2013 ... 21 & 22

These questions were, for me , quite challenging. I got places with #21, but didn't get close enough to a solution to continue working on it during the test time (I take the test under the same constraints as the students).

Difficulty: Medium - Hard.

Difficulty: Medium. Finding the pattern and breaking the psychological blocks? Yeah, I got this one wrong. I forgot a whole set of numbers. Hope you do better.


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 4/28.

2013 ... 17 & 18

Geometry ... it's starting to get interesting.

Difficulty: It should have been easy, but this one gave me fits.

Difficulty: Another one that ran me around for too long. Medium difficulty..

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 17, answer 18.

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.

2007: 17 and 25.

Day Seventeen

Difficulty: easy-schmeasy, if you subtract. More complicated if you try to add.

Problem 25 = 5².
(I wonder how often you can switch the digits and still write an equivalent expression.)

Difficulty: Medium. More damned logarithms, but there's a neat little prime factorization going on, too.

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 17 and answer 25.

2007: 14 and 28

Day Fourteen

Difficulty: easy-ish. It's similar to a lot of SAT questions in that you don't actually solve for a, b or c but use them all in concert to find some other value.

Problem 28

Difficulty: Medium. Advanced Logarithmic manipulation.

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 14 and answer 28.

2004 #19 and 23

This year was 2004.  They had to work that in somehow.

Difficulty: easy.

Difficulty: Pretty complex. I was chasing log rules around for a while trying to get all this worked out.

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 19, answer 23.

2002 #17 and 25

Using every possible rule of Logarithms and a bit of combinatorial thinking:

Difficulty: Pretty Tough for students.

Difficulty: Much simpler than it appears. Brute force solution works best.

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 17 and answer 25.

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.

1990 - 11 & 12

This new set is from the 1990 test.

Difficulty: Easy. My algebra II kids did this one without algebra and then realized how much easier it is with systems.

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 11, answer 12, Published 5/11.