An inequality involving integrals of squares of functions.
Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
This is a beautiful result involving a parabola and parallels.
Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?