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.

2007:. 41

Since there are so many truly able mathematicians among my readers, I've decided to give them something to keep busy with! This set will start at the hardest and work backwards.

Difficulty: hard.
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
Answer is here.

2007: 18 and 24

Problem 2*3²

Difficulty: easy-ish. A little trigonometric - algebraic manipulation and "Surprise!"

Problem 2³*3

Difficulty: Easy. At least once in every test, in some form or another, the creators work the year into a problem.  This test was for 2007.

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

answer 18 and answer 24.

2007, 12 and 30

Day Twelve

Difficulty: easy-ish. Does your student remember his trig identities?

Problem 30

Difficulty: Medium.

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

answer 12 and answer 30.

2004 #20, 21 and 22

Probably my favorite problem.  Looks so fierce and imposing, yet so tame.

Difficulty: easy.

Difficulty: easy.

Difficulty: Pretty complex.

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 2004

answer 20, answer 21, answer 22.

2002 #16 and 26

Trig rules. Did'ya memorize the half-angle formulae or will you need to derive them?

Difficulty: Easy if memorized. Difficult, if not..

Difficulty: Pretty easy, if you draw the diagram correctly from the description.

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

answer 16 and answer 26.

2002 #10 and 32

Fractions and reasoning!

Difficulty: Pretty easy, for us old fogies who aren't scared of fractions.

Difficulty: Double angle formula. Yum. Algebra. Yummier.

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

answer 10 and answer 32.

2002 #4 and 38

The first one is very similar to a classic SAT question that always trips up students who aren't paying attention.  The second - do they remember LoC?

Difficulty: simple.

Difficulty: Not bad, if they remember.

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

answer 04 and answer 38.

2002: 1 and 41

Starting a new set!  This group is from 2002.  As with the previous ones, I'll post two at a time so you won't be tempted to work through all 41 at once.  You have to eat, you know.  Just looking out for your basic health.

Problem 1

Difficulty: Easy and fun. I really don't get why students freak out over these simple fraction problems. Okay, I do understand ... not enough practice.  So here's another practice problem.

Problem 41

Difficulty: Until you see it, "What?" When you see it, "D'oh!"
Simple geometry and two nifty trigonometric doodads.


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

answer 01 and answer 41.

1990 - 21 & 22

This new set is from the 1990 test.

Difficulty: Medium. Framing this algebraically ...

Difficulty: Medium. Finding ALL the solutions and then realizing how to answer the question ...

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 21, answer 22, Published 5/16.