Tag Archives: grade 6

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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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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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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How Old Are They?

Mary’s and Bob’s ages combined are twice Jane’s age. Mary is years older than Bob. Jane’s age plus Bob’s age is years. How old are they? Source: NCTM Mathematics Teacher, September 2006 Solution Let , and represent the ages of … Continue reading

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Values of Integers

If and are integers such that , what are the possible values of ? (a) only (b) only (c) only multiples of (d) any integer (e) none of these Source: NCTM Mathematics Teacher, September 2006 Solution Let be an integer … Continue reading

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Length of Side of Square

If the numerical value of the area of a square plus two times the numerical value of its perimeter is equal to , what is the length of one side of the square? Source: NCTM Mathematics Teacher, September 2006 Solution … Continue reading

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Lemonade Stand

John has a lemonade stand. He sells a small lemonade for cents and a large lemonade for . A small serving contains cup of lemonade; a large contains cups. At the end of the day, John has made and sold … Continue reading

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Red and Yellow Plums

One store sold red plums at for and yellow plums at for . A second store sold red plums at for and yellow plums at for . You bought red plums and yellow plums from each store, spending a total … Continue reading

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