1. Find the largest integer less than or equal to .

 
  1.   1
  1. If , what is the value of ?

 
  1.   27
  1. The perimeter of a rectangle is 22 inches, and the area is 28 square inches.  What is the product of the lengths of the diagonals, in square inches?

 

 

              65     sq. in.

  1. Given , express  as a common fraction.

 
  1. Paula rides  of a mile in  minutes on her bicycle.  What is her average speed in miles per hour?

 

 

         15       mph

  1. What is the value (as a common fraction) of     ?

 
  1. On a number line, the coordinates of P and Q are 8 and 48 respectively.  The midpoint of  is B, the midpoint of  is C, and the midpoint of  is D.  What is the coordinate of D?

 
  1. 23
  1. Suppose .  What is the greatest possible positive difference of the expressions ?

 
  1. 63
  1. If  and , what is the value of ?  Express your answer as a common fraction.

 
  1. Of the four integers that satisfy , which has the least value?

 
  1. The diameter of a circle is increased so that the circumference is increased by 20%.  By what percent does the area of the circle increase?

 

                 44    %

  1. A ferris wheel with a radius of 75 feet makes a complete circuit every 6 minutes.  To the nearest tenth, how fast is a person in a seat traveling in feet per minute?

 

 

               78.5  ft/min

  1. Joan invests $20,000 in a government bond that pays 6% interest compounded annually.  To the nearest dollar, what is the value of the investment at the end of six years?

 

  $  28,370

 

  1. For how many whole numbers, M, is  between  and ?

 
  1. 2

 

  1. How many positive, odd, three-digit numbers exist such that the sum of the tens digit and the units digit equals the hundreds digit?

 
  1. 25
  1. Text Box: How many distinct triangles are in this figure? 

 
  1. 18
  1. Eleven girls are standing around a circle.  A ball is thrown clockwise around the circle.  The first girl, Ami, starts with the ball, skips the next three girls and throws the ball to the fifth girl, who then skips the next three girls and throws the ball to the ninth girl.  If the pattern continues, including Ami’s initial throw, What is the least number of throws necessary for the ball to return to Ami?

 
  1. 11
  1. The measures of the four interior angles of a quadrilateral are   degrees.  How many degrees are in the measure of the smallest interior angle of the quadrilateral?

 

 

 

               84  degrees

  1. If , find the value of  when .

 
  1. 10100
  1. The digits of a two-digit number “AB” are reversed to form a second two-digit number “BA” and the lesser of the two numbers is subtracted from the greater.  What prime number must be a factor of the difference if ?

 
  1. 3
  1. Kiley ran up a hill at 4 miles per hour and back down the same hill at 7 miles per hour.  What is her average speed in miles per hour to the nearest tenth?

 

 

                5.1   mph

  1. What non-zero real value for x satisfies ?  Express your answer as a common fraction.

 
  1. Each of the 40 letters of “THE OKLAHOMA SCHOOL OF SCIENCE AND MATHEMATICS” is cut out and placed in a bag.  What is the probability of drawing the letters “OSSM” in order if the letters are not replaced after being drawn?  Express your answer as a common fraction.

 
  1. When the average of 2006 positive numbers is divided by their sum, the result is t.  What is the value of t?

 
  1. What is the probability that if you roll two fair, standard six-sided dice, the difference between the two numbers rolled will be a multiple of 2?  Express your answer as a common fraction.

 
  1. What is the largest 4-digit number, with all different digits, that is divisible by each of its digits?

 
  1. 9864

 

  1. George’s first trip was 300 miles.  If on his second trip, the time necessary to complete the trip is doubled and his average speed is two-thirds the average speed of his first trip, how many miles is his second trip?

 

 

 

            400   miles

  1. If Team A won 30% of its games in the first third of the season, what percent of its remaining games must they win to finish the season having won 50% of its games?

 

 

                60   %

  1. The sum of three numbers is 77.  If a decreased by 5 is equal to b increased by 5 and is also equal to c multiplied by 5, what is the value of b?

 
  1. 30
  1. We define a lattice point as a point whose coordinates are integers.  Find the number of lattice points on the boundary or inside the region bounded by the x-axis, the line x = 4, and the parabola .

 
  1. 19

 

Tie breaker:  How many ordered triples  have the property that each member of the ordered triple is the product of the other two members?  Show your work.