# Resources tagged with: Maths Supporting SET

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Broad Topics > Cross-curricular Contexts > Maths Supporting SET ### 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. ### 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. ### Flight Path

##### Age 16 to 18 Challenge Level:

Use simple trigonometry to calculate the distance along the flight path from London to Sydney. ### Taking Trigonometry Series-ly

##### Age 16 to 18 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series. ### 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. ### 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? ### 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. ### Efficient Packing

##### Age 14 to 16 Challenge Level:

How efficiently can you pack together disks? ### Bessel's Equation

##### Age 16 to 18 Challenge Level:

Get further into power series using the fascinating Bessel's equation. ### Building Approximations for Sin(x)

##### Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series ### 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. ### 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. ### Transformations for 10

##### Age 16 to 18 Challenge Level:

Explore the properties of matrix transformations with these 10 stimulating questions. ##### Age 14 to 18 Challenge Level:

How would you design the tiering of seats in a stadium so that all spectators have a good view? ### Back Fitter

##### Age 14 to 18 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? ### 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? ### Scientific Curves

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect. ### 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. ### Speed-time Problems at the Olympics

##### Age 14 to 16 Challenge Level:

Have you ever wondered what it would be like to race against Usain Bolt? ### 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. ### 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? ### Matrix Meaning

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Is it really greener to go on the bus, or to buy local? ### Crystal Symmetry

##### Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals. ### Square Pair

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions. ### What's That Graph?

##### Age 14 to 18 Challenge Level:

Can you work out which processes are represented by the graphs? ### Perspective Drawing

##### Age 11 to 16 Challenge Level:

Explore the properties of perspective drawing. ### 3D Drawing

##### Age 11 to 16

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods. ### Witch's Hat

##### Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat? ### 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? ### Fill Me up Too

##### Age 14 to 16 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

##### Age 11 to 16 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat. ### Alternative Record Book

##### Age 14 to 18 Challenge Level:

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book. ### Robot Camera

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing? ### 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. ### How Do You React?

##### Age 14 to 16 Challenge Level:

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling... ### 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. ### Pdf Stories

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

Estimate these curious quantities sufficiently accurately that you can rank them in order of size ### The Wrong Stats

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT? ### Equation Matcher

##### Age 16 to 18 Challenge Level:

Can you match these equations to these graphs? ### Electric Kettle

##### Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature