# Tag Archives: grade 8

## U.S. Senate Committee

There are members in the U.S. Senate ( from each state). In how many ways can a committee of senators be formed if no state may be represented more than once? Source: NCTM Mathematics Teacher, August 2006 Solution We want … Continue reading

## Interest Earned

At the end of every month, Elle deposits into a savings account with an annual interest rate of percent, compounded monthly. How much interest will be earned at the end of four years? Source: NCTM Mathematics Teacher, August 2006 Solution … Continue reading

## Sum of Three Integers

For certain positive integers , and , . If and are prime, find . Source: SCVMA Math Olympiad 2010 Solution Since and are odd, and are odd which implies that is even. Hence is even because the sum is even. … Continue reading

## Cot(C) and Sine(2C)

If (a positive integer), express as a fraction involving . Source: SCVMA Math Olympiad 2010 Solution thus Answer:

## Sum of Infinite Geometric Series

The sum of the infinite geometric series is , and the sum of the series whose terms are the squares of the terms of this series is . Find the sum of the infinite geometric series Source: SCVMA Math Olympiad … Continue reading

## Difference of Two Squares

Which one of the following numbers cannot be expressed as the difference of the squares of two integers? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September 2006 Solution Let be an odd integer and for some integer and … Continue reading

## Maximum Angle

The measures of five angles of a convex polygon are each equal to . In which of the five open intervals does the maximum angle of all such polygon lie? (a) (b) (c) (d) (e) Source: NCTM Mathematics Teacher, September … Continue reading

## 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

## 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

## 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