Absolute Value and Exponents
You can remember absolute value by thinking 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 , then f 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, such as or . 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 could 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.
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