2 out of 3
Can you prove the angle properties described by some of the circle theorems?
3 out of 3
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
1 out of 3
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
2 out of 3
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
1 out of 3
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
1 out of 3
I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?
1 out of 3
2 out of 3
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
2 out of 3
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?
2 out of 3
