3 out of 3
Can you use the diagram to prove the AM-GM inequality?
3 out of 3
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
3 out of 3
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
3 out of 3
What is the units digit of the given expression?
1 out of 3
How can you decide if a graph is traversable?
1 out of 3
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
2 out of 3
Can you tangle yourself up and reach any fraction?
2 out of 3
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
1 out of 3
Can you find the sum of the squared sine values?
1 out of 3
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 PQR?
