Monthly Archives: December 2016

Rectangle Inside a Square

An isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains. What is the length of a diagonal of the rectangle if the sum of the areas of the removed pieces … Continue reading

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Equiangular Hexagon

An equiangular hexagon with consecutive side lengths , and can be inscribed in an equilateral triangle with side length . This same equiangular hexagon can also be inscribed in a second (distinct, noncongruent) equilateral triangle with side length . What … Continue reading

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Absolute Value Function

What is the area of the region bounded by the graph of ? Source: NCTM Mathematics Teacher, October 2006 Solution If and If and If and If and The four graphs intersect and form a square of side length . … Continue reading

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2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

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Least Positive Integer

What is the least positive integer for which the expression simplifies to an integer? Source: NCTM Mathematics Teacher, October 2006 Solution We look for the smallest sum of positive consecutive integers that is a perfect square  a perfect square Answer: Alternative solution … Continue reading

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Thirteen Power of (1+i)

If  represents the imaginary unit, find real values for and such that . Source: NCTM Mathematics Teacher, October 2006 Solution Answer: Alternative solution Write the complex number in polar form Applying De Moivre’s theorem

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