the trap with worked solutions, because watching feels like learning and is not.

Each guide then ends with a mixed set with no labels. Deciding which method applies is the skill ordinary revision skips, and it is most of what an exam question is really asking.

Where school teaches it differently. Wherever the school method and the shorter method disagree — percentages and money mostly — the guides show both, side by side, with the same boxed answer. Neither is wrong. Use your teacher's layout in class; the other one is there so you can see why they agree.
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The one page that is not non-calculator — E1.14
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Because everything else here is deliberately non-calculator, E1.14 was the only Extended sub-topic on the syllabus with no teaching anywhere on this site. This is it: when brackets are compulsory, the fraction key and S⇔D, Ans and STO so you never round in the middle, spotting that you are in radians, and estimating to 1 s.f. to check what came back. Paper 4 insurance only — it is worth nothing on the non-calculator paper, and the page says so. Keys assume a Casio fx-83GT/85GT.