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Broad Topics > Applications > Maths Supporting SET

Reaction Rates

Stage: 5 Challenge Level:

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

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.

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.

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Bessel's Equation

Stage: 5 Challenge Level:

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

Approximately Certain

Stage: 4 and 5 Challenge Level:

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

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?

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?

Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

Electric Kettle

Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

Stirling Work

Stage: 5 Challenge Level:

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

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?

Investigating the Dilution Series

Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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.

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.

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.

Bigger or Smaller?

Stage: 4 Challenge Level:

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

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

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.

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

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

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

Pdf Stories

Stage: 5 Challenge Level:

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

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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

Dangerous Driver?

Stage: 5 Challenge Level:

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

Crystal Symmetry

Stage: 5 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

How Do You React?

Stage: 4 Challenge Level:

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

The Wrong Stats

Stage: 5 Challenge Level:

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

Pdf Matcher

Stage: 5 Challenge Level:

Which pdfs match the curves?

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?

Counting Dolphins

Stage: 4 Challenge Level:

How would you go about estimating populations of dolphins?

Fix Me or Crush Me

Stage: 5 Challenge Level:

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

Debt Race

Stage: 5 Challenge Level:

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

Nutrition and Cycling

Stage: 4 Challenge Level:

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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.

Stats Statements

Stage: 5 Challenge Level:

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

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Differential Equation Matcher

Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

Square Pair

Stage: 5 Challenge Level:

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

Polygon Walk

Stage: 5 Challenge Level:

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

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.

Weekly Challenge 48: Quorum-sensing

Stage: 4 Short Challenge Level:

This problem explores the biology behind Rudolph's glowing red nose.

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Vector Walk

Stage: 4 and 5 Challenge Level:

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

Alternative Record Book

Stage: 4 and 5 Challenge Level:

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

Production Equation

Stage: 5 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Carbon Footprints

Stage: 4 Challenge Level:

Is it really greener to go on the bus, or to buy local?