One of the more popular SAT subject tests is Mathematics Level 2. Until recently, this test was technically called the Math IIC test, the “C” referring to the fact that the use of a graphing calculator was allowed, and even encouraged. In fact, the College Board itself estimates that a calculator is useful on more than half of the questions.
In order to get an elite score on the Math Level 2 test, proper use of the calculator is essential. In particular, a calculator can be especially useful on any question involving graphing a function. Consider the following example:
Many students will realize that vertical asymptotes occur when the denominator of a function equals zero. Setting the denominator equal to zero yields us two answers: x = -3 and x = 5. Thus, answer choice B seems very attractive, and a good number of students will fall for this trap.
However, a savvy test-taker will realize that this is a problem that the calculator can help us with and will take 20 seconds to plug in. If you do this, you’ll see that – in fact – there is only one vertical asymptote, and it occurs at x = 5.
For the purposes of the test, we are done. We had a hypothesis that there were two vertical asymptotes, and we successfully used the calculator to disprove one of those. The correct answer is E.
If you’re interested in the mathematical concept behind this distinction, factor the polynomial in the numerator, and you’ll find that the term (x + 3) cancels out in the numerator and denominator. Therefore, x = -3 is not an asymptote, but a hole.
This is just one example of a problem where the graphing calculator can help us find the correct answer. Keep an eye out for problems like these, and you’ll reap the benefits with a higher score!
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