[MathI] Math Questions and Time

There are often several ways to answer a Math IC question. You can usetrial and error, you can set up and solve an equation, and, for somequestions, you might be able to answer the question quickly,intuitively, and elegantly, if you can just spot how to do it. Thesedifferent approaches to answering questions vary in the amount of timethey take. Trial and error generally takes the longest, while theelegant method of relying on an intuitive understanding of conceptualknowledge takes the least amount of time.
    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 most obvious way to solve this problemis simply to plug 4 into the formula for the area of a square and areaof 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. 16πis obviously bigger than 16, so the circle must be bigger. That workednicely. But a faster approach would have been to draw a quick to-scalediagram with the square and circle superimposed.

    An even quicker way would have been tounderstand the equations for the area of a square and a circle so wellthat it was obvious that the circle was bigger, since the equation forthe 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 knowthe answer, you can learn to look for a quicker route, such as choosingto draw a diagram instead of working out the equation. And, as with theexample above, a quicker route is not necessarily a less accurate one.Making such choices comes down to practice, having an awareness thatthose other routes are out there, and basic mathematical ability.

    The value of time-saving strategies isobvious: less time spent on some questions allows you to devote moretime to difficult problems. It is this issue of time that separates thestudents who do terrifically on the math section and those who merelydo well. Whether or not the ability to find accurate shortcuts is anactual measure of mathematical prowess is not for us to say (though wecan think of arguments on either side), but the ability to find thoseshortcuts absolutely matters on this test.

    Shortcuts Are Really Math Intuition

    We’ve told you all about shortcuts, but nowwe're going to give you some advice that might seem strange: youshouldn't go into every question searching for a shortcut. If you haveto search and search for a shortcut, it might end up taking longer thanthe typical route. But at the same time, if you're so frantic aboutcalculating out the right answer, you might miss the possibility that ashortcut exists. If you go into each question knowing there might be ashortcut and keep your mind open, you have a chance to find theshortcuts you need.

    To some extent, you can teach yourself torecognize when a question might contain a shortcut. From the problemabove, you know that there will probably be a shortcut for all thosequestions that give you the dimensions of two shapes and ask you tocompare them. A frantic test-taker might compulsively work out theequations every time. But if you are a little calmer, you can see thatdrawing a diagram is the best, and quickest, solution.

    The fact that we advocate using shortcutsdoesn'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 unlessyou know how to work it out the long way. After all, a shortcutrequires using your existing knowledge to spot a faster way to answerthe question. When we use the term math shortcut, we're really referring to your math intuition.