Monthly Archives: April 2014

Threaded Screw

A -inch screw is threaded for of its length. If the screw has threads, how far will it go into a piece of wood with each complete turn? Source: NCTM Mathematics Teacher 2008 SOLUTION Length of threaded part Depth of … Continue reading

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Units Digit of Seven

How many numbers in the above set will have a ones digit of seven? Source: mathcontest.olemiss.edu 4/28/20134 SOLUTION Imagine the exponents¬† plotted on the number line. Of these exponents we want . How many of them? Numbers in the set … Continue reading

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Median of a Trapezoid

The trapezoid has and . The three congruent sides have lengths . Find the length of the median in terms of . Source: NCTM Mathematics Teacher 2008 SOLUTION Triangle is a triangle with hypotenuse equal . Likewise Median of trapezoid … Continue reading

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Sum of Two Odd Primes

In about 1742, in a celebrated correspondence with Leonard Euler, Christian Goldbach conjectured that every even integer greater than or equal to is the sum of two odd prime numbers. Write as the sum of two primes. Source: NCTM Mathematics … Continue reading

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Nonagon

A nonagon has nine interior angles, of which sum to degrees. Two of the remaining three angles are supplementary and two of the remaining three angles are complementary. Find the angle measures of the remaining three angles. Source: mathcontest.olemiss.edu 4/21/2014 … Continue reading

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Fourth Vertex

Points , and are coordinates of three vertices of a parallelogram. What are the possible coordinates of , the fourth vertex? Source: NCTM Mathematics Teacher 2008 SOLUTION 1) opposite 2) opposite 3) opposite Method 1: Apply the midpoint formula to … Continue reading

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Sum of Powers of Two

Every positive integer can be expressed in a unique way as the sum of powers of . Express as the sum of powers of . Source: NCTM Mathematics Teacher 2008 SOLUTION Answer:

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Area of Rectangle

A triangle has side lengths , and . The area of the rectangle with side lengths and is a two-digit number, with both digits equal to . The sum of the digits in is one-third the value of . What … Continue reading

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Inscribed Rectangle

In the diagram below, the inscribed rectangle has side length . The length of that side is percent of the side length of the circumscribed square. What is the area of the unshaded region? Source: NCTM Mathematics Teacher 2008 SOLUTION … Continue reading

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Walk in a Meadow

Maxwell is walking in a meadow. First, he walks north for m and then northeast for m. From there he walks m south and then southeast for m. At that point, he turns and walks in a straight line back … Continue reading

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