Other tags that relate to Consecutive Squares
Powers & roots. Mathematical reasoning & proof. Simultaneous equations. Creating and manipulating expressions and formulae. Graphs. Quadratic functions. Surds. Polynomial functions and their roots. Inequalities. Generalising.There are 12 results
Broad Topics > Functions and Graphs > Quadratic functions
Consecutive Squares
Age 14 to 16 Challenge Level:
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
' Tis Whole
Age 14 to 18 Challenge Level:
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?
Converse
Age 14 to 16 Challenge Level:
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?
Geometric Parabola
Age 14 to 16 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
Parabolic Patterns
Age 14 to 18 Challenge Level:
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.
More Parabolic Patterns
Age 14 to 18 Challenge Level:
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.
Parabolas Again
Age 14 to 18 Challenge Level:
Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
Minus One Two Three
Age 14 to 16 Challenge Level:
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 ?
Fence It
Age 11 to 14 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Which Quadratic?
Age 14 to 18 Challenge Level:
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.
Spaces for Exploration
Age 11 to 14
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Guessing the Graph
Age 14 to 16 Challenge Level:
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
NRICH is part of the family of activities in the Millennium Mathematics Project.