A Level Further Maths Core Pure Year 2 Chapter 3: Mini test

What makes an integral improper?

• Top heavy integral
• Its limits are undefined
• Its limits are infinite
• It is not continous in the interval

Mean value

• \frac{1}{a-b}\int_a^bf\left(x\right)dx
• \frac{1}{b-a}\int_a^b\left(f\left(x\right)\right)^2dx
• \pi\int_a^b\left(f\left(x\right)\right)^2dx
• \frac{1}{b-a}\int_a^bf\left(x\right)dx

Graph reminder...

• arccos
• arcsin
• arsin
• arctan

Partial fractions \frac{20}{\left(x^2-9\right)\left(x^2+3\right)}

• \frac{A}{\left(x^2-9\right)}+\frac{B}{\left(x^2+3\right)}
• \frac{A}{\left(x^2-9\right)}+\frac{Bx+C}{\left(x^2+3\right)}
• 
• \frac{Ax+B}{\left(x^2-9\right)}+\frac{Cx+D}{\left(x^2+3\right)}

What does this need to become? \frac{1}{\sqrt{10-2x^2}}

• \frac{1}{10\sqrt{1-2x^2}}
• \frac{1}{\sqrt{10}\sqrt{1-\frac{1}{5}x^2}}
• \frac{1}{\sqrt{10}\sqrt{1-\frac{2}{\sqrt{10}}x^2}}
• \frac{1}{\sqrt{10}\sqrt{1-2x^2}}