Resources tagged with: Maths Supporting SET

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Broad Topics > Cross-curricular Contexts > Maths Supporting SET

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?

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.

Perfect Eclipse

Age 14 to 16 Challenge Level:

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

Spherical Triangles on Very Big Spheres

Age 16 to 18 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.

Matrix Meaning

Age 16 to 18 Challenge Level:

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

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.

Counting Dolphins

Age 14 to 16 Challenge Level:

How would you go about estimating populations of dolphins?

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?

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Bessel's Equation

Age 16 to 18 Challenge Level:

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

Dangerous Driver?

Age 16 to 18 Challenge Level:

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

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?

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.

Brimful

Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

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?

Vector Walk

Age 14 to 18 Challenge Level:

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

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?

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

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.

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

Approximately Certain

Age 14 to 18 Challenge Level:

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

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.

Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

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.

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.

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.

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

Track Design

Age 14 to 16 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

Square Pair

Age 16 to 18 Challenge Level:

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

Flight Path

Age 16 to 18 Challenge Level:

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

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

Differential Equation Matcher

Age 16 to 18 Challenge Level:

Match the descriptions of physical processes to these differential equations.

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.

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.

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.

Taking Trigonometry Series-ly

Age 16 to 18 Challenge Level:

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

Reaction Rates

Age 16 to 18 Challenge Level:

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

Debt Race

Age 16 to 18 Challenge Level:

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

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.

More or Less?

Age 14 to 16 Challenge Level:

Are these estimates of physical quantities accurate?

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.