Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Age 16 to 18 Short Challenge Level:

To do this question you need to be really sure what the two symbols $\Rightarrow$ and $\Leftrightarrow$ mean.

$p\Rightarrow q$ essentially means that IF $p$ is True THEN $q$ is true.

$p\Leftrightarrow q$ means that $p$ is true if and only if $q$ is true. Alternatively, they are either both true or both false.

To get started, pick one of the simpler looking statements for $p$.

Go through the other statements in turn and see which of them work as $q$ in $p\Rightarrow q$. You will soon be able to pair-off possible partners.

Finally, don't forget to read the details of the question carefully!