Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Explore the shape of a square after it is transformed by the action of a matrix.

Can you draw the height-time chart as this complicated vessel fills with water?

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Why MUST these statistical statements probably be at least a little bit wrong?

Which line graph, equations and physical processes go together?

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Use vectors and matrices to explore the symmetries of crystals.

Explore the relationship between resistance and temperature

Simple models which help us to investigate how epidemics grow and die out.

Explore the properties of matrix transformations with these 10 stimulating questions.

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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

Can you sketch these difficult curves, which have uses in mathematical modelling?

Explore the meaning of the scalar and vector cross products and see how the two are related.

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Where should runners start the 200m race so that they have all run the same distance by the finish?

Which dilutions can you make using only 10ml pipettes?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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?

Invent scenarios which would give rise to these probability density functions.

Formulate and investigate a simple mathematical model for the design of a table mat.

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Get some practice using big and small numbers in chemistry.

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