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 $k$.

Quadratic Rotation

Age 14 to 16 Short Challenge Level:

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