2013 - 31 & 32

If you're not clear on the process, these two are difficult.

Difficulty: Hard.

Difficulty: Pretty easy, although most kids would rate it a 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 2013

answer 31, answer 32. Published 5/2.

2013 - 27 & 28

Some people like these questions. I don't care for them and I rarely attempt them on the test.

 

Difficulty: I guess it's a medium, but I have no real sense 'cause I didn't try it !

Difficulty: Medium, if they have done conics; hard, if not.

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 27, answer 28. Published 4/30.

2007. 38

Daily, they'll get harder.  How hard? Try this one:

Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.

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: 11 and 31

First, an easy one.

And then something more complicated, though personally, I'm not a fan of probability questions.

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 11 and answer 31.

2007. 5 and 37

Day Five, Number 5

Difficulty: easy.
and Problem 37 because 38 was already posted and I didn't want to lose any of the comments.

Difficulty: Hard. (Last page)

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 5 and answer 37.

2007. 4 and 39

Problem (4)

Difficulty: first page.

Problem 39

Note: Remainder.
Difficulty: Hard. (last page)

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
Yeah, I know, it should read "larger" and "smaller" but I didn't have the energy to fix it.


answer 4 and answer 39.

2004 #15 and 27

Slope. Parallel and perpendicular lines and a big honking radical. What joy!

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 15, answer 27.

2004 #12 and 30

I find it probable that even sum of your odd students will get this one.

Difficulty: Easy.

Difficulty: This one took a minute to even get started.

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 12, answer 30.

2002 #20, 21, and 22

Greatest Integer Function and Radicals in one problem? Be still my beating heart. A problem where intuition works best? Awesome. Similar triangles masquerading as a tough problem. Wow!

Difficulty: moderately difficult for students who don't see how the GIF is applied here. Of course, the resulting radicals are complicated, too.

Difficulty: Simple answer is the correct one.  Proving it is an interesting discussion.

Difficulty: Again, pretty simple if they're paying attention.

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 20, answer 21 and answer 22.

2002 #8 and 34

A complex function that creates a pattern that, once understood, is beautifully simple.

Difficulty: Few students have dealt with a function of this nature.

Difficulty: To be honest, I had no clue on this one. I would have to rate it difficult because the answer method seems so esoteric to this engineer.  Maybe the math majors will face-palm on my obtuseness, but I'll have to risk it.

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 08 and answer 34.

2002 #5 and 37

Geometry rules. Then number theory.

Difficulty: Not too bad. Arc length, anyone?

Difficulty: Just algebra. Okay, there's some heavy lifting here, but LOTS of stuff cancels.

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 05 and answer 37.

1990- 35 & 36

Absolute value equations? Tasty.

Difficulty: Medium.

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 2013

answer 35, answer 36, Published 5/23.