Ed Barbeau

Office: Bahen Centre/BA 6176 Email: barbeau@math.toronto.edu Phone: (416) 653-1961

Links for secondary teachers

• Preparation for university
• Problems in logic and analysis
• Exercises on factoring differences of squares
• The quadratic formula
• The inverse of a quadratic function
• Exercises on quadratic polynomials
• Exercises and problems on complex numbers
• Grade 12 calculus: The Plank Problem
• Arithmetic-geometric means inequality
• Area under a cycloid
• Angle subtended by a diamenter
• Pythagorean triples generalized
• Simultaneous equations with an extraneous solution
• Mathematics in a deck of cards
• Classic puzzles old and new
• Recreational problems
• Composing linear polynomials
• Composing quadratic and higher degree polynomials

Vignettes: links for elementary and secondary teachers

• The four points
• The law of cosines
• Fun with pythagoras
• Quadratic forms
• A magic square
• Passacaglia on an odd theme
• Reducible quadratics
• Squares of the form ab+k
• Number rings
• Products of integers that are powers
• Can products of consecutive numbers be square?
• A minimization example
• Prague clock sequences
• Consecutive multiples following consecutive squares
• Sums and multiples using all the digits
• Polynomials with no positive roots
• Polynomials: the Cauchy radius
• The theatre lines problem
• Interlocking pair sums and products
• Square-pair numbers
• The $4/n$ problem
• Products equal to sums
• Triangles with 60 and 120 degree angles
• Round robin tournaments
• Two periodic sequences
• Sets of integer additions
• Commuting exponentials
• A mixed-degree diophantine equation
• Harmonious quartets
• A cubic form
• Powers of 2, 5 and 10
• Oblong numbers
• Congenial and reclusive triples
• A collection of patterns

Links for Ontario Grade XIII examination papers

• Algebra 1956
• Geometry 1956
• Trigonometry and Statics 1956
• Problems 1942
• Problems 1943
• Problems 1944
• Problems 1945
• Problems 1946
• Problems 1947
• Problems 1948
• Problems 1949
• Problems 1950
• Problems 1951
• Problems 1952
• Problems 1953
• Problems 1954
• Problems 1955
• Problems 1956
• Problems 1957
• Problems 1958
• Problems 1959
• Problems 1960
• Problems 1961
• English Composition 1956

TO TOP

Links for secondary students

I am grateful to M. Jean-David Houle for providing French translations for the Tips for Writing up Solutions.

• Tips for writing up solutions
• En 'ecrivant les solutions
• List of Olymon problems 1-300
• List of Olymon problems 301-600
• List of Olymon problems 601-present
• Olymon Volume 1 (2000)
• Olymon Volume 2 (2001)
• Olymon Volume 3 (2002)
• Olymon Volume 4 (2003)
• Olymon Volume 5 (2004)
• Olymon Volume 6 (2005)
• Olymon Volume 7 (2006)
• Olymon Volume 8 (2007(
• Olymon Volume 9 (2008)
• Olymon Volume 10 (2009)
• Olymon Volume 11 (2010)
• Olymon for January, 2008
• Olymon for March, 2008
• Olymon for April, 2008
• Olymon for May, 2008
• Olymon for July, 2008
• Olymon for September, 2008
• Olymon for October, 2008
• Olymon for November, 2008
• Olymon for December, 2008
• Olymon for January, 2009
• Olymon for February, 2009
• Olymon for March, 2009
• Olymon for April, 2009
• Olymon for May, 2009
• Olymon for June, 2009
• Olymon for August, 2009
• Olymon for October, 2009
• Olymon for November, 2009
• Olymon for January, 2010
• Olymon for February, 2010
• Olymon for March, 2010
• Olymon for May, 2010
• Olymon for June, 2010

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Report for Topic Study Group 4 at ICME-10 (2004)

• The report