2013 - 39, 40 & 41

And we now wrap up the 2013 test. Next set will be from the early years.

Some algebra for today. Typical for the last questions, there is one infinite geometric series. Here is the one for this test:

Difficulty: Medium.

Difficulty: Hard, sort of.  The units digit is easy but the tens digit follows a more complicated pattern and takes a while to find.

Difficulty: Medium, but the kids will find it 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 39, answer 40, answer 41. Published 5/6.

2013 - 33 &34

Most of the time, I hate questions that include the words "How many different ways  ...", but this one wasn't bad. The other one? Wasn't to be this year.  Didn't have the slightest clue.

Difficulty: Hard, until you ask the question correctly. Then it's medium.

Difficulty: No clue.

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 33, answer 34. Published 5/3.

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 ... 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 ... 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 ... 5 & 6

This first one looks weird, but it's just triangles. The second is good old number theory..

"Simple" area.

Difficulty: relatively easy, but again, many students stumbled on it.

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 05, answer 06.

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 #14 and 28

Thinking is fun.

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 14, answer 28.

2004 #10 and 32

Algebra and number theory.  Easy day..

Difficulty: Algebra rules.

Difficulty: 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 2004

answer 10, answer 32.

2004 #04 and 38

How well do yours remember exponents?

Difficulty: Simple, maybe.

Difficulty: Number theory. Tough little bastard until the AHA! moment.

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 04, answer 38.

1990 - 39, 40, & 41

What is the "AHA!" moment?

Difficulty: Hard.

Now it's time to just make shit up.

Difficulty: Medium - Hard.

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 1990

answer 39, answer 40, answer 41, Published 5/25.

1990 - 33 & 34

What can I say? This first one is cool.

Difficulty: Easy-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 33, answer 34, Published 5/22.

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 - 29 & 30

A little geometry and some number theory today.

Difficulty: Easy-Medium.

Difficulty: 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 29, answer 30, Published 5/20.

1990 - 25 & 26

I hate to admit it, but I stared at this for a while, then I said to myself, "Self, this is something I'm just not going to see. There's some Geometry theorem I'm missing." So I looked at another problem and then went back to this one; still nothing. The next day, I came back to it and had the big face-palm - OMFG, it's right there.
.

Difficulty: Easy if you're paying attention ...

Difficulty: Medium. Clever how the answer is possible but not obvious until you have that flash of insight ...

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 5/18.

1990 - 23 & 24

This new set is from the 1990 test.

Difficulty: Easy if you've got a good imagination ...

Difficulty: Medium. I like how this seems to not have enough information but when you model it algebraically, BOOM ...

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 5/17.

1990 - 21 & 22

This new set is from the 1990 test.

Difficulty: Medium. Framing this algebraically ...

Difficulty: Medium. Finding ALL the solutions and then realizing how to answer the question ...

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 5/16.

1990 - 19 & 20

This new set is from the 1990 test.

Difficulty: Medium. I didn't bother with this one - too lazy. Anyone? Post them in the comments for the answer sheet !

Difficulty: Medium because of time pressure. Easy to understand, though. A good one for all levels.

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, Published 5/15.


Latex test:

What is \(\dfrac{9}{10}+\dfrac{9}{100}+\dfrac{9}{1000}+\dfrac{9}{10000}+ ...\)?
Put another way, what is the value of $0.\overline{9}$ or $0.999999 ...$?

1990 - 9 &10

This new set is from the 1990 test.I'm thinking that these questions have been easier than more recent tests, with simplistic questions that don't really lead to any epiphanies.

Difficulty: Too 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 09, answer 10, Published 5/10.