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.

Bucket of Water

KS 2 & 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?

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 ?

Graphical Triangle

KS 3 Short Challenge Level:

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

Circumference and Diameter

KS 3 & 4 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 ?

Straight Line Spin

KS 3 & 4 Short Challenge Level:

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