Sick for Christmas

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It’s just a few days before my wife, my 16 month-old son and I start our Christmas vacation, and we’re spending it the same way we spent Christmas last year: dealing with a sick baby. For those of you non-parents out there, trust me, this is even worse that you imagine. Sickness isn’t fun for anyone, but dealing with a sick baby is especially bad because he can’t communicate with us how we can make him feel better. All he can do is cry and hope that we can discern from that particular blend of shrieks how we could help. Throw in the fact that since he’s not sleeping we’re not sleeping and you’ve got a recipe that does not equal fun.

But being sick at Christmastime is especially bad. And it’s all about expectations. When you’re feeling bad at a time when you expected to feel good, it’s feels especially awful. The difference between expectation and reality is a pretty accurate measure of happiness. If I went into the Christmas season knowing it’s a time when we commonly get sick and not expecting much out of it, I might not have been so disappointed.

In the same vein, I see many students who sabotage their chances of coming out of the test prep process happy by bringing in unrealistic expectations. I see students who expect 99th percentile scores with a moderate amount of effort even though nothing in their transcript suggests that’s at all realistic. At the end of the process, even if they’ve made great strides and accomplished quite a bit they feel as if they have failed.

So how do you avoid that letdown? First, make your goal to do the best job preparing for the test than you can do. That doesn’t sound as daunting as getting a 2300 or a 165 or a 34 or 720, but it’s an extremely high standard. The expectation is that you will do whatever is in your power to prepare and you will spend your study time as well as you possibly can. You gauge success not by the score that comes in the mail, but by how ready you are when you walk into that test room.

When that test score arrives it tells you which doors are open to you, and which doors may not be, but you don’t run the risk of the bubble popping when you realize your dream doesn’t match reality.

Set reasonable goals for yourself, aim to meet them every day, and stretch the next day’s goal a little further. Realistic expectations allow you to be proud of what you’ve accomplished. Unrealistic goals lead to a feeling almost as bad as being sick at Christmas.

 

 Imagine This

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Imagine you are given a question that describes the following situation:

There is an isosceles triangle inscribed in a circle with radius = 5. The center of the circle is at (0,0). The triangle is symmetrical about the y-axis.

Do you have a picture in your head about what that would look like? If the answer is no, it could be because you’re unfamiliar with some of the terms that were described. Perhaps you’ve forgotten what an isosceles triangle is (a triangle with two sides of equal length) or perhaps you don’t quite remember which one is the y-axis (it’s the vertical one). If that’s the case, it’s time to go back and review some of the core mathematical terms that you’ll need to know in order to be successful on your test. The Barron’s video course for your test would be a great place to start.

However, even if you got that far, there’s potentially another problem. My guess is that most of you have imagined something like this:

But did you also consider that this green triangle is a possibility as well?

The common advice we give when figures in the coordinate plane is that you should draw a picture. This is sound insofar as your brain can much more easily interpret the graphical information than a set a words given to describe that information. However, draw a picture can get you into trouble when you need to draw the picture or even the pictures.

It’s a word of caution that I hope you’ll remember. When you’re given some graphical information in word form it’s great to translate that into a picture. However, make sure you really take the time to dissect what all of the information means and could mean, so that you aren’t overlooking a part of the solution.

Good luck and happy studying!

 The 12 Days of Christmas

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It’s that time of year when you’re hearing all kinds of holiday music everywhere you go. Maybe the music reminds you of old memories with family. Maybe the music stirs generosity in your heart. Or maybe the music causes you to contemplate mathematical problems.

Okay, so unless you’re me, you problem don’t fall into that last category. But, now that you’re reading I started wondering how many total gifts are given in the 12 Days of Christmas song? If you’re not familiar with it, here’s a link to the lyrics.

The answer to this question isn’t so important to me as the process. How would you go about figuring out a question like that? Would you go gift by gift and count on your fingers and toes? Would you go day by day and sum the 12 totals? Would you be able to divine some other solution?

Since this really isn’t a test-type question that you’re likely to face, this is more an exercise in mathematical thinking. How would you go about it?

Once you’re done figuring that out, take a look at this excellent solution to the problem I proposed.

Isn’t math great?

 Thanksgiving Leftovers Part 2

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Auntie Donna makes a special drink for the Thanksgiving family gathering. All the kids love it. Little do they know that it’s just watered down grocery store punch. She has purchased 9 liters of punch from the store. If she wants to make punch that is 0.6 times as strong as the original, how much drink can she make?

A) 12 liters

B) 15 liters

C) 18 liters

D) 27 liters

E) 54 liters

In order to make punch that is 0.6 times as strong as the original that means that for every 1 liter of mixed drink there are 0.6 liters of punch. Consequently, that means there are 0.4 liters of water in every liter of mixed drink. That’s a ratio of 3 parts punch to 2 parts water. Since Donna purchased 9 liters of punch, she needs to add 6 liters of water for a total of 15 liters of mixed drink.