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Ball Bearings

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.

Air Routes

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.


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?

Pdf Matcher

Age 16 to 18 Challenge Level:

Part 1:

Statement 1: All

Statement 2:None

Statement 3: Curves 2 and 3

Statement 4: Curves 4 and 5

Statement 5: Curve 2

Statement 6: Curve 2, 3, 4 and 6

Curve A:
IV characteristics of an ohmic device

Curve B:

Curve C:

Curve D:

Curve E:
This curve appears to be the integral of a sinusoid. It could therefore represent the total electrical power dissipated as a function of time for a device through which we pass an alternating current

Curve F:
This curve could represent the amplitude of oscillation of an undammed spring which is the suddenly stopped.

Curve G:
This curve could represent the magnitude of a pendulums displacement from its equilibrium position (assuming the pendulum begins at maximum displacement).

Curve H:
Charging of a capacitor

Curve I:
Radioactive decay. This curve could represent the number of nuclei decaying per second from some radioactive source.

Curve J:
Normal distribution: Height or weight
This could also be a resonance curve. The Y axis could be the amplitude of osciallation and the X axis could represent the frequency of the input, at the natural frequency we would get a very high amplitude response.

Curve K:

Curve L:
This curve could represent the fracture toughness of an alloyed metal, the Y axis representing the fracture toughness and the x - axis representing the volume fraction of the alloy.