Oklahoma School of Science and Mathematics
Middle School Mathematics: An Awesome Contest

 

Directions:  Write the answer to each question in the box to the right of the question.  Use scratch paper provided to do your work.  Calculators are allowed, but not necessary.

 

  1. In how many years after 2003 will the number representing the year be a perfect square?

 

1.

  1. A sector (pie-shaped piece) of a circle graph representing 40% of the data should have a central angle of what degree measure?

 

2.

  1. How many cubic feet are there in ten boxes if each box is a cube measuring six feet on a side?

 

3.

  1. Mary has an average of 84% on five math tests.  What score must she make on the next test to raise her average to 86%?

 

4.

  1. What is the least positive integer, n, for which ?

 

5.

  1. What is the largest possible area of a rectangle with integer sides and a perimeter of 26?

 

6.

  1. A cone has radius 1 inch and height 4 inches.  What is the number of inches in the radius of a sphere of ice cream which has the same volume as the cone?

 

7.

  1. After being painted, a solid wooden cube whose edge is 4 cm is cut into 64 small 1-cm cubes.  How many of these small cubes have exactly two painted faces?

 

8.

  1. If one pair of opposite sides of a rectangle is increased by 20% and the other pair of opposite sides is decreased by 20%, by what percent does the area of the rectangle increase or decrease (indicate which)?

 

9.

  1.  What is the 50th digit in the decimal expansion of 1/7?

 

10.

  1.  What is the measure in degrees of the angle formed by the minute and hour         hands of a clock at 2:20?

 

11.

  1.  How many three-digit numbers are divisible by both 2 and 3?

 

12.

  1.  How many three-digit numbers are divisible by either 2 or 3?

 

13.

  1.  Which is larger, 2150 or 3100?

 

14.

  1.  A factorial is denoted by n! and means (n)(n – 1)(n – 2)(n – 3)...(3)(2)(1).  How many zeros are there at the end of 100!?

 

15.

  1. There are 101 red marbles and 101 black marbles in a box.  Let Ps be the probability that two marbles drawn at random (without replacement) are the same color, and let Pd be the probability that they are different colors.  Find Ps/Pd as a fraction in lowest terms.

 

16.

Disclaimer:  This is not an exact copy of the round 1 contest.  This is a faxcimily of the contest due to differemnces in software used for web display.