Resources tagged with: Maths Supporting SET

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Broad Topics > Cross-curricular Contexts > 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.

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

Pdf Stories

Age 16 to 18 Challenge Level:

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

Differential Equation Matcher

Age 16 to 18 Challenge Level:

Match the descriptions of physical processes to these differential equations.

Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

Dangerous Driver?

Age 16 to 18 Challenge Level:

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

Bessel's Equation

Age 16 to 18 Challenge Level:

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

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?

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.

Debt Race

Age 16 to 18 Challenge Level:

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

Reaction Rates

Age 16 to 18 Challenge Level:

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

The Wrong Stats

Age 16 to 18 Challenge Level:

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

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?

Integration Matcher

Age 16 to 18 Challenge Level:

Can you match the charts of these functions to the charts of their integrals?

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

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.

Taking Trigonometry Series-ly

Age 16 to 18 Challenge Level:

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

Truth Tables and Electronic Circuits

Age 11 to 18

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

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

Approximately Certain

Age 14 to 18 Challenge Level:

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

Scientific Curves

Age 16 to 18 Challenge Level:

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

Brimful

Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

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.

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.

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?

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.

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.

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?

Quorum-sensing

Age 16 to 18 Short Challenge Level:

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

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

Transformations for 10

Age 16 to 18 Challenge Level:

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

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

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.

Curve Fitter 2

Age 16 to 18 Challenge Level:

Can you construct a cubic equation with a certain distance between its turning points?

Production Equation

Age 16 to 18 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?

Brimful 2

Age 16 to 18 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

Choose Your Units

Age 14 to 16 Challenge Level:

Which units would you choose best to fit these situations?

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.

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.

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?

Bigger or Smaller?

Age 14 to 16 Challenge Level:

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

Stats Statements

Age 16 to 18 Challenge Level:

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

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.

Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

Big and Small Numbers in Biology

Age 14 to 16 Challenge Level:

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

Matrix Meaning

Age 16 to 18 Challenge Level:

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

Square Pair

Age 16 to 18 Challenge Level:

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

More or Less?

Age 14 to 16 Challenge Level:

Are these estimates of physical quantities accurate?