2013 ... 11 & 12

Classic trigonometry problem that demonstrates the spirit of the UVM Math Contest. Do you remember your angle formulas?

Difficulty: medium, if only because of the time pressure.

Difficulty: Pretty easy, once you see where you're going.


Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 11, answer 12.

2013 ... 9 & 10

We've got some real, rootin'-tootin' algebra to contend with today!.

In Ms. Direction's class? Really?

Difficulty: easy.

Here it is!

Difficulty: easy-medium, depending on whether they have that flexibility that allows them to follow a dead-end idea to a point and recognize it's a dead end, and then re-focus on a better tack.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 09, answer 10.

2013 ... 7 & 8

The first is easy enough, if you understand alternate bases. Many kids don't and I'm not sure that it's worth spending much time on besides a real quick, 20-minute "check this out" session.

"Base eight is just like base ten ... if you're missing two fingers." - Tom Lehrer. (What? can't handle 30-50 year old cultural references?)

Difficulty: easy.

Difficulty: easy.


Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 07, answer 08.

2013 ... 5 & 6

This first one looks weird, but it's just triangles. The second is good old number theory..

"Simple" area.

Difficulty: relatively easy, but again, many students stumbled on it.

Difficulty: Easy.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 05, answer 06.

2013 ... 3 & 4

Here's two that I really enjoyed. This first one looks like a real doozy without a calculator, but lots of stuff cancels. Classic problem that demonstrates the spirit of the UVM Math Contest.

"Simple" logarithms.

Difficulty: easy.

Difficulty: Easy, but my students got all wrapped up in it. Don't know why..

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 03, answer 04.

2013 ... 1 & 2

So, we start another set. It's been a while since I did these. I think I'm going to do them in sequential order instead of the 1&41, 2&40 pattern. This will be easier for me to keep track of.

Simple algebra.

Difficulty: easy.

Difficulty: Easy.
Note: the exponent on the second () changed to -3/2. Sorry about that.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 01, answer 02.

Answers 2013

This post is backdated intentionally.


Problem 01: $\frac{163}{60}$
Problem 02: $\frac{9}{32}$
Problem 03: 6
Problem 04: 1620 feet
Problem 05: $\frac{15}{2}$ - NOT 7.5. "Rational number in lowest terms."
Problem 06: Mincle has 22 toes
Problem 07: 5604
Problem 08: 21 minutes
Problem 09: 73
Problem 10: $\frac{5}{6}$
Problem 11: $\sqrt{3}$
Problem 12: 132
Problem 13: $\frac{5}{12}$
Problem 14: 36 square units
Problem 15: $\frac{4\pi\sqrt{3}}{3}$
Problem 16: 15
Problem 17: $\frac{10}{3}$
Problem 18: $\frac{-11}{12}$
Problem 19: 18
Problem 20: $\frac{5}{8}$
Problem 21: $\frac{12}{7}$
Problem 22: 4500
Problem 23: 3375
Problem 24: 162 square units
Problem 25: 19
Problem 26: -8
Problem 27: 122 paths
Problem 28: $\frac{12}{5}$ units
Problem 29: 10 units
Problem 30: 2
Problem 31: (2,1) and (0,2)
Problem 32: 10004
Problem 33: $\frac{1}{66}$
Problem 34: 90
Problem 35: $6\sqrt{10}$
Problem 36: (2, 5/6)
Problem 37: 38
Problem 38: $\frac{3}{8}$
Problem 39: 6 square units
Problem 40: t=8, u=7
Problem 41: $\frac{34}{3}$

Sample box for copying purposes..