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#### Resources tagged with Maths Supporting SET similar to Is Your DNA Unique?:

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Broad Topics > Applications > Maths Supporting SET

### Population Dynamics Collection

##### Age 16 to 18 Challenge Level:

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

### The Wrong Stats

##### Age 16 to 18 Challenge Level:

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

### Bigger or Smaller?

##### Age 14 to 16 Challenge Level:

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

### Transformations for 10

##### Age 16 to 18 Challenge Level:

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

### Guessing the Graph

##### Age 14 to 16 Challenge Level:

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

### Pdf Stories

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Which units would you choose best to fit these situations?

### Over-booking

##### Age 16 to 18 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?

### Scale Invariance

##### Age 16 to 18 Challenge Level:

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

### Real-life Equations

##### Age 16 to 18 Challenge Level:

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

### Big and Small Numbers in the Physical World

##### Age 14 to 16 Challenge Level:

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

### Stirling Work

##### Age 16 to 18 Challenge Level:

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

### Bessel's Equation

##### Age 16 to 18 Challenge Level:

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

### A Question of Scale

##### Age 14 to 16 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?

### Time to Evolve 2

##### Age 16 to 18 Challenge Level:

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

### Big and Small Numbers in the Living World

##### Age 11 to 16 Challenge Level:

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

### Elastic Maths

##### Age 14 to 18

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.

### Approximately Certain

##### Age 14 to 18 Challenge Level:

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

### Whose Line Graph Is it Anyway?

##### Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

### Stats Statements

##### Age 16 to 18 Challenge Level:

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

### Dangerous Driver?

##### Age 16 to 18 Challenge Level:

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

### Global Warming

##### Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

### Building Approximations for Sin(x)

##### Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

### Designing Table Mats

##### Age 11 to 16 Challenge Level:

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

### Reaction Rates

##### Age 16 to 18 Challenge Level:

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

### Biology Measurement Challenge

##### Age 14 to 16 Challenge Level:

Analyse these beautiful biological images and attempt to rank them in size order.

### Far Horizon

##### Age 14 to 16 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Investigating the Dilution Series

##### Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

### Operating Machines

##### Age 16 to 18 Challenge Level:

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

### Big and Small Numbers in Physics

##### Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

### Robot Camera

##### Age 14 to 16 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

### Nine Eigen

##### Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

### Fill Me up Too

##### Age 14 to 16 Challenge Level:

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?

### Fix Me or Crush Me

##### Age 16 to 18 Challenge Level:

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

### Crystal Symmetry

##### Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

### Cross with the Scalar Product

##### Age 16 to 18 Challenge Level:

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

### Square Pair

##### Age 16 to 18 Challenge Level:

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

### Carbon Footprints

##### Age 14 to 16 Challenge Level:

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

### Constantly Changing

##### Age 14 to 16 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.

### Perfect Eclipse

##### Age 14 to 16 Challenge Level:

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

### Vector Walk

##### Age 14 to 18 Challenge Level:

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

### Polygon Walk

##### Age 16 to 18 Challenge Level:

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

### Scientific Curves

##### Age 16 to 18 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

### Matrix Meaning

##### Age 16 to 18 Challenge Level:

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

### Pdf Matcher

##### Age 16 to 18 Challenge Level:

Which pdfs match the curves?

### Aim High

##### Age 16 to 18 Challenge Level:

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

### Brimful 2

##### Age 16 to 18 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

### Electric Kettle

##### Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

### Quorum-sensing

##### Age 16 to 18 Short Challenge Level:

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

### Ball Bearings

##### Age 16 to 18 Challenge Level:

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.
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