2013 - 37 & 38

Some algebra for today.

Difficulty:Medium if the AHA ! moment is found. Hard if you don't see the path.

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 37, answer 38. Published 5/5.

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 ... 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.

2007: 19 and 23

Problem 19

Difficulty: easy. Notice we didn't specify which color.

Problem 23

Difficulty: Very clever geometry 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

answer 19 and answer 23.

2007: 15 and 27

Day Fifteen ... We're almost there.

Difficulty: pretty easy. Kids will get wrapped up in the P(A) and if-then, but it's an example of a problem that is much easier if you imagine the grid of all possibilities. Definitely a candidate for the SAT.

Problem 27

Difficulty: Medium. It's funny how easily the kids get thrown by an infinite series.

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 15 and answer 27.

2007: 11 and 31

First, an easy one.

And then something more complicated, though personally, I'm not a fan of probability questions.

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 11 and answer 31.

2007. 10 and 32

Day Ten

Difficulty: easy-ish.

Problem 32:

Difficulty: Tricky. It seems easy, but then tries to kneecap you.

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 10 and answer 32.

2004 #12 and 30

I find it probable that even sum of your odd students will get this one.

Difficulty: Easy.

Difficulty: This one took a minute to even get started.

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 12, answer 30.

2002 #12 and 30

More set theory! And Combinations! and Probability! And Exclamation Points!

Difficulty: moderately difficult for students who haven't done combinations in a while.

Difficulty: Much simpler than the location in the test would indicate. I'd be curious to know how your kids solved 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 12 and answer 30.

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 $0.999999 ...$?