Resources tagged with: Maths Supporting SET

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Broad Topics > Cross-curricular Contexts > Maths Supporting SET

Bessel's Equation

Age 16 to 18 Challenge Level:

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

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Approximately Certain

Age 14 to 18 Challenge Level:

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

Dangerous Driver?

Age 16 to 18 Challenge Level:

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

Reaction Rates

Age 16 to 18 Challenge Level:

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

Taking Trigonometry Series-ly

Age 16 to 18 Challenge Level:

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

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.

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.

Pdf Stories

Age 16 to 18 Challenge Level:

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

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.

Differential Equation Matcher

Age 16 to 18 Challenge Level:

Match the descriptions of physical processes to these differential equations.

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.

Choose Your Units

Age 14 to 16 Challenge Level:

Which units would you choose best to fit these situations?

The Wrong Stats

Age 16 to 18 Challenge Level:

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

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?

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

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.

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

Stats Statements

Age 16 to 18 Challenge Level:

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

Debt Race

Age 16 to 18 Challenge Level:

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

Bigger or Smaller?

Age 14 to 16 Challenge Level:

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

What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

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

Quorum-sensing

Age 16 to 18 Short Challenge Level:

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

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

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?

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.

Root Hunter

Age 16 to 18 Challenge Level:

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Construct the Solar System

Age 14 to 18 Challenge Level:

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

Brimful

Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

Vector Walk

Age 14 to 18 Challenge Level:

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

Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

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.

Scientific Curves

Age 16 to 18 Challenge Level:

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

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.

Transformations for 10

Age 16 to 18 Challenge Level:

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

Aim High

Age 16 to 18 Challenge Level:

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

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?

Brimful 2

Age 16 to 18 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

Truth Tables and Electronic Circuits

Age 11 to 18

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

Air Routes

Age 16 to 18 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

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?

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.

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?