As we’ve already mentioned, the calculator is a very important part of the Math IC test. You need to have the right kind of calculator, be familiar with its operations, and, above all, know how to use it intelligently.
There are four types of questions on the test: those that are calculator-friendly, calculator-neutral, calculator-unfriendly, and calculator-useless. According to ETS, about 60 percent of the test falls under the calculator-neutral and -friendly categories. That is, calculators are useful or necessary on 30 of the 50 questions on SAT II Math IC. The other 20 questions are calculator-unfriendly and -useless. The trick is to be able to identify the different types of questions when presented with them on the test. Here’s a breakdown of each of the four types, with examples. If you’re not certain about the math discussed in the examples, don’t worry. We cover all these topics in this book.
Calculator-Friendly Questions
A calculator is extremely helpful and often necessary to solve calculator-friendly questions. Problems demanding exact values for exponents, logarithms, or trigonometric functions will most likely need a calculator. Computations that you can’t do easily in your head are prime candidates. Here’s an example:
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If f(x) = , then what is f(3.4)? |
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(A) |
–18.73 |
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(B) |
–16.55 |
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(C) |
–16.28 |
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(D) |
–13.32 |
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(E) |
–8.42 | |
This is a simple function question in which you are asked to evaluate f(x) at the value 3.4. As you will learn in the Functions chapter, all you have to do to solve this problem is plug in 3.4 for the variable x and carry out the operations in the function. But unless you know the square root and square of 3.4 off the top of your head (which most test-takers wouldn’t), this problem is extremely difficult to answer without a calculator.
But with a calculator, all you need to do is take the square root of 3.4, subtract twice the square of 3.4, and then add 5. You get answer choice C, –16.28.
Calculator-Neutral Questions
You have two choices when faced with a calculator-neutral question. A calculator is useful for these types of problems, but it’s probably just as quick and easy to work the problem out by hand.
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If 8x = 43  23, what is the value of x? |
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(A) |
2 |
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(B) |
3 |
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(C) |
5 |
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(D) |
7 |
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(E) |
8 | |
When you see the variable x as a power, you should think of logarithms. A logarithm is the power to which you must raise a given number to equal another number, so in this case, we need to find the exponent x, such that 8x = 43 23. From the definition of logarithms, we know that if given an equation of the form ax = b, then loga b = x. So you could type in log8 (43 23) on your trusty calculator and find that x = 3.
Or, you could recognize that
2 and
4 are both factors of
8, and, thinking a step further, that
23 = 8 and
43 = 64 = 82. Put together,
43 
23 = 82 
8 = 83. We come to the same answer that
x = 3 and that
B is the right answer.
