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When adding or subtracting fractions, we must always start by putting the fractions over the same denominator, that is the number on the bottom half of the fraction. To do this, we need to find ...
The key concepts to apply in this question will be the product and chain rules, namely: if f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x). Equivalently, you...
We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half o...
The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area...
A ratio of 1:4 means there are 5 parts to the mixture. 2 litres of drink divided into 5 parts means there are 400 ml per part (2000ml/5 parts). As Fruit Juice has 1 part, Callum would need 400...
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