Can you match these equations to these graphs?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you find the volumes of the mathematical vessels?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match the charts of these functions to the charts of their integrals?
Which line graph, equations and physical processes go together?
Which pdfs match the curves?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Who will be the first investor to pay off their debt?
Which of these infinitely deep vessels will eventually full up?
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Why MUST these statistical statements probably be at least a little bit wrong?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out which processes are represented by the graphs?
Can you draw the height-time chart as this complicated vessel fills with water?
Work out the numerical values for these physical quantities.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Get some practice using big and small numbers in chemistry.
Can you make matrices which will fix one lucky vector and crush another to zero?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
A problem about genetics and the transmission of disease.
Explore how matrices can fix vectors and vector directions.
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?
Get further into power series using the fascinating Bessel's equation.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Which dilutions can you make using only 10ml pipettes?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
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.
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
Invent scenarios which would give rise to these probability density functions.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?