Absolute Value and Exponents
You can remember absolute value
of the two thin upright bars that denote it,
as the Chipper Police
. The Chipper Police are determined
that everyone be positive, so no number that comes out from between
those two bars is negative.
Any value inside the Chipper Police bars has to emerge
as zero or greater. So
and if you have
could equal either 5 or –5. This either/or
ambiguity is what the test-makers like about absolute value, so
once you see those bars, alarms should start ringing. There’s a
reason absolute value works this way. Feel free to look it up if that’s
your thing. For the SAT, just remember the Chipper Police
are always turning a negative into a positive.
This same tricky can-be-positive-or-negative gambit also
crops up when you have even-numbered exponents
Exponents are those raised numbers that show how many times a quantity
is multiplied by itself. When you multiply two negatives, you get
a positive, so if you have
, then x
be either 3 or –3. When rushing through the test or when time is
running out, many students jump to x
= 3 without
considering the fact that x
can also be negative.
Expect this trap to appear at least once on the Math section.