Visualising and representing

problem

Quick Sum

Age

16 to 18

Challenge level

Is this surd sum exactly 3?
problem

Calculus Analogies

Age

16 to 18

Challenge level

Consider these analogies for helping to understand key concepts in calculus.
problem

Speedo

Age

16 to 18

Challenge level

Investigate the relationship between speeds recorded and the distance travelled in this kinematic scenario.
problem

Polar Bearings

Age

16 to 18

Challenge level

What on earth are polar coordinates, and why would you want to use them?
problem

Trig Reps

Age

16 to 18

Challenge level

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
problem
Favourite

Circles Ad Infinitum

Age

16 to 18

Challenge level

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
problem
Favourite

Areas and Ratios

Age

16 to 18

Challenge level

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

Orthogonal Circle

Age

16 to 18

Challenge level

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.
problem

Five Circuits, Seven Spins

Age

16 to 18

Challenge level

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
problem
Favourite

Cubestick

Age

16 to 18

Challenge level

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