Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?
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 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. . . .
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?
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?
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Construct a line parallel to one side of a triangle so that the
triangle is divided into two equal areas.
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. . . .
Which dilutions can you make using only 10ml pipettes?
Can you break down this conversion process into logical steps?
Can you fill in the mixed up numbers in this dilution calculation?
Which exact dilution ratios can you make using only 2 dilutions?
Can you work out which drink has the stronger flavour?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?
Making a scale model of the solar system
When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?
Which dilutions can you make using 10ml pipettes and 100ml
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. . . .
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .
Which is a better fit, a square peg in a round hole or a round peg
in a square hole?
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?
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
Practise your skills of proportional reasoning with this interactive haemocytometer.
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.
A garrison of 600 men has just enough bread ... but, with the news
that the enemy was planning an attack... How many ounces of bread a
day must each man in the garrison be allowed, to hold out 45. . . .
Mainly for teachers. More mathematics of yesteryear.
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. . . .
Build a scaffold out of drinking-straws to support a cup of water
Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?
The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at
100°C (212°Fahrenheit). Is there a temperature at which
Celsius and Fahrenheit readings are the same?