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Broad Topics > Applications > Maths Supporting SET

Bessel's Equation

Stage: 5 Challenge Level:

Get further into power series using the fascinating Bessel's equation.

Dangerous Driver?

Stage: 5 Challenge Level:

Was it possible that this dangerous driving penalty was issued in error?

Big and Small Numbers in the Physical World

Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Stats Statements

Stage: 5 Challenge Level:

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

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Construct the Solar System

Stage: 4 and 5 Challenge Level:

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Population Dynamics Collection

Stage: 5 Challenge Level:

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Stirling Work

Stage: 5 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Constantly Changing

Stage: 4 Challenge Level:

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Scale Invariance

Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Over-booking

Stage: 5 Challenge Level:

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?

Epidemic Modelling

Stage: 4 and 5 Challenge Level:

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

Integration Matcher

Stage: 5 Challenge Level:

Match the charts of these functions to the charts of their integrals.

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Aim High

Stage: 5 Challenge Level:

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

A Question of Scale

Stage: 4 Challenge Level:

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?

Pdf Stories

Stage: 5 Challenge Level:

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

Approximately Certain

Stage: 4 and 5 Challenge Level:

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Crystal Symmetry

Stage: 5 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Square Pair

Stage: 5 Challenge Level:

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

Operating Machines

Stage: 5 Challenge Level:

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

Pdf Matcher

Stage: 5 Challenge Level:

Which pdfs match the curves?

The Wrong Stats

Stage: 5 Challenge Level:

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

Real-life Equations

Stage: 5 Challenge Level:

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

Time to Evolve 2

Stage: 5 Challenge Level:

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

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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

Data Matching

Stage: 5 Challenge Level:

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

Debt Race

Stage: 5 Challenge Level:

Who will be the first investor to pay off their debt?

Reaction Rates

Stage: 5 Challenge Level:

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

The Monte Carlo Method

Stage: 5 Challenge Level:

Estimate areas using random grids

Bigger or Smaller?

Stage: 4 Challenge Level:

When you change the units, do the numbers get bigger or smaller?

Guessing the Graph

Stage: 4 Challenge Level:

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

Choose Your Units

Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Cross with the Scalar Product

Stage: 5 Challenge Level:

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

Investigating the Dilution Series

Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

Polygon Walk

Stage: 5 Challenge Level:

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

Perfect Eclipse

Stage: 4 Challenge Level:

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

Transformations for 10

Stage: 5 Challenge Level:

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

Track Design

Stage: 4 Challenge Level:

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

Perspective Drawing

Stage: 3 and 4 Challenge Level:

Explore the properties of perspective drawing.

Truth Tables and Electronic Circuits

Stage: 3, 4 and 5

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

Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Fix Me or Crush Me

Stage: 5 Challenge Level:

Can you make matrices which will fix one lucky vector and crush another to zero?