ESAT methods
The methods that turn a long question into a short one. Each page names the question it is for, works one example in full, and shows the case where the method gives the wrong answer. Free to read, no account needed.
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Mathematics 1
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Pick one coefficient, without expanding
A question asks for one power of x in a product of brackets. Only a handful of pairs of terms can make it, so neither bracket needs expanding.
Pick one coefficient, without expanding
Mathematics 2
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Use symmetry to kill half a definite integral
Over an interval symmetric about zero, the odd part of the integrand contributes nothing, so half the work can be deleted before any integration starts.
Use symmetry to kill half a definite integral -
Count the roots by sliding a line
When a question asks for which values of a constant an equation has a given number of real roots, the answer is read off the two turning values rather than by solving anything.
Count the roots by sliding a line
Physics
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Solve by ratio, so the constants never appear
When a question changes one quantity and asks what happens to another, the ratio of before and after cancels every constant, and a minute of substitution becomes one line.
Solve by ratio, so the constants never appear
More to come
Methods are added as they earn it: a method gets a page when it has been taught to a student and changed what they could do, not because it would rank. Chemistry and Biology are next.