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 ... 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. 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: 1

Day one. Question 1

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
Answer is here.

2004 #08 and 34

We're mixing it up today.

Difficulty: Algebra rules.

Difficulty: Boring ... but that's solely my personal feelings.

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 08, answer 34.

2002 #9 and 33

An easy one and then one to make you iRate!

Difficulty: Pretty easy, once they understand the idea.

Difficulty: Rates and people going every which way ... whatever. Complex but not terribly 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

answer 09 and answer 33.

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 #2 and 40

One from the beginning (generally easier) and one from the end (generally harder for the kids) so you can have a choice.

Difficulty: pretty easy for most 12th graders.

Difficulty: Some substitutions that will challenge them.

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 02 and answer 40.

1990 - 13 & 14

This new set is from the 1990 test.

Difficulty: Easy for teachers, not so much for students -- my students come to me with little experience with fractions and no knowledge of the repeating decimal to fraction techniques. Fractions in all phases of math are so important yet the elementary and middle school don't seem to be doing much with them.

Difficulty: Almost too Easy. And yet, the tenth graders spent lots of time trying to find lengths of AE and BC.

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 13, answer 14, Published 5/12.

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.

1990 - 4, 5, and 6

This new set is from the 1990 test.

Difficulty: Easy.

Difficulty: Easy.

Difficulty: Easy, but with a twist.

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 04, answer 05, answer 06, Published 5/8.