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?

Middle Man

Age 16 to 18 Challenge Level:

Mark a point $P$ inside a closed curve.

Is it always possible to find two points that lie on the curve, such that $P$ is the mid point of the line joining these two points?