2013 - 27 & 28

Some people like these questions. I don't care for them and I rarely attempt them on the test.

 

Difficulty: I guess it's a medium, but I have no real sense 'cause I didn't try it !

Difficulty: Medium, if they have done conics; hard, if not.

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 4/30.

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.

2007. 38

Daily, they'll get harder.  How hard? Try this one:

Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.

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.

2007: 17 and 25.

Day Seventeen

Difficulty: easy-schmeasy, if you subtract. More complicated if you try to add.

Problem 25 = 5².
(I wonder how often you can switch the digits and still write an equivalent expression.)

Difficulty: Medium. More damned logarithms, but there's a neat little prime factorization going on, too.

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.

2007: 16 and 26

Sweet Sixteen

Difficulty: easy-ish. Another SAT-type reasoning question. Fun to watch the students work out the ramifications.

Problem 26

Difficulty: Medium. Is it wrong of me to get really annoyed at this question?  It's not terribly difficult, but it is so ... artificial.

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 16 and answer 26.

2007: 14 and 28

Day Fourteen

Difficulty: easy-ish. It's similar to a lot of SAT questions in that you don't actually solve for a, b or c but use them all in concert to find some other value.

Problem 28

Difficulty: Medium. Advanced Logarithmic manipulation.

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 14 and answer 28.

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.

2007. 8 and 34

Day Eight will make you think a second ... or ten.

Difficulty: easy.

Difficulty: Hard-ish
(if they don't know the 3D Pythagorean theorem and have to work it out.)

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 8 and answer 34.

2007. 7 and 35

Problem 7

Difficulty: so easy the kids kept second-guessing themselves. ;-)

Problem 35

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 7 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.