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Resources tagged with Maths Supporting SET similar to What Do Functions Do for Tiny X?:

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Broad Topics > Applications > Maths Supporting SET

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

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

Bessel's Equation

Stage: 5 Challenge Level:

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

Reaction Rates

Stage: 5 Challenge Level:

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Counting Dolphins

Stage: 4 Challenge Level:

How would you go about estimating populations of dolphins?

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?

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.

Stats Statements

Stage: 5 Challenge Level:

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

Pdf Matcher

Stage: 5 Challenge Level:

Which pdfs match the curves?

More or Less?

Stage: 4 Challenge Level:

Are these estimates of physical quantities accurate?

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Stirling Work

Stage: 5 Challenge Level:

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

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.

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.

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.

Crystal Symmetry

Stage: 5 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Big and Small Numbers in Biology

Stage: 4 Challenge Level:

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

Approximately Certain

Stage: 4 and 5 Challenge Level:

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

Back Fitter

Stage: 4 Challenge Level:

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

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.

Biology Measurement Challenge

Stage: 4 Challenge Level:

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

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.

Debt Race

Stage: 5 Challenge Level:

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

Transformations for 10

Stage: 5 Challenge Level:

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

Square Pair

Stage: 5 Challenge Level:

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

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.

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.

Polygon Walk

Stage: 5 Challenge Level:

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

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.

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?

Robot Camera

Stage: 4 Challenge Level:

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

Fix Me or Crush Me

Stage: 5 Challenge Level:

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

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.

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...

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?

Investigating the Dilution Series

Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

Perspective Drawing

Stage: 3 and 4 Challenge Level:

Explore the properties of perspective drawing.

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?

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?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

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?

Weekly Challenge 48: Quorum-sensing

Stage: 4 Short Challenge Level:

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

Electric Kettle

Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Pdf Stories

Stage: 5 Challenge Level:

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

Vector Walk

Stage: 4 and 5 Challenge Level:

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