Search over 10,000 free study notes

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...

You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x)

For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule

V'=dx/dy(e^x)dx/dy(x)...