# 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 ShortChallenge Level

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

##### 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? ### Straight Line Spin

##### Age 11 to 14 ShortChallenge Level

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

##### 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 ? ### Paper Weight

##### Age 11 to 14 ShortChallenge Level

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

##### Age 11 to 14 ShortChallenge Level

Find the area of the triangle enclosed by these lines. ### Lattice Points on a Line

##### Age 11 to 14 ShortChallenge 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 ShortChallenge 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 ShortChallenge 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 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

Sketch the graph of the curve $y^2 = x(2âˆ’x)$ ### Triangular Slope

##### Age 14 to 16 ShortChallenge Level

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

##### 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. ### Closer to Home

##### Age 14 to 16 ShortChallenge Level

Which of these lines comes closer to the origin? ### Inside a Parabola

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