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.
problem
Spiral snail
Age
11 to 14
Challenge level
A snail slithers around on a coordinate grid. At what position does he finish?
problem
Bucket of water
Age
11 to 14
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?
problem
Circumference and diameter
Age
11 to 14
Challenge level
Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?
problem
Paper weight
Age
11 to 14
Challenge level
How could you use this graph to work out the weight of a single sheet of paper?
problem
Straight line spin
Age
11 to 14
Challenge level
Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?
problem
Lattice points on a line
Age
11 to 14
Challenge level
How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
problem
Graph area
Age
11 to 14
Challenge level
Can you find the area between this graph and the x-axis, between x=3 and x=7?
problem
Point in between
Age
11 to 14
Challenge level
Find the point on the line segment AB that is twice as far from B as it is from A.
problem
Linear area
Age
11 to 14
Challenge level
Find the area of the triangle enclosed by these lines.
problem
Graphical triangle
Age
14 to 16
Challenge level
What is the area of the triangle formed by these three lines?
problem
Favourite
Curve fitter
Age
14 to 18
Challenge level
This problem challenges you to find cubic equations which satisfy different conditions.
problem
Quadratic rotation
Age
14 to 16
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?
problem
Inside a parabola
Age
14 to 16
Challenge level
A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.
problem
Triangular slope
Age
14 to 16
Challenge level
Can you find the gradients of the lines that form a triangle?
problem
Graph triangles
Age
14 to 16
Challenge level
Use the information about the triangles on this graph to find the coordinates of the point where they touch.
problem
Closer to home
Age
14 to 16
Challenge level
Which of these lines comes closer to the origin?