Category Archives: Problem solving

Length of Hypotenuse

Consider the line containing the points and . What is the length of the hypotenuse of the right triangle formed by the intersections of and the -and -axes? Source: NCTM Mathematics Teacher, September 2006 Solution Points , and are the … Continue reading

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Ten-Card Game

A game is played with a deck of ten cards numbered from to . Shuffle the deck thoroughly. Take the top card. If it is numbered , you win. If it is numbered , where , then replace the card … Continue reading

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Rolling Wheel

If a wheel completes exactly revolutions while rolling feet, what is the diameter of the wheel? Source: NCTN Mathematics Teacher, September 2006 Solution The above figure shows the ground distance traveled by the rolling wheel of radius feet in revolutions. … Continue reading

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Smallest Quantity

If and , which of the following is never greater than any of the others? (a) (b) (c) (d) (c) Source:NCTM Mathematics Teacher, September 2006 Solution Suppose and (a) (b) (c) (d) (e) (a),(d),(e) have the smallest value Suppose and … Continue reading

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Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

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Which Triangle is Largest?

Of the following triangles given by the lengths of their sides, which one has the greatest area? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September 2006 Solution Heron’s Area Formula: area = where and are the lengths of … Continue reading

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Area of a Disc

If the area of a disc inscribed in a square is square centimeters, what is the area of the square? Source: NCTM Mathematics Teacher, September 2006 Solution Area of disc = Area of square = Answer: square centimeters

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Product of Consecutive Integers

How many integer pairs satisfy the equation ? Source: NCTM Mathematics Teacher, September 2006 Solution We construct products of positive consecutive integers and see which ones if any can be expressed as a power of . is the only such … Continue reading

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Real Solutions (x,y)

How  many real solutions are there that satisfy the two equations and ? Source: NCTM Mathematics Teacher, September 2006 Solution The graph of is a circle centered at the origin and radius = . The graph of is a hyperbola … Continue reading

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Twin Liars

Kerry and Kelly are twins. One of them lies on Mondays, Tuesdays, and Wednesdays and tells the truth on the other days of the week. The other lies on Thursdays, Fridays, and Saturdays and tells the truth on the other … Continue reading

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