Question

Dear Mitch,

I know you've been getting lots of requests for SAT tips, so all I'm going to say is we only have a few more weeks before the PSAT, and I would appreciate the same thing everybody else seems to want: More helpful SAT TRICKS, POINTERS, TIPS, TECHNIQUES, IDEAS, AND WHATEVER ELSE PEOPLE CALL THEM.

YOURS ARE GREAT!!

So, please keep them coming.... I have quickly become hooked on them!!!

Sincerely,

Allan G.,

Miami, Florida

Answer

Dear Allan,

Here goes:

While each and every area of math is real in its own way, GEOMETRY IS SO OBVIOUSLY "REAL", that without having much prior knowledge or experience, you can find the correct answers to many of the questions by relying on the concrete aspect of the subject.

Example: Even without a protractor, you can measure angles pretty well on a test like that.

How?

Well, starting with the easiest ones: 90 degrees: any angle that you can get a corner of another page into perfectly without overlap, 45 degree: any angle that a corner folded in half fits perfectly, 135 degrees would be one of those ninety degree corners plus a corner folded in half (use your pencil to draw a line after each angle, so combining them is easy).

Then what? 180 degrees is a straight line you can check with the edge of your pencil, 270 degrees would be that line plus a page's corner, 225 the line plus the half corner.

Then what?

After folding a corner in half, that half can be folded in half. So you would have half of 45, which is 22 1/2 degrees. Or, when necessary, a corner can be folded into thirds, then used to measure angles of thirty and sixty.

60 + 90 = 150

Doing this twice shows:

150 +150 = 300

And other combos:

300 +30 = 330

300 +45 = 345

45 + 22.5 = 67.5

SO, when selecting a multiple choice, for example, it shouldn't be too difficult to estimate, based on the looks of your collection:

1) 22 1/2

2) 30

3) 45

4) 60

5) 67.5

6) 90

7) 135

8) 150

9) 180

10) 225

11) 270

12) 300

13) 330

14) 345

And those are just the easy ones!

But there are other ways the 'reality of geometry' can help you test shapes and figures out on the test. For example: To measure and compare sides of figures a ruler is helpful. But you don't have a ruler, correct? Then you make one during the test; it takes about ten seconds. How? Well, if you keep in mind that the ruler does not have to be useful in the 'real world' or 'standard' in any way, just a ruler to make relative measurements (measurements used to compare two different items, such as 'twice the size of', 'one-third the size of', 'longer than', etc., use the edge of a page to mark off the beginning and end point of the one measurement they do give you of a shape, or, in the case none is given, call it 'length one'. Then fold it in half, open the fold, and the crease is half-length-line; then, folding from there to the beginning, you get your quarter, and adding the quarter to the mid-point, three-quarters. From there you simply fine-tune with a few more dots until you can answer the question and check your answer with your ruler.

Symmetry? Fold the shape, and to see where it will land when reflected through line AB or the x-axis or whatever, fold it, and then jam your pencil down so hard it makes an impression through the fold, open it up and mark the indent. Or, if you prefer, press until you've punctured a hole. Open the fold... PEEKABOO!

Hope this helps,

Mitch