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 - 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 - 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 - 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 - 31 & 32

If you're not clear on the process, these two are difficult.

Difficulty: Hard.

Difficulty: Pretty easy, although most kids would rate it a 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 31, answer 32. Published 5/2.

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 ... 25 & 26

Today, we have a nice addition to the questions about synthetic division and complex numbers.

Difficulty: Easy, but the "three solutions must be positive" is a nice twist on this.

Difficulty: Medium, because of the time pressure ... determining the patterns is straightforward.

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 4/29.

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 ... 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 ... 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 ... 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 ... 11 & 12

Classic trigonometry problem that demonstrates the spirit of the UVM Math Contest. Do you remember your angle formulas?

Difficulty: medium, if only because of the time pressure.

Difficulty: Pretty easy, once you see where you're going.


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 11, answer 12.

2013 ... 9 & 10

We've got some real, rootin'-tootin' algebra to contend with today!.

In Ms. Direction's class? Really?

Difficulty: easy.

Here it is!

Difficulty: easy-medium, depending on whether they have that flexibility that allows them to follow a dead-end idea to a point and recognize it's a dead end, and then re-focus on a better tack.

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.

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.

2013 ... 3 & 4

Here's two that I really enjoyed. This first one looks like a real doozy without a calculator, but lots of stuff cancels. Classic problem that demonstrates the spirit of the UVM Math Contest.

"Simple" logarithms.

Difficulty: easy.

Difficulty: Easy, but my students got all wrapped up in it. Don't know why..

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 03, answer 04.

2013 ... 1 & 2

So, we start another set. It's been a while since I did these. I think I'm going to do them in sequential order instead of the 1&41, 2&40 pattern. This will be easier for me to keep track of.

Simple algebra.

Difficulty: easy.

Difficulty: Easy.
Note: the exponent on the second () changed to -3/2. Sorry about that.

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 01, answer 02.

Answers 2013

This post is backdated intentionally.


Problem 01: $\frac{163}{60}$
Problem 02: $\frac{9}{32}$
Problem 03: 6
Problem 04: 1620 feet
Problem 05: $\frac{15}{2}$ - NOT 7.5. "Rational number in lowest terms."
Problem 06: Mincle has 22 toes
Problem 07: 5604
Problem 08: 21 minutes
Problem 09: 73
Problem 10: $\frac{5}{6}$
Problem 11: $\sqrt{3}$
Problem 12: 132
Problem 13: $\frac{5}{12}$
Problem 14: 36 square units
Problem 15: $\frac{4\pi\sqrt{3}}{3}$
Problem 16: 15
Problem 17: $\frac{10}{3}$
Problem 18: $\frac{-11}{12}$
Problem 19: 18
Problem 20: $\frac{5}{8}$
Problem 21: $\frac{12}{7}$
Problem 22: 4500
Problem 23: 3375
Problem 24: 162 square units
Problem 25: 19
Problem 26: -8
Problem 27: 122 paths
Problem 28: $\frac{12}{5}$ units
Problem 29: 10 units
Problem 30: 2
Problem 31: (2,1) and (0,2)
Problem 32: 10004
Problem 33: $\frac{1}{66}$
Problem 34: 90
Problem 35: $6\sqrt{10}$
Problem 36: (2, 5/6)
Problem 37: 38
Problem 38: $\frac{3}{8}$
Problem 39: 6 square units
Problem 40: t=8, u=7
Problem 41: $\frac{34}{3}$

Sample box for copying purposes..