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Solve the following equations showing your method clearly. 3(2x + 9) − 7x = 4(x + 3)

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

Answered by Mehdi A. • Maths tutor

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Write down 56 as the product of its prime factors.

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

Answered by Mehdi A. • Maths tutor

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a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

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] - ...

Answered by Mario R. • Maths tutor

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A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term...

Answered by Alex C. • Maths tutor

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Simplify fully: (24 - √ 300)/(4√ 3 - 5). Give your answer in the form a√ b where a and b are integers and find the values of a and b.

rationalise the denominator (remove the surds) by multiplying by a fraction = 1, known as the rationalising factor = (24 - √ 300)/(4√ 3 - 5) * (4√ 3 + 5)/(4√ 3 + 5) = (24 - √ 300)(4√ 3 + 5)/(48 - 25) = (2...

Answered by Aloysius L. • Maths tutor

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