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In order to integrate ln x you have to use integration by parts, even though it appears there is only one term to be integrated. We get around this by instead writing it as (ln x)(1), where we treat the 1...

multiple choice question.answer: 27taken from CGP Sample 11+ Assessment Test

3(2x + 9) − 7x = 4(x + 3)so 6x + 27 -7x = 4x + 12so 27 - 12 = 5xso 15 = 5xso x=5taken from The Haberdashers' Aske's Boys’ SchoolElstree, Herts 13+ Entrance Examination 2016

56 / 2 = 2828 / 2 = 1414 / 2 = 77 / 7 = 1so, 56 = 2x2x2x7 = 2³x7Example of a non calculator GCSE paper question, higher tier

A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - ...