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 ... 25 & 26

Today, we have a nice addition to the questions about synthetic division and complex numbers.

Difficulty: Easy, but the "three solutions must be positive" is a nice twist on this.

Difficulty: Medium, because of the time pressure ... determining the patterns is straightforward.

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 25, answer 26. Published 4/29.

2013 ... 19 & 20

Function - sequence question and a clever probability that requires close attention to the framing of the problem.

Difficulty: Medium, if only because the function makes the pattern elusive. Once you have it, it's simple.

Difficulty: Medium. I found this one tough to frame, but easy to solve. I did take too much time.


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 19, answer 20.

2004 #16 and 26

Simple algebra -- as soon as you've stated the problem with algebra.

Difficulty: easy.

Difficulty: Functions. Meh.

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 16, answer 26.

2004 #11 and 31

What percent will get this correct answer? Correct!

Difficulty: Quick.  Only the reckless will get this wrong.

Difficulty: Oddly difficult.

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 11, answer 31.

2004 #01 and 41

Start of a new series. A nice fraction and a holy craptastic function thing. Wow!

Difficulty: Simple.

Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

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 01, answer 41.

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: #19 and 25

Odd little function.

Difficulty: Moderate.  How do primes get involved?

Difficulty: Combinations annoy me.

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 19 and answer 25.

2002 #13 and 29

Patterns!

Difficulty: Easier than it looks. Getting students to begin seems to be the key.

Difficulty: Patterns, again.

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 13 and answer 29.

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: #3 and 39

This group is from 2002.

Problem 3

 

Difficulty: Easy.  About those fractions .... similar to the Harmonic Mean and to resistance in parallel if if were addition.

Problem 39

Difficulty: Fairly difficult for your students.

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 03 and answer 39.

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.

1990 - 31 & 32

You'll need a good understanding of logarithms today ... and an ability to understand the weirdest function question I've ever seen.

Difficulty: Easy-Medium.

Difficulty: Medium-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 31, answer 32, Published 5/21.