Theta Geom Answers with solutions.pdf - Mu Alpha Theta 2006...

Answers
Mu Alpha Theta Theta Geometry
2006 National Convention Theta Division
1. B or E
2. C
3. C
4. C
5. D
6. D
7. B
8. D
9. E
10. B
11. A
12. C
13. C
14. D
15. A
16. B
17. E
18. D
19. A
20. D
21. A
22. D
23. C
24. D
25. B
26. D
27. A
28. B
29. E
30. B

Solutions
Mu Alpha Theta Theta Geometry
2006 National Convention Theta Division
SOLUTIONS
1. (B) The other leg of the triangle is 48, and the circumference of the semicircle is
22
(7) 22
7
r π
⎛ ⎞
= =
⎜ ⎟
⎝ ⎠
.
The sum is .
22 48 50 120 + + =
2. (C) The wheel’s circumference is
3
4
2 2 8 r π π
π
⎛ ⎞
2 = = =
⎜ ⎟
⎝ ⎠
.
5
2
3
2
2 4
2
= =
.
3. (C) The only way to score 10 points is to score 3+7, 7+3, or 5+5. The sum of the respective probabilities
is
7 3 3 7 5 5 67
16 16 16 16 16 16 256
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞
+ + =
⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠
4. (C) By definition.
5. (D) The square’s perimeter is
2
4 4 2 5.6
2
r
r = ≈ r
. The hexagon’s perimeter is 6 r . The circle’s
circumference is
2 6.3 r r π ≈
.
6. (D) An interior angle of a regular dodecagon (which is the supplement of an exterior angle) is
180 (12 2)
150
12
° −
= ° .
7. (B) The woman ends 2 miles east and 6 miles south of her starting point, a distance of
2 2
2 6 40 + =
.