MathCounts - Open ended responses

Mrs. Weeks is starting a weekly math club to help students in her area prepare for the

MATHCOUNTS Competition Series. There are 8 students in the club, and the club will

have a total of 10 one-hour weekly meetings before the local Chapter Competition.

Each week, Mrs. Weeks gives her students a large collection of challenging math problems,

and they work individually to solve as many as they can during the one-hour meeting.

If each problem takes 5 minutes on average for a student to solve individually, and no

problem is solved twice, what is the total number of problems that Mrs. Weeks’s students

will solve in the weeks before the Chapter Competition?

Tags

CCSS.HSF.BF.A.2

What is the sum of the five smallest prime numbers?

If 5 nims are equal to 12 nyms, and 4 nyms are equal to 3 neems, then how many nims

are equal to 18 neems?

Tags

CCSS.6.RP.A.3D

Class scores on a math test in Mrs. Wright’s class were spread from 52% to 99%. What is the range for this test?

(Reminder: Due to variety of possible typos in a free response, include only the numerical value and not units.)

Tags

CCSS.4.MD.B.4

The difference between the range and the median of a dataset is 35. When the values in the dataset are doubled, what is the difference between the new range and the new median?

Mr. Mathis walks into the first meeting of the Katherine Johnson Middle School Math Club.

He looks up and says, “Although I don’t know your birthdays, I know at least four of you

were born on the same day of the week.” What is the smallest number of students who

could be in the classroom to guarantee that Mr. Mathis’s statement is correct?

The sum of two even positive integers and the positive difference of those same two integers differ by 16. What is the least possible product of the two integers?

Tirza makes a small snowman out of modeling clay and calculates that it requires $2.50 of clay to make. Selalini makes a snowman that is 4 times longer in every dimension than Tirza’s snowman. When dimensions increase by a factor of x, the volume increases by a factor of x^3. What is the value of the clay that Selalini uses to build her snowman?

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A theater sells tickets at adult and child prices. One day, the theater makes $1380 in ticket sales. If all the tickets were adult tickets, the sales would have been $1500. If instead, all the tickets were upgraded to 3D for $2.00 extra per ticket, the sales would have been $1580. A child ticket costs $9. How many child tickets did the theater sell?

(Reminder: Due to variety of possible typos in a free response, include only the numerical value and not units.)

Tags

CCSS.8.EE.C.8C

What is the maximum possible value of a/b if a and b are two numbers chosen from the list −6, 10, −4, 2, −40, 15, −3? Express your answer as a common fraction.

Tags

CCSS.7.NS.A.2B