These two processes take about the same amount of time, so choosing one over the other is more a matter of personal preference than one of strategy. If you feel quite comfortable with your calculator, then you might not want to risk the possibility of making a mental math mistake and should choose the first method. But if you’re more prone to error when working with a calculator, then you should choose the second method.
Calculator-Unfriendly Questions
While it’s possible to answer calculator-unfriendly questions using a calculator, it isn’t a good idea. These types of problems often have built-in shortcuts—if you know and understand the principle being tested, you can bypass potentially tedious computation with a few simple calculations. Here’s a problem that you could solve much more quickly and effectively without the use of a calculator:
|
|
|
|
|
(A) |
.3261 |
|
(B) |
.5 |
|
(C) |
.6467 |
|
(D) |
.7598 |
|
(E) |
.9238 | |
If you didn’t take a moment to think about this problem, you might just rush into it wielding your calculator, calculating the cosine and sine functions, squaring them each and then adding them together, etc. But take a closer look:
cos2(3 
63°) + sin2(3 
63°) is a trigonometric identity. More specifically, it’s a Pythagorean identity:
sin2q + cos2q = 1 for any angle
q. So, the expression {
cos2(3 
63°) + sin2(3 
63°)} 4/2 simplifies to 1
4 /2 = 1/2 = .5.
B is correct.
Calculator-Useless Questions
Even if you wanted to, you wouldn’t be able to use your calculator on calculator-useless problems. For the most part, problems involving algebraic manipulation or problems lacking actual numerical values would fall under this category. You should be able to easily identify problems that can’t be solved with a calculator. Quite often, the answers for these questions will be variables rather than numbers. Take a look at the following example:
|
|
|
(x + y – 1)(x + y + 1) = |
|
(A) |
(x + y)2 |
|
(B) |
(x + y)2 – 1 |
|
(C) |
x2 – y2 |
|
(D) |
x2 + x – y + y2 + 1 |
|
(E) |
x2 + y2 + 1 | |
This question tests you on an algebraic topic—that is, it asks you how to find the product of two polynomials—and requires knowledge of algebraic principles rather than calculator acumen. You’re asked to manipulate variables, not produce a specific value. A calculator would be of no use here.
To solve this problem, you need to notice that the two polynomials are in the format of a Difference of Two Squares: (a + b)(a – b) = a2 – b2. In our case, a = x + y and b = 1. As a result, (x + y – 1)(x + y + 1) = (x + y)2 – 1. B is correct.
Don't Immediately Use Your Calculator
The fact that the test contains all four of these question types means that you shouldn't get trigger-happy with your calculator. Just because you've got an awesome shiny hammer doesn't mean you should try to use it to pound in thumbtacks. Using your calculator to try to answer every question on the test would be just as unhelpful.
