Math Questions and Time
Math Questions and Time
There are often several ways to answer a Math IIC 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 elegant method of relying on an intuitive understanding of conceptual knowledge 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 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, so 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 of area for a square and circle so well that it was just obvious that the circle was bigger, since the equation for the circle will square the 4 and multiply it by whereas the equation for the square will only square the 4.
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. And, as with the example above, a quicker route is not necessarily a less accurate one. Making such choices comes down to practice, being aware 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 test 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, but the ability to find those shortcuts absolutely matters on this test.
Shortcuts Are Really Math Intuition
Now that you know all about shortcuts, you should use them wisely. Don’t go into every question searching for a shortcut; it might end up taking longer than the normal route. Instead of seeking out math shortcuts, you should simply be mindful of the possibility that one might exist. If you go into each question knowing there could be a shortcut and keep your mind open as you think about the question, you will find the shortcuts you need.
To some extent, with practice you can teach yourself to recognize when a question might contain a shortcut. For example, simply from the problem above, you know that there will probably be a shortcut for questions that give you the dimensions of two shapes and ask you to compare them: you can just draw a diagram. A frantic test-taker might see the information given and then seize on the simplest route and work out the equations. But with some calm and perspective you can see that drawing a diagram is the best idea.
The fact that we advocate using shortcuts doesn’t mean you shouldn’t focus on learning how to work out problems. In fact, we can guarantee that you’re not going to find a shortcut for a problem unless you know how to work it out the long way. After all, a shortcut just uses your knowledge to find a faster way to answer the question. When we use the term math shortcut, we are really referring to your math intuition.
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