# Functions and Graphs Stage 3 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Functions and Graphs - Stage 3.

### Straight Line Spin

##### KS 3 Short Challenge Level:

Weekly Problem 40 - 2014
Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?

### Bucket of Water

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2006
Lisa's bucket weighs 21 kg when full of water. After she pours out half the water it weighs 12 kg. What is the weight of the empty bucket?

### Circumference and Diameter

##### KS 3 Short Challenge Level:

Weekly Problem 15 - 2008
Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

### Paper Weight

##### KS 3 Short Challenge Level:

Weekly Problem 46 - 2008
How could you use this graph to work out the weight of a single sheet of paper?

### Lattice Points on a Line

##### KS 3 Short Challenge Level:

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

### Graph Area

##### KS 3 Short Challenge Level:

Can you find the area between this graph and the x-axis, between x=3 and x=7?

### Graphical Triangle

##### KS 3 Short Challenge Level:

Weekly Problem 35 - 2007
What is the area of the triangle formed by these three lines?