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.

2007, 12 and 30

Day Twelve

Difficulty: easy-ish. Does your student remember his trig identities?

Problem 30

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

answer 12 and answer 30.

2004 #13 and 29

Multiply or divide? You decide..

 Difficulty: Algebra rules.

Difficulty: Well, do we count her different personalities as different people?

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 13, answer 29.

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.

2004 #07 and 35

Wordiness.

Difficulty: Too simple? Maybe.

Difficulty: Interesting. Don't count ties.

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 07, answer 35.

2002: #19 and 25

Odd little function.

Difficulty: Moderate.  How do primes get involved?

Difficulty: Combinations annoy me.

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 25.

2002 #18 and 24

Permutations with a twist. Let's go do the twist. And ARCLength!

 Difficulty: medium.

Difficulty: Are they paying attention?  It's a lead-pipe cinch that most will get the degrees of arc and forget to RTFQ.

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 18 and answer 24.

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.

2002 #7 and 35

Complex numbers, binomial expansion, rationalizing the denominator, oh-my! Then combinations!

Difficulty: moderately difficult, time is the problem for some.

Difficulty: Combinations annoy me.

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 07 and answer 35.

1990 - 27 & 28

The "How many squares are on a chessboard?" question, updated slightly.

Difficulty: Medium.

Difficulty: Medium. To me it smacks of fractions and a common denominator.

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 27, answer 28, Published 5/18.

1990 - 17 & 18

This new set is from the 1990 test.

Difficulty: Medium, because of the "Description without Diagram" issue.

Difficulty: Medium. I haven't thought about this one yet. Somebody mind posting a comment to the answer 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 2013

answer 17, answer 18, Published 5/14.

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.