There's a recurring question type on the SAT math section which tends to intimidate most students. The question type can be shown most easily by first showing an example:
P = 13 + 0.2 *F
A pneumatic device is used to exert pressure upon a small circular area, comprised of a semi-dense material and placed on the ground. The pressure P the device exerts depends upon the force F being applied by a precise mechanical robot, as shown in the equation above. When a certain threshold pressure is surpassed, the circular area begins to sink into the semi-dense material beneath it. What expresses the force F being expressed by the robot, in terms of the pneumatic pressure P?
Characteristics of the question
The question type we'll discuss today is characterized by the following:
A great deal of text, usually touching upon a concept from physics.
An 2-variable equation, often a linear one. You're meant to isolate one of the variables.
There are two slightly different versions of this question. The first is to find the variable parameterically. (That is, find one variable in terms of the other.) In the second version, you're given a numeric value for one parameter, and you have to find the numeric value of the other.
Now that we've gone over the fundamentals, let's reexamine the example we brought earlier.
P = 13 + 0.2 *F
A pneumatic device is used to exert pressure upon a small circular area, comprised of a semi-dense material and placed on the ground. The pressure P the device exerts depends upon the force F being applied by a precise mechanical robot, as shown in the equation above. When a certain threshold pressure is surpassed, the circular area begins to sink into the semi-dense material beneath it.
What expresses the force F being expressed by the robot, in terms of the pneumatic pressure P?
In order to answer the question, note that there is absolutely no need to read any of the text. And there never is, for this question type.
Here's the equivalent of the above equation:
P = 13 + 0.2 *F Question
What is F in terms of P?
The answer is F = (P - 13) / 0.2
Please note: today's tutorial is not an article on how to isolate variables. If you're not yet adept at doing that, please practice until you master it. Algebra questions are by far the important topic on SAT math, both in the non-calculator as well as in the non-calculator section, and isolating variables is a necessary part of solving them.
What makes these questions tricky?
In truth, this is an easy question masquerading as a difficult one, which makes it a favorite on the SAT. There are two things that make this question type confusing:
There's a lot of technical reading involved. Always confusing
The equations are drawn from scientific topics, usually physics. Students tend to think they need to understand the concepts described, in order to solve the question.
Note that there are certain question types where it's important to read carefully, and important to understand the real-life significance of the provided equations. This question type isn't one of them.
How to approach this question
Here's my simple tip:
Don't read the text.
In the best case scenario, you're wasting time / focus. In the worse, you'll be stressed out and intimidated, and possibly wondering if you even have the knowledge to solve this question at all.
That includes the text of the question. Don't read it.
Luckily for you, this question type is always in the same format. You get the equation in terms of one variable, and you need it in terms of another. Skip the text, look at the equation, and isolate the variable that isn't isolated yet. That's all.
For example, if the equation they gave you is T=4+N, you're expected to find N=T-4.
The only time you might have to glance over the text is if they're asking for a numerice value. For example, in the equation above, if the ask for the value of N, they must have given you the value of T. Find it and ignore the rest.
Let's look at an example of where a numeric value is required.
A wave is traveling through space by way of a gelatinous mixture slowing its progress. Condensing the material has an inverse effect with the velocity, v, of the wave, in meters per second. If u represents the reciprocal of the viscosity of the gelatinous mixture through which the wave is traveling, its velocity can be represented by the following equation: v = (23 +u) / 2
If the velocity is currently 15 meters per second, what is the reciprocal of the viscosity, u?
Glancing at the answer options is enough to tell us that u is required as a numeric value, not as a parameter. As we learned earlier, this means that the value of the other variable, v, must have been given. Sure enough, it's there in the text of the question: v = 15.
The question is equivalent to the following:
v = (23 +u) / 2
v = 15
u = ?
D) 22 The answer is of course B), 7.
Do you see how much simpler the amended question looks than the original? In both examples? It should always be like that.
If you're having trouble ignoring the text, write down your equation on a piece of paper, along with the variable you're searching for, and focus on that. If you're taking a paper test, it may help simply to highlight the equation and the relevant variable.
A few last notes Your likelihood of having a question like this on your exam is perhaps 50 / 50. Familiarize yourself with how it looks. Being familiar with this question type on the SAT will save you time and energy, but more importantly, it will save you undue stress. On the SAT, that's priceless.
For more tips and methods, or to get help personally tailored to your needs, consider working with me. I've helped people from all over the world get into their dream school. Studying privately with a skilled teacher is the best way to increase your test score, and in coaching you, I adopt my methods specifically to your personality, schedule, and learning style.