Can you match the charts of these functions to the charts of their integrals?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you match these equations to these graphs?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you construct a cubic equation with a certain distance between its turning points?
Can you find the volumes of the mathematical vessels?
Who will be the first investor to pay off their debt?
Use vectors and matrices to explore the symmetries of crystals.
Which line graph, equations and physical processes go together?
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little bit wrong?
Match the descriptions of physical processes to these differential equations.
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you make matrices which will fix one lucky vector and crush another to zero?
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How much energy has gone into warming the planet?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Build up the concept of the Taylor series
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Was it possible that this dangerous driving penalty was issued in error?
Explore how matrices can fix vectors and vector directions.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
Can you work out which processes are represented by the graphs?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.