# 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

##### Age 11 to 14 Short Challenge Level:

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

### Straight Line Spin

##### Age 11 to 14 Short Challenge Level:

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

### Bucket of Water

##### Age 11 to 14 Short Challenge 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?

### Circumference and Diameter

##### Age 11 to 14 Short Challenge Level:

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

### Paper Weight

##### Age 11 to 14 Short Challenge Level:

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

### Linear Area

##### Age 11 to 14 Short Challenge Level:

Find the area of the triangle enclosed by these lines.

### Lattice Points on a Line

##### Age 11 to 14 Short Challenge Level:

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

### Graph Area

##### Age 11 to 14 Short Challenge Level:

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

### Point in Between

##### Age 11 to 14 Short Challenge Level:

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

### Graphical Triangle

##### Age 14 to 16 Short Challenge Level:

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

### Sketchorama

##### Age 14 to 16 Short Challenge Level:

Sketch the graph of the curve $y^2 = x(2−x)$

### Triangular Slope

##### Age 14 to 16 Short Challenge Level:

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

### Graph Triangles

##### Age 14 to 16 Short Challenge Level:

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

### Closer to Home

##### Age 14 to 16 Short Challenge Level:

Which of these lines comes closer to the origin?

### Inside a Parabola

##### Age 14 to 16 Short Challenge Level:

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

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