Math Questions and Time
As we’ve just discussed, there are often several ways
to answer an ACT math question. You can use trial and error; you
can set up and solve an equation; and, for some questions, you might
be able to answer the question quickly, intuitively, and elegantly,
if you can just spot how. These different approaches to answering
questions vary in the amount of time they take. Trial and error
generally takes the longest, while the flash-of-intuition method either
happens very quickly or not at all.
Take, for example, the following problem:
has a greater area, a square with sides measuring 4 cm, or a circle
with a radius of the same length?
The obvious way to solve this problem is simply to plug 4
the formula for the area of a square and the area of a circle. Let’s
do it: the area of a square is equal to s2
so the area of this square = 42
The area of a circle is equal to πr2
and the area of this circle must therefore be
is obviously bigger than 16
the circle must be bigger. That worked nicely. But a faster approach
would have been to draw a quick to-scale diagram with the square
and circle superimposed.
An even quicker way would have been to understand the
equations of area for a square and a circle so well that it was
just obvious that the circle was bigger, since
the equation for the circle will square the radius and multiply
it by π, whereas the equation for the square will only
square the radius.
While you may not be able to become a math whiz and just know the
answer, you can learn to look for a quicker route, such as choosing
to draw a diagram instead of working out the equation. As with the
example above, a quicker route is not necessarily a less accurate
one. Making such choices comes down to practice, an awareness that
those other routes are out there, and basic mathematical ability.
The value of timesaving strategies is obvious:
less time spent on some questions allows you to devote more time
to difficult problems. It is this issue of time that separates the
students who ace the math section from those who merely do well.
Whether or not the ability to find accurate shortcuts is an actual
measure of mathematical prowess is not for us to say (though we
can think of arguments on either side), but the ability to find
those shortcuts absolutely matters on this test.