### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Doesn't Add Up

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

# Steady Free Fall

##### Stage: 4 Challenge Level:

Vertical velocity means that the sideways speed doesn't count at all, just the rate at which height is lost.

Think about what it is in the shape of the rail that makes vertical velocity increase or decrease at any point, and connect that with how increases or decreases of vertical velocity show up on the graph.

Here are the actual four curves. Can you matchthem with the graphs?