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.

2004 #19 and 23

This year was 2004.  They had to work that in somehow.

Difficulty: easy.

Difficulty: Pretty complex. I was chasing log rules around for a while trying to get all this worked 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 2004

answer 19, answer 23.

2004 #17 and 25

Fraction fun. Maybe simple enough for the SAT but maybe not.

Difficulty: easy.

Difficulty: Another one of the problems that needs you to manipulate one expression until it looks like another.  Try cubing.

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 17, answer 25.

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.

2004 #03 and 39

Every year, they manage to work the date into question.  Here's this year's:

Difficulty: Pretty Simple.

Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

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 03, answer 39.

2004 #02 and 40

A nice fraction and a seemingly simply area question. Nice!

Difficulty: Simple.

Difficulty: Easy after the AHA! moments. 

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 02, answer 40.

2004 #01 and 41

Start of a new series. A nice fraction and a holy craptastic function thing. Wow!

Difficulty: Simple.

Difficulty: Relies on a bunch of work and a couple AHA! moments.  Tough.

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 01, answer 41.

2002 #10 and 32

Fractions and reasoning!

Difficulty: Pretty easy, for us old fogies who aren't scared of fractions.

Difficulty: Double angle formula. Yum. Algebra. Yummier.

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.

2002: 1 and 41

Starting a new set!  This group is from 2002.  As with the previous ones, I'll post two at a time so you won't be tempted to work through all 41 at once.  You have to eat, you know.  Just looking out for your basic health.

Problem 1

Difficulty: Easy and fun. I really don't get why students freak out over these simple fraction problems. Okay, I do understand ... not enough practice.  So here's another practice problem.

Problem 41

Difficulty: Until you see it, "What?" When you see it, "D'oh!"
Simple geometry and two nifty trigonometric doodads.


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 01 and answer 41.

1990 - 15 & 16

This new set is from the 1990 test.

Difficulty: Medium. It is, of course, a simple system but algebra II kids don't see that until you point it out. Pre-Calc should have no difficulty.

Difficulty: It Should Be Easy. See yesterday's mini-rant on fractions.

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, Published 5/13.

1990 - 1, 2, and 3

This new set is from the 1990 test. I'd forgotten how much easier the questions seem to be. What do you think?

Difficulty: Easy.

Difficulty: Easy, but you know someone is going to say 1/13, right?

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 01, answer 02, answer 03, Published 5/7.