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Resources tagged with Maths Supporting SET similar to Weekly Challenge 47: Weird Universes:

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Broad Topics > Applications > Maths Supporting SET

Perspective Drawing

Stage: 3 and 4 Challenge Level:

Explore the properties of perspective drawing.

Flight Path

Stage: 5 Challenge Level:

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Spherical Triangles on Very Big Spheres

Stage: 5 Challenge Level:

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

Air Nets

Stage: 2, 3, 4 and 5 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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.

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

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.

Stirling Work

Stage: 5 Challenge Level:

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

Approximately Certain

Stage: 4 and 5 Challenge Level:

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

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

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?

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?

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?

Bessel's Equation

Stage: 5 Challenge Level:

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

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?

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.

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?

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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

Investigating the Dilution Series

Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Robot Camera

Stage: 4 Challenge Level:

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

Efficient Packing

Stage: 4 Challenge Level:

How efficiently can you pack together disks?

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.

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.

Polygon Walk

Stage: 5 Challenge Level:

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

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

Reaction Rates

Stage: 5 Challenge Level:

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

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

Bigger or Smaller?

Stage: 4 Challenge Level:

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

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 the Living World

Stage: 3 and 4 Challenge Level:

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

Stats Statements

Stage: 5 Challenge Level:

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

Air Routes

Stage: 5 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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?

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?

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...

Pdf Stories

Stage: 5 Challenge Level:

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

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Matrix Meaning

Stage: 5 Challenge Level:

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

Differential Equation Matcher

Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Odd One Out

Stage: 5 Short Challenge Level:

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Genetics

Stage: 4 Challenge Level:

A problem about genetics and the transmission of disease.

Fill Me up Too

Stage: 4 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?

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.