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Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you work out which processes are represented by the graphs?
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
How do you choose your planting levels to minimise the total loss at harvest time?
Was it possible that this dangerous driving penalty was issued in error?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Is it really greener to go on the bus, or to buy local?
Use vectors and matrices to explore the symmetries of crystals.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Which of these infinitely deep vessels will eventually full up?
Can you draw the height-time chart as this complicated vessel fills with water?
Can you match the charts of these functions to the charts of their integrals?
Get further into power series using the fascinating Bessel's equation.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Which dilutions can you make using only 10ml pipettes?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Use your skill and judgement to match the sets of random data.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
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.