Visualising - Advanced

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated.

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

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

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

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

How can you decide if a graph is traversable?

This problem challenges you to sketch curves with different properties.

Use your skill and judgement to match the sets of random data.

Can you work out which spinners were used to generate the frequency charts?

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

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

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

Find the sum of this series of surds.

Can you make sense of the three methods to work out what fraction of the total area is shaded?

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

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

This problem challenges you to find cubic equations which satisfy different conditions.

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?

Explore the lattice and vector structure of this crystal.

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?

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

This is a beautiful result involving a parabola and parallels.

Go on a vector walk and determine which points on the walk are closest to the origin.

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

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

There are many different methods to solve this geometrical problem - how many can you find?

How many different colours of paint would be needed to paint these pictures by numbers?

Use functions to create minimalist versions of works of art.

Is this surd sum exactly 3?

If you know some points on a line, can you work out other points in between?

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

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

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

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Which curve is which, and how would you plan a route to pass between them?

Which line graph, equations and physical processes go together?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

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

Make a functional window display which will both satisfy the manager and make sense to the shoppers

Explore the properties of these two fascinating functions using trigonometry as a guide.

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

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

Draw graphs of the sine and modulus functions and explain the humps.

Discover how networks can be used to prove Euler's Polyhedron formula.

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?

Match the descriptions of physical processes to these differential equations.

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?

How do you choose your planting levels to minimise the total loss at harvest time?

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

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Can you find the link between these beautiful circle patterns and Farey Sequences?

Can you make a curve to match my friend's requirements?

Can you work out what simple structures have been dressed up in these advanced mathematical representations?