Algebra

Upcoming SAT tests

January 1, 2012
By

The next SAT test is scheduled for January 28.  That is only 27 days away!  If you are registered to take this test it is time to buckle down and finish your preparation. 

What should you be doing? 

Sign up for word of the day by Dictionary.com  Pay attention to the derivatives of the word when you get each new word.  Don't worry so much about memorizing the word, although that is a good thing, but try to memorize the prefixes and suffixes of that word.

Review the most basic math formulas and practice using each one a few times.  This includes finding the area of squares, rectangles, parallelograms, trapezoids, circles and triangles.  You will also need perimeter of quadrilaterals and other polygons and the circumference of a circle.  Add to that finding the surface area of cones, cylinders, cubes and pyramids and the volume of those figures are well.  Yes you are provided these formulas at the beginning of each math section on the SAT, but you don't want to spend time shuffling through the pages to find them each time you need to use one and you certainly don't want to have to spend time staring at them to figure out what the letters in the formulas stand for.  The best way to do this is to put each formula on one side of an index card and put at least 2 examples on the other side of the card.

Don't complain about the critical reading.  Yes, everyone knows you aren't interested in the subject matter of each reading; they are boring; they use tough vocabulary.  Remember, the SAT is a measure of how well you will do in college and there will be many times in college when you will be required to read something that doesn't interest you, even in your major subject.

The night before the test don't study at all.  Do something you like to do, but don't go out partying; watch TV, listen to music, read for fun or play video games.  Gather your pencils and make sure they are sharpened.  Be certain you have fresh batteries in your calculator.  Get a good night's sleep and be sure to eat a good breakfast before you leave for the test.  Include some protein in that breakfast to provide you with long lasting energy. 

Most of all, don't panic.  Enjoy the experience.  GOOD LUCK!!

Cramer’s Rule

November 10, 2011
By

Cramer’s Rule is a method of solving systems of equations. There are many methods including substitution and elimination. Sometimes though the coefficients of the equation are ugly. (Ugly isn’t my terminology, it is one given to me by a student.) To many students anything that isn’t a small whole number is ugly. So, when a system of equations includes fractions or decimal numbers, Cramer’s Rule has a way of simplifying what might be an otherwise cantankerous solution method.

Cramer’s Rule involves setting up something called a determinant using the coefficients (numbers before the variables).

Given the following system of equations:

Where x and y are variables and A, B, C, D, E, F are constants

Ax + By = E
Cx + Dy = F

The determinants are placed in a fraction to solve for each variable X and Y

It is written as

FOR X:

|E  B |
| F D |
_____
| A B |
| C D |

 

FOR Y:

| A E |

| C F |
_____
| A B |
| C D |

As you might have noticed, the denominators are the same and in alphabetical order for X and Y. That makes the denominator pretty easy to remember, but what about the numerators????

Well, mnemonic devices are memory techniques that utilizes acronyms or sentences or even music to help a student remember important items. One of my latest favorites is a method to remembering Cramer’s Rule.

My mnemonic for Cramer’s Rule is EVERY BOY FINDS DOGS for X and ALL ELEPHANTS CAN’T FORGET for Y. I had a student change the Y to ALL ELEPHANTS CAN’T FLY. Whatever works for you is the one to use.

Anyhow, so what does the alphabet soup tell you once you have remembered it???

Well, after you have set up the determinants, it is just arithmetic from here on in.

For X = (E*D – B*F) divided by (A*D – B*C)
And Y = (A*F – E*C) divided by (A*D – B*C)

 

 

Here is one example:

2x-3y = 9
x+5y =-2

FOR X

|9   -3|
|-2  5|                                      (9 * 5) – (-3 * -2)                           45 – 6               39
____         =                         ____________        =                        ______      =    __       =       3
|2  -3|                                      (2 * 5) – (-3 * 1)                            10 – -3               13
|1    5|

 

FOR Y

|2   9|
|1  -2|                                     (2 * -2) – (9 * 1)                                   -4 – 9                 -13
____          =                       ___________             =                           ____        =        __      =       -1
|2  -3|                                     (2 * 5) – (-3 * 1)                                  10 – -3                13
|1    5|

 

 

So, the solution set for the above example is (3, -1)

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