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 - 35 & 36

Two nice geometry questions.

Difficulty: Medium?

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 35, answer 36. Published 5/4.

2013 - 29 & 30

Another geometry question? This test seemed to have a bunch in a row.

Difficulty: Hard.

Difficulty: Medium. Series and complex numbers in the same question? What fun !

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 5/1.

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 ... 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.

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:. 41

Since there are so many truly able mathematicians among my readers, I've decided to give them something to keep busy with! This set will start at the hardest and work backwards.

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
Answer is here.

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: 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: 13 and 29

Day Thirteen

Difficulty: easy-ish. Mostly, it's an interpretation question.

I love this next problem. So very cool.
Problem 29

i.e., find the shaded area.
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 13 and answer 29.

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.

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.

2007: 6 and 36

Day Six will make you think a bit.

Difficulty: easy - ish.

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 6 and answer 36.

2007. 3 and 40

Day Three

Difficulty: easy.

I'm going to save my self some time and just include the difficult one with the easy one every day.
 Please enjoy this mathematical tidbit.

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

answer 3 and answer 40.

2004 #20, 21 and 22

Probably my favorite problem.  Looks so fierce and imposing, yet so tame.

Difficulty: easy.

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 20, answer 21, answer 22.

2004 #18 and 24

Surprisingly easy for this late in the test.

Difficulty: easy.

Difficulty: Changing everything to a common base goes a long way here.

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 18, answer 24.

2004 #15 and 27

Slope. Parallel and perpendicular lines and a big honking radical. What joy!

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 15, answer 27.

2004: 9 and 33

Round and Round we go!

Difficulty: Can they complete the square?

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 09, answer 33.