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Show that if n ∣ m, where n and m are integers greater than 1, and if a ≡ b (mod m), where a and b are integers, then a ≡ b (mod n).


Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.


20 trucks were tested at a check point. 6 trucks failed the test for brakes. 7 trucks failed the test for light. 9 trucks passed the tests for both brakes and lights
A) complete the Venn diagram
B) find n(B'nL')

If there are three roads from Goshen to Gravette and two roads from Gravette to Tontitown, how many ways are there to go from Goshen to Tontitown through Gravette?


 Design a single error correcting code for m=3 & n=7


Explain with illustrations how you would use rounding off and compensation as calculation techniques to judge the reasonableness of solutions. Give one example in each case.

Set up a number pattern with six terms for square numbers



4C2 is equal to _____________


Proof of rational points on the general form of conic sections?


A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)


B. Determine if each of the following numbers is a prime or composite.


6.  828


7. 1666


8. 1781


9. 1125


10. 107


C. Find the greatest common divisor of each of the following pairs of integers.


11. 60 and 100


12. 45 and 33


13. 34 and 58


14. 77 and 128


15. 98 and 273


D. Find the least common multiple of each of the following pairs of integers.


16. 72 and 108


17. 175 and 245


18. 150 and 70


19. 32 and 27


20. 540 and 504





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