56
14. How many of the expressions
x3 + y4; x4 + y3; x3 + y3; and x4 , y4; are positive for all possible numbers x and y for which x > y ? A. 0
B. 1
C. 2
D. 3
E. 4.
15. In triangle ABC , the altitude from A to BC meets BC at D, and the altitude from B to CA meets AD at H . If AD = 4, BD = 3 and CDp= 2, then the length of HD is p p A. 25 B. 23 C. 5 D. 52 E. 3 2 5 . 16. Which of the folowing is the best approximation to (23 , 1)(33 , 1)(43 , 1) (1003 , 1) ? (23 + 1)(33 + 1)(43 + 1) (1003 + 1)
A. 35
B. 33 50
C. 333 500
D. 35;;333 000
;333 E. 33 50;000 .
Last issue we gave the SHARP U.K. Intermediate Mathematical Challenge, written February 2, 1995. Here are answers. 1. E 2. C 3. D 4. E 5. A 6. B 7. C 8. B 9. D 10. A 11. E 12. D 13. C 14. D 15. B 16. A 17. A 18. C 19. C 20. D 21. D 22. E 23. B 24. B 25. A That completes this month's Skoliad Corner. I need materials of a suitable level to build up a bank of contests. Please send me suitable materials as well as comments, criticisms, and suggestions. I would like to have some feedback too about how your students do with these materials.