Year 11+ Visualising and representing

problem

Triathlon and fitness

Age

11 to 14

Challenge level

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

problem

Vector walk

Age

14 to 18

Challenge level

Starting with two basic vector steps, which destinations can you reach on a vector walk?

problem

Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

problem

Sitting pretty

Age

14 to 16

Challenge level

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?

problem

Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

problem

The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.

problem

Always perfect

Age

14 to 18

Challenge level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

problem

Perfectly square

Age

14 to 16

Challenge level

The sums of the squares of three related numbers is also a perfect square - can you explain why?

problem

Back fitter

Age

14 to 18

Challenge level

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?

problem

What's that graph?

Age

14 to 18

Challenge level

Can you work out which processes are represented by the graphs?

problem

Bendy quad

Age

14 to 16

Challenge level

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.

problem

Funnel

Age

14 to 16

Challenge level

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 ?

problem

Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?

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For younger learners

Year 11+ Visualising and representing

Triathlon and fitness

Vector walk

Summing geometric progressions

Sitting pretty

Iff

The root of the problem

Always perfect

Perfectly square

Back fitter

What's that graph?

Bendy quad

Funnel

Partly circles