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Write √5 ( √8 + √18 ) in the form a√10, where a is an integer, without using a calculator.

We start by expanding the brackets : (√5 x √8) + (√5 x √18). A common mistake here is to attempt to add √8 and √18 together. We can't do this because of algebra rules. BIDMAS states that multiplication is do...
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Answered by Adrienn J. • Maths tutor
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Given f(x)=2x^3 - 2x^2 + 8x, find f'(x) and f"(x).

The first step in scoring full marks on this typically 4 mark question is to recognise what it's asking you to do. We use the process of differentiation to solve it. f(x)=2x^3 - 2x^2 + 8xf'(x) = 6x^2 - 4x + ...
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Integrate (x-5)/(x+1)(x-2) using partial fractions

We need to split the initial fraction into two. We know that (x-5)/(x+1)(x-2) is equivalent to A/(x+1) + B/(x-2). Multiplying by (x+1)(x-2) we get x-5 = A(x-2) + B(x+1). Expanding the brackets gives x - 5 = ...
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Answered by Joshua A. • Maths tutor
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Solving simultaneous questions, e.g. 3x + y = 11 and 2x + y = 8

The unknowns in a simultaneous equation need to be solved, which in this case are x and y.The method I will be using is by elimination:First, find which unknown has the same coefficient. In this example this...
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Answered by Simran S. • Maths tutor
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A particle of mass M is being suspended by two ropes from a horizontal ceiling. Rope A has a tension of 15N at 30 deg and rope B has a tension of xN at 45 deg, find M assuming the particle remains stationary.

This is a classic "picture frame" resolving forces question. By resolving horizontally we can use the "assuming the particle remains stationary" meaning the forces must cancel out, so, xC...
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