Resources tagged with: Maths Supporting SET

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There are 90 results

Broad Topics > Cross-curricular Contexts > Maths Supporting SET

Flight Path

Age 16 to 18 Challenge Level:

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

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.

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.

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?

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?

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.

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

Square Pair

Age 16 to 18 Challenge Level:

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

Maths Filler 2

Age 14 to 16 Challenge Level:

Can you draw the height-time chart as this complicated vessel fills with water?

Immersion

Age 14 to 16 Challenge Level:

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Vector Walk

Age 14 to 18 Challenge Level:

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

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?

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?

Matrix Meaning

Age 16 to 18 Challenge Level:

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

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

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.

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?

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?

Stadium Sightline

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?

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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?

Nutrition and Cycling

Age 14 to 16 Challenge Level:

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Gym Bag

Age 11 to 16 Challenge Level:

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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.

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.

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Perfect Eclipse

Age 14 to 16 Challenge Level:

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

Transformations for 10

Age 16 to 18 Challenge Level:

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

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.

Differential Equation Matcher

Age 16 to 18 Challenge Level:

Match the descriptions of physical processes to these differential equations.

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?

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?

Pdf Stories

Age 16 to 18 Challenge Level:

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

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.

Genetics

Age 14 to 16 Challenge Level:

A problem about genetics and the transmission of disease.

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...

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.

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?

What's That Graph?

Age 14 to 16 Challenge Level:

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

Scientific Curves

Age 16 to 18 Challenge Level:

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

Designing Table Mats

Age 11 to 16 Challenge Level:

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

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?

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?

Investigating Epidemics

Age 11 to 16 Challenge Level:

Simple models which help us to investigate how epidemics grow and die out.

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.

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

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.

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.