Equal touching circles have centres on a line. From a point of this
line on a circle, a tangent is drawn to the farthest circle. Find
the lengths of chords where the line cuts the other circles.
Four jewellers possessing respectively eight rubies, ten saphires,
a hundred pearls and five diamonds, presented, each from his own
stock, one apiece to the rest in token of regard; and they. . . .
Two ladders are propped up against facing walls. The end of the
first ladder is 10 metres above the foot of the first wall. The end
of the second ladder is 5 metres above the foot of the second. . . .
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
A right circular cone is filled with liquid to a depth of half its
vertical height. The cone is inverted. How high up the vertical
height of the cone will the liquid rise?
Practise your skills of proportional reasoning with this interactive haemocytometer.
Triangle ABC is equilateral. D, the midpoint of BC, is the centre
of the semi-circle whose radius is R which touches AB and AC, as
well as a smaller circle with radius r which also touches AB and
AC. . . .
Two right-angled triangles are connected together as part of a
structure. An object is dropped from the top of the green triangle
where does it pass the base of the blue triangle?
Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?
One night two candles, one of which was 3 cm longer than the other
were lit. The longer one was lit at 5.30 pm and the shorter one at
7 pm. At 9.30 pm they were both the same length. The longer. . . .
Solve an equation involving the Golden Ratio phi where the unknown
occurs as a power of phi.
Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
A circular plate rolls inside a rectangular tray making five
circuits and rotating about its centre seven times. Find the
dimensions of the tray.
Draw any triangle PQR. Find points A, B and C, one on each side of
the triangle, such that the area of triangle ABC is a given
fraction of the area of triangle PQR.
A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?
Do each of these scenarios allow you fully to deduce the required
facts about the reactants?
When a mixture of gases burn, will the volume change?
Investigate some of the issues raised by Geiger and Marsden's
famous scattering experiment in which they fired alpha particles at
a sheet of gold.
Ever wondered what it would be like to vaporise a diamond? Find out
A brief introduction to PCR and restriction mapping, with relevant
In this question we push the pH formula to its theoretical limits.
Making a scale model of the solar system
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Mainly for teachers. More mathematics of yesteryear.
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .
Two perpendicular lines lie across each other and the end points
are joined to form a quadrilateral. Eight ratios are defined, three
are given but five need to be found.
P is the midpoint of an edge of a cube and Q divides another edge
in the ratio 1 to 4. Find the ratio of the volumes of the two
pieces of the cube cut by a plane through PQ and a vertex.
Construct a line parallel to one side of a triangle so that the
triangle is divided into two equal areas.
Which dilutions can you make using 10ml pipettes and 100ml
Can you break down this conversion process into logical steps?
Which exact dilution ratios can you make using only 2 dilutions?
Which dilutions can you make using only 10ml pipettes?
Can you fill in the mixed up numbers in this dilution calculation?