This is part of our collection of Short Problems.

You may also be interested in our longer problems on Functions and Graphs Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here.

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### Bucket of Water

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?

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### Circumference and Diameter

Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

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### Paper Weight

How could you use this graph to work out the weight of a single sheet of paper?

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### Straight Line Spin

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

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### Lattice points on a line

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

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### Point in between

Find the point on the line segment AB that is twice as far from B as it is from A.

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Favourite

### Curve fitter

This problem challenges you to find cubic equations which satisfy different conditions.

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### Quadratic Rotation

The curve $y=x^2âˆ’6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?

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### Inside a Parabola

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

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### Graph Triangles

Use the information about the triangles on this graph to find the coordinates of the point where they touch.