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 ... 23 & 24

Two questions today include a very cool number theory/algebra reasoning question and a graph of a type to make them think.

Difficulty: Medium. My absolute favorite  question on the whole test. So cool how this works out.

Difficulty: Easy-Medium. Graphing piecewise functions with absolute value mixed in is not something that most students have had experience with. Easy enough to figure out from principles, but time pressure makes this harder than it really is.

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 23, answer 24. Published 4/29.

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 ... 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.

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 ... 15 & 16

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

Difficulty: Easy..

 

Difficulty: medium, unless you know the rule about chords intersecting in a circle.

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 15, answer 16.

2013 ... 13 & 14

A little probability and a nice geometry morsel.

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 13, answer 14.