Weird Symbols Questions (Algebra in Disguise)
The writers of the SAT seem to get a wacky thrill from
creating odd symbols and then defining those symbols as mathematical
functions. For example, a typical easy symbol SAT question might
say:
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Let a @ b be
defined as a2⁄b,
where  What is the value of
4 @ 2? |
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To answer this question, simply take the given numbers
and plug them into the appropriate parts of the function assigned
to a @ b. In other
words, symbol questions are often just a glorified type of algebraic
substitution question: you look at the formula with its variables and
plug in the given numbers. In this specific problem,
Some students get frazzled when they see the odd symbols
in their test booklet, which is exactly what the SAT wants. The
test-makers figure that if you get nervous and can’t get the answer
right, then you can’t be all that good or comfortable with math.
But if you know that you shouldn’t be frightened of these problems,
you can answer them easily because they really aren’t all that hard.
More Difficult Symbol Questions
Having said that symbol questions aren’t all that hard,
we must admit that the SAT does throw out some more difficult variations.
For example, the SAT might “stack” a symbol question, asking you
to perform the operation defined by the symbol twice.
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Let a#b#c#d be
defined for all numbers by a#b#c#d = ab – cd. If x =
6#3#5#4, then what is the value of 7#x#3#11? |
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Here you have a question with strange symbols all over
the place, and, furthermore, the question is asking you to calculate
the value of a strange symbol with a variable in it! Again, many
students will see this question and be overwhelmed. But you shouldn’t
be. To answer this question, you have to do two things:
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Calculate the value of x.
- Calculate
the value of 7#x#3#11 (which
won’t be very hard, since by that time you’ll know exactly what x equals).
Since
Now that it is clear that x =
–2, you can easily calculate the value of 7#x#3#11:
You should see from this example that the difficult symbol
questions are simply more intricate versions of the simpler symbol
questions. In both cases, you have to substitute numbers into the
function with which the symbol is associated. It’s just that in
the difficult questions, you have to substitute into the function
more than once.
The key to answering symbol questions is to avoid
getting bogged down in the symbol at all. Whenever you see the symbol,
you should immediately think of the associated function. To make
sure you don’t get confused by symbols, it is always a good idea
to write in the function above the symbol each time it appears in
the question.
