Being resourceful

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

Can you find the area of the central part of this shape? Can you do it in more than one way?

Can you work out the equations of the trig graphs I used to make my pattern?

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

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

See how the motion of the simple pendulum is not-so-simple after all.

Things are roughened up and friction is now added to the approximate simple pendulum

What two-digit numbers can you make with these two dice? What can't you make?

How do you know whether you will reach these numbers when you count in steps of six from zero?