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Variation
One way that the new SAT tests whether you understand
an equation is to ask questions about the relationship between certain
variables. For example,
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The easiest way to solve such problems is to just plug
in:
So the value of y will be
2/3 of
what it was.
Essentially, these sorts of problems are testing to see
if you understand how an equation works and how different variables
interact. While in a simple equation like the first example, this
is easy to see, it becomes a little more complicated as the equations
get more complex:
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Once again, you can still find the answer by plugging
in 2x for x and 3z for z.
You just have to do some additional math:
The value of y will be
8/3 of
what it was. Since the original expression was y = x3/2z, we
must figure out what fraction times 1
/2 is equal to
4/3 :
It’s also possible that you’ll have to know some variation
jargon for the new SAT. There are two terms you need to know: direct and inverse.
A direct relationship between two variables exists when, if one
variable increases, the other variable increases. In the equation
y and x share
a direct relationship, since if x increases,
so does y.
An inverse relationship is just the opposite. In the same
example, y and z have
an inverse relationship, because if z were
to increase, y would decrease.
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