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Remember that the equation of a straight line (when given two points OR a point and a gradient) is y-y_1 = m(x-x_1) where m is the gradient and (x_1,y_1) is a point on the line.

Since we have two p...

Rates and differential equations is a topic many students find difficult, especially when solving the differential equation is combined with techniques from other topics on the C4 syllabus. I hope my walk...

Firstly we must notice that we can differentiate each term separately.

Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and...

In order to rationalise the denominator we need to get rid of the surd (square-root) on the bottom of the fraction.

To do this, we can multiply the denominator by sqrt(5).

But we must notice...

We want to determine whether a function has a tangent which is horizontal. To answer the question we need to know what a horizontal tangent to a function means. A tangent to a graph of a function is a lin...