# Tag Archives: NCTM Mathematics Teacher

## 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

## 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

## 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

## Arc of a Circle

is a diameter of a circle of radius unit. is a chord perpendicular to that cuts at . If the arc is of the circumference of the circle, what is the length of the segment ? Source: NCTM Mathematics Teacher, … Continue reading

## Multiplicative Inverse

If , then in the form of , what does equal? Source: NCTM Mathematics Teacher, September 2006 Solution By definition of multiplication inverse Answer:

## Second Number Larger Than The First

Suppose a six-sided die has sides numbered through . If a person throws the die two times, what is the probability that the second number will be larger than the first? Source: NCTM Mathematics Teacher, September 2006 Solution The desirable … Continue reading

## 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

## 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

## 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

## 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