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This is an example of completing the square. Notice that when we expand y = (x + a)^2 + b we get y = x^2 + 2ax + a^2 + b. By comparing coefficients (ie, making sure the number x is multiplied by and the c...

This is a typical AS-level Maths question.

1. We see it’s a definite integral so start by drawing some big square brackets with the “limits” (2 and 1).

2. We go through the ex...

To sketch a graph of an equation, there are several key features to consider. Firstly, we can consider where the graph crosses the x- and y-axes. When x=0, y=0, so the graph goes through the origin. If y=...

If the two graphs intersect, it means that they will share the same y and x coordinates at one particular point. (I will draw diagram to show point).

Therefore, you can set f(x)=g(x) so that x^2 -...

• First, factorise the quadratic equation.
• Find two numbers that multiply to give 21 and add to give 10. 7 and 3
• (x-7)(x-3)=0
• Now find the value x so that when these bracket...