Monthly Archives: February 2014

Mini-triathlon

While competing in a school mini-triathlon, Ray ran miles in minutes, swam mile in minutes, and biked miles in minutes. What was his average rate for the race? Source: NCTM Math Teacher 2008 SOLUTION Average rate = distance/time Unit conversion from … Continue reading

Tree Height

A certain kind of tree increases in height by percent each year. It was feet tall when it was planted in January 2000. Approximately how tall will the tree be in December 2008? Source: NCTM Math Teacher 2008 SOLUTION Height … Continue reading

Toymaker

A toymaker is making miniature 3-wheel and 4-wheel all-terrain vehicles (ATVs). He has a total of wheels and sets of handlebars. How many 4-wheel ATVs can he make? Source: NCTM Math Teacher 2008 SOLUTION If the toymaker makes 4-wheel ATVs, … Continue reading

Candy Bars

A school fund-raiser has students selling candy bars in two sizes: and . Anthony collected but forgot what he sold. If remembers selling at least candy bars and at least of the jumbo size, how many possible combinations could he … Continue reading

Block Schedule

A school system plans to switch to block schedule. Currently, there are seven 47-minute teaching periods in a day, minutes passing time, and minutes for lunch. In the new schedule, there will be four teaching periods each day, minutes between … Continue reading

Math Exam

The American High School Mathematics Competition level-12 exam has multiple-choice questions. Students receive points for each correct answer, points for each problem unanswered, and points for incorrect answers. Given this scoring system, in how many ways can a student receive … Continue reading

Newton’s Class

More than percent of the students in Mr. Newton’s math class are girls. If Mr. Newton’s class has at least one boy, what is the least possible size of his class? Source: mathcontest.olemiss.edu 2/24/2014 SOLUTION Ratio    Percent The least possible size … Continue reading

New Movie

A new movie opened with gross box-office sales of million. The producers were disappointed because this figure was percent less than expected. How much did the producers think they would make during the first weekend? Source: NCTM Math Teacher 2008 … Continue reading

Successive Zeros

How many seven-digit sequences of and are there that have a block of three successive but do not have a block of four or more successive ? Source: mathcontest.olemiss.edu 2/17/2014 SOLUTION Seven-digit binary sequences start from to , in decimal … Continue reading

Fibonacci-type Sequence

In a Fibonacci-type sequence of increasing positive integers, each number after the first two is equal to the sum of the two numbers that immediately precede it. If the tenth number is 322, compute the fifth number. Source: NCTM Math … Continue reading