Triathlon and fitness
Vector walk
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Summing geometric progressions
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Iff
Always perfect
Perfectly square
Areas of parallelograms
Can you find the area of a parallelogram defined by two vectors?
Back fitter
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Fill me up too
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
What's that graph?
Can you work out which processes are represented by the graphs?
Sitting pretty
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Funnel
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
Partly circles
What is the same and what is different about these circle questions? What connections can you make?
Ladder and cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Bendy quad
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.