There are often several ways to answer a Math IC 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 to do it. These different approaches to answering questions vary in the amount of time they take. Trial and error generally takes the longest, while the elegant method of relying on an intuitive understanding of conceptual knowledge takes the least amount of time.
Take, for example, the following problem:
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The most obvious way to solve this problem is simply to plug 4 into the formula for the area of a square and area of a circle. Let's do it: Area of a square = s2, so the area of this square = 42 = 16. Area of a circle = πr2, and the area of this circle must therefore be π42 = 16π. 16π is obviously bigger than 16, so 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 for the area of a square and a circle so well that it was obvious that the circle was bigger, since the equation for the circle will square the 4 and multiply it by π, whereas the equation for the square will only square the 4.
While you may be 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. And, as with the example above, a quicker route is not necessarily a less accurate one. Making such choices comes down to practice, having an awareness that those other routes are out there, and basic mathematical ability.
The value of time-saving 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 do terrifically on the math section and 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.
Shortcuts Are Really Math Intuition
We’ve told you all about shortcuts, but now we're going to give you some advice that might seem strange: you shouldn't go into every question searching for a shortcut. If you have to search and search for a shortcut, it might end up taking longer than the typical route. But at the same time, if you're so frantic about calculating out the right answer, you might miss the possibility that a shortcut exists. If you go into each question knowing there might be a shortcut and keep your mind open, you have a chance to find the shortcuts you need.
To some extent, you can teach yourself to recognize when a question might contain a shortcut. From the problem above, you know that there will probably be a shortcut for all those questions that give you the dimensions of two shapes and ask you to compare them. A frantic test-taker might compulsively work out the equations every time. But if you are a little calmer, you can see that drawing a diagram is the best, and quickest, solution.
The fact that we advocate using shortcuts doesn't mean you shouldn't focus on learning how to work out problems. We can guarantee that you're won't find a shortcut for a problem unless you know how to work it out the long way. After all, a shortcut requires using your existing knowledge to spot a faster way to answer the question. When we use the term math shortcut, we're really referring to your math intuition.