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Oklahoma School of Science and Mathematics

Third Annual Middle School Mathematics Contest

Round One, Spring, 2005

 

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.  All fractions should be in simplest form.  Units are not necessary unless specified in the problem.

  1. Find the next number suggested by the sequence 2, 5, 9, 14, 20, __?

 

1.    27
  1. 2005 is a composite number (5 x 401).  What is the next year that is a prime number?

 

2.    2011
  1. A cube 6 units on each side is painted on all sides then cut into smaller cubes by making 2 equally spaced cuts through each of the three sets of parallel faces.  What is the total volume of the smaller cubes with exactly two faces painted?

 

3.    96
  1. What is the date and time 147 hours after noon March 12?

 

4. March 18, 3 pm
  1. Evaluate .

 

5.      – 2

  1. Find the average of the numbers .

 

6.      2x – 2

  1. A rectangular piece of cardboard measures 10-inches by 20-inches.  How many 4-inch squares can be cut from the large piece?

 

7.      10
  1. If , compute .

 

8.      12
  1. Given , find r.

 

9.     ½

  1. Jason drove at a constant rate of 54 miles per hour.  How many miles did he travel in 80 minutes?

 

10.    72
  1.  What is the measure in degrees of the angle formed by the minute and hour hands of a clock at 2:15?

 

11.    22 ½

  1. Find the sum .

 

12.    1003
  1. The top three winners in a tennis tournament share the prize money in the ratio 5:3:1.  If the first place winner receives $15,000, what is the total prize money awarded?

 

13.    27,000
  1. What is the 2005th term of the sequence ?

 

14.    63
  1. Mary can do two-thirds of a job in one-third of an hour.  How many minutes does it take Mary to do the entire job?

 

15.    30
  1. A regular hexagon, 12 centimeters on a side, is inscribed in a circle.  What is the diameter of the circle in centimeters?

 

16.    24
  1. A bag contains 10 marbles, each either red or blue.  If two marbles are randomly selected, the chance that they are both blue is 2/15.  How many red marbles are in the bag?

 

17.    6
  1. Sam computed an answer to be 2.25.  He did everything correctly until the last step where he multiplied by 0.3 instead of dividing by 0.3.  What is the correct answer?

 

18.   25
  1. What is the radius, in inches, of a right circular cylinder if the lateral surface area is  square inches and the volume is  cubic inches?

 

19.   2