# Monthly Archives: December 2015

## Pennies on Table

Some pennies are piled on a table. If you put them into piles of size , or , you always end up with penny left over. There is more than penny on the table. What is the fewest number of … Continue reading

## 2015 in review

## Value of x and y

You are given that and . Calculate the value of . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Factoring out Factoring out If and , then and are the zeros of the quadratic function in The function has two zeros It is easy … Continue reading

## Tetrahedron

Four of the nonadjacent vertices of a cube form a regular tetrahedron. What is the ratio of the surface area of the cube to the surface area of the tetrahedron? Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let the side … Continue reading

## Collinear Points

The points , and lie on straight line. Find all possible values for . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Slope of line using the points and Slope of line using the points and If the three points lie … Continue reading

## Interior Angles

The interior angles of a pentagon form an arithmetic sequence. The measure of one angle is . Find all possible values of the largest angle. Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let be the arithmetic sequence formed by the … Continue reading

## Perfect Square

What is the smallest positive integer such that is a perfect square? Source: NCTM Mathematics Teacher, December 2005 SOLUTION will be smallest when we make the numerator as large a perfect square as it can be. Answer:

## Multiple of 72

The seven-digit integer is a multiple of (where are digits). Determine all possible ordered pairs . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Since and , we multiply by , etc. and by , etc. to find the possible digits … Continue reading

## Big and Small Circles

Two circles of radius are tangent to each other as shown. A line is drawn tangent to both circles. A third circle is drawn so that it is tangent to both circles and the line. The radius of this smaller … Continue reading

## Jet Plane

A jet plane makes a round trip from Yarmouth to Sydney. When the plane is flying into a headwind during the trip, its speed is km/h, and its speed with a tail wind is km/h. What is the average speed … Continue reading