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# Functions and Graphs - Short Problems

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.

### Spiral Snail

### Bucket of Water

### Straight Line Spin

### Circumference and Diameter

### Paper Weight

### Linear Area

### Lattice Points on a Line

### Graph Area

### Point in Between

### Graphical Triangle

### Quadratic Rotation

### Triangular Slope

### Graph Triangles

### Inside a Parabola

### Curve Fitter

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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.

Age 11 to 14

ShortChallenge Level

A snail slithers around on a coordinate grid. At what position does he finish?

Age 11 to 14

ShortChallenge Level

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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Find the area of the triangle enclosed by these lines.

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

What is the area of the triangle formed by these three lines?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Can you find the gradients of the lines that form a triangle?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 18

ShortChallenge Level

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