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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 = 2 3 x7Example of a non calculator GCSE paper question, higher tier
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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(cosec 2 (2x)) - (cosec 2 (x)) = 4/(sin 2 (2x)) - 1/(sin 2 (x)) = 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) B) 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) = 4/(4 sin 2 (x) cos 2 (x)) - 1/(sin 2 (x)) = 1/(sin...
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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 in...
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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) = (24 -...
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Answered by Aloysius L. • Maths tutor
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Solve the simultaneous equations. 2x + y = 18 . x - y = 6

x = 6 + y 2(6+y) + y = 18 12+2y+y = 18 3y = 18-12 3y=6 y = 6/3 = 2. So y = 2 if y = 2 then x is = ? x - y = 6 so, x-2 = 6 so x is 6+ 2 = 8 x = 8 and y = 2
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Answered by Olufunke O. • Maths tutor
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