Math Questions and Time
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:
Which 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 into 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 = 16. The area of a circle is equal to  πr2, and the area of this circle must therefore be = 16π. Since 16π 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.
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