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Seven squares are drawn inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.
The centre square has the area of 1 (one) square unit.
Draw the diagram. You can download square dotty paper here.
What is […]
In how many ways can you fit all three pieces together, edge to edge, to make shapes with line symmetry?
The first of these examples shows a symmetrical arrangement, the second is not allowed because the pieces are not placed edge to edge and the third is not symmetrical.
This is a unit circle with a tangent at A.
The angle marked in the diagram is angle a.
Copy the diagram and find all the angles in terms of the angle a.
Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.
Find the areas of […]
In how many ways can you half cover one big square using two smaller yellow squares as in diagram A.
What are the similarities and differences between the patterns?
Suppose you half cover four big squares by half covering each square as in diagram B.
Diagram B is unchanged when you rotate […]
A container holds 4 yellow balls, 2 blue balls and a red ball. The balls are identical in all ways except colour. When you shake the container the balls settle into a hexagonal pattern as shown in the diagram.
You win if two blue balls touch.
How many different ways can […]
Start with the set of the twenty-one numbers 0 – 20.
Can you arrange these numbers into 7 subsets, each of three numbers, so that the totals of the three numbers in each subset make seven consecutive numbers?
For example, one subset adding up to 27 might be {0, 13, 14}. […]
Which of the following products are close to 1368:
20 x 40 20 x 50 20 x 70
40 x 50 40 x 70 or 50 x 70?
In these three multiplication sums, using the digits 1 to 8 once and only […]
(1) Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once.
Can you use the digits 1 to 9 once, but only once, to replace the stars and complete the multiplication * *9 […]
Can you use the digits 1, 2, 3, 4, 5 and 6, each only once, to make a number which is divisible by 6
… so that when the final or last digit is removed it becomes a 5-digit number divisible by 5, and when the last digit is removed from that number […]
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