A Diophantine Equation: “How can I find all natural numbers a &b such that a^2 + a + 1 = b^2?”
Answer We assume “natural numbers here includes the number zero” (an old convention – may not be valid…
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Function: Range Problem
Question What is the range of the function f ( x ) = xsquared + 4 when the…
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Symmetry 3
Question Use algebraic tests to determine whether the graph of the equation 4x² – 9y² = 1 is…
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Symmetry 2
Question Use algebraic tests to determine whether the graph of the equation x = y³ – 4y is…
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Symmetry
Question The given point (-2,9) lies on the graph that is symmetric about x-axis, y-axis, and origin. State…
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A Difficult Applied Math Question
Question One end of a piece of elastic is attached to a point at the top of a…
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A Round Table Probability Question
Question Mr. Blue, Mr. Black, Mr. Green, Mrs. White, Mrs. Yellow and Mrs. Red sit around a circular…
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In triangle ABC, angle ABC=15 degrees, angle ACB=30 degrees, AD is the median to side BC, A-D-C. angle BAD=?
Answer We will use the Sine Rule. In triangle ABD, AD / sin(ABD) = BD / sin(BAD) So…
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Calculate the square root of this number (without a calculator): 2000*2001*2002*2003+1
Answer The trick is to realize that the product of four consecutive integers is always less than 1…
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Add to make Perfect Squares
Question What must be added to each of the following expressions to obtain a perfect square? [Q1] a^2…