See also: Matching topics (16) Matching titles (121)
Gravity Paths
Stage: 5 Challenge Level: 
Where will the spaceman go when he falls through these strange planetary systems?
The Not-so-simple Pendulum 2
Stage: 5 Challenge Level:
Things are roughened up and friction is now added to the approximate simple pendulum
Aim High
Stage: 5 Challenge Level:
How do you choose your planting levels to minimise the total loss at harvest time?
Building up Friction
Stage: 5 Challenge Level:
A series of activities to build up intuition on the mathematics of friction.
Dangerous Driver?
Stage: 5 Challenge Level:
Was it possible that this dangerous driving penalty was issued in error?
Go Spaceship Go
Stage: 5 Challenge Level:
Show that even a very powerful spaceship would eventually run out of overtaking power
2009 Challenge
Stage: 3, 4 and 5 Challenge Level:
We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.
What's Your Mean?
Stage: 5 Challenge Level:
Can you work out the means of these distributions using numerical methods?
Direct Logic
Stage: 5 Challenge Level:
Can you work through these direct proofs, using our interactive proof sorters?
Understanding Hypotheses
Stage: 3, 4 and 5
This article explores the process of making and testing hypotheses.
Blood Buffers
Stage: 5 Challenge Level:
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
The Not-so-simple Pendulum 1
Stage: 5 Challenge Level:
See how the motion of the simple pendulum is not-so-simple after all.
Stats Statements
Stage: 5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Into the Exponential Distribution
Stage: 5 Challenge Level:
Get into the exponential distribution through an exploration of its pdf.
Cannon Balls
Stage: 5 Short Challenge Level:
How high will a ball taking a million seconds to fall travel?
Escape from Planet Earth
Stage: 5 Challenge Level:
How fast would you have to throw a ball upwards so that it would never land?
Circular Circuitry
Stage: 5 Challenge Level:
What will happen when you switch on these circular circuits?
Taking Trigonometry Series-ly
Stage: 5 Challenge Level:
Look at the advanced way of viewing sin and cos through their power series.
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.
Making More Tracks
Stage: 5 Challenge Level:
Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?
Differential Equation Matcher
Stage: 5 Challenge Level:
Match the descriptions of physical processes to these differential equations.
It's Only a Minus Sign
Stage: 5 Challenge Level:
Solve these differential equations to see how a minus sign can change the answer
Overarch 1
Stage: 5 Short Challenge Level:
This short question asks if you can work out the most precarious way to balance four tiles.
More Bridge Building
Stage: 5 Challenge Level:
Which parts of these framework bridges are in tension and which parts are in compression?
Dam Busters 2
Stage: 5 Challenge Level:
Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?
Dam Busters 1
Stage: 5 Challenge Level:
At what positions and speeds can the bomb be dropped to destroy the dam?
Equation Attack
Stage: 5 Challenge Level:
The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
Tens
Stage: 5 Challenge Level:
When is 7^n + 3^n a multiple of 10? Can you prove the result by two different methods?
All about Ratios
Stage: 5 Challenge Level:
A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.
Intersections
Stage: 4 and 5 Challenge Level:
Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Product Sudoku 2
Stage: 3, 4 and 5 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
Product Sudoku
Stage: 3, 4 and 5 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Whirlyball
Stage: 5 Challenge Level:
Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?
Whoosh
Stage: 5 Challenge Level:
A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?
Epidemic Modelling
Stage: 5 Challenge Level:
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Squareness
Stage: 5 Challenge Level:
The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
Loch Ness
Stage: 5 Challenge Level:
Draw graphs of the sine and modulus functions and explain the humps.
Cubestick
Stage: 5 Challenge Level:
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Exponential Trend
Stage: 5 Challenge Level:
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
Multiplication of Vectors
Stage: 5
An account of multiplication of vectors, both scalar products and vector products.
Vectors - What Are They?
Stage: 5
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .
Put Out
Stage: 5 Challenge Level:
After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?
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