To see the explanations of the answers, click on the answer.

 

 
Oklahoma School of Science and Mathematics

Fourth Annual Middle School Mathematics Contest

Round One, Spring, 2006

 

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.  Common fractions should be in simplest form (  ).

ANSWERS1.  There are 12 eggs in a carton, 8 cartons in a crate, and 9 crates in a container.  How many eggs are in a container?

 

1.   864     eggs                                                                                                                                                                                                                                                                                                                                                                   

2.  Write  in scientific notation.

 

2.  

3.  What is the value of if the sequence is an arithmetic sequence?

 

3.     40

4. What is the value of  as a common fraction?                                                                

 

4.      

5.  A shape is translated so that the point  moves to.  Under the same translation, to what point  does the point  move?

 

5.     ( 6 ,  6 )

6.  For how many positive integers,, is ?

 

6.        7

7. For how many positive integers,,is ?

 

7.      249

8.  The function for integers  generates prime numbers.  What is the value of ?

 

8. 

           20

9.  Bubba Bigbucks used a $100 bill to pay for two books that cost $11.98 each, two CDs that cost $12.94 each, and a shirt that cost $21.50.  If the tax rate is 8.25%, how much does Bubba receive in change from his $100?

 

9.       $ 22.77

10. What is the smallest 3-digit number that can be obtained from 4921508 by crossing out 4 digits?

 

10.    108

11. Julia jogs at a rate of six miles per hour.  What is her rate in feet per second?  Express your answer as a decimal to the nearest tenth.

 

11.   8.8      ft/sec

12. Which is larger, ?

 

12.   

13. If  and , what is the positive difference between  and ?

 

13.      11

14.  How many two-digit numbers are divisible by both 2 and 7?

 

14.        7

15. Given , if , what is the length of ?  Give your answer as a common fraction.

 

15.    

                                                                                                                              

16. What is the value of  as a common fraction?

 

16.      

17. Solve for :  .

 

17. 

             15

18. How many digits does  have when multiplied out?

 

18.  

          18

19. On a number line, point M is the midpoint of .  The coordinate of A and M are  and  respectively.  What is the coordinate of point B?

 

19.  

          16

20.  A rectangular wall is being covered with 4-inch by 4-inch square tiles.  How many tiles are needed to completely cover a wall that is 5 feet by 7 feet?

 

20. 

             315  tiles