On your SAT MATH exam, you will need to be strategic in choosing what algebraic operations that you actually perform.
Certainly the most reliable general strategy is to isolate on one side of the equation the variable (e.g, “x”) that the SAT test makers are requesting. However, even this time-tested rule has its exceptions on the exam. For instance, you may encounter a question that asks for something other than the value of a single variable (e.g., you may be asked for the ratio or difference or fraction of two unknowns). Our Smashing The SAT curriculum looks at all of these SAT-style twists and turns that you’re virtually guaranteed to encounter on the exam.
Another SAT gambit is as follows— asked to determine x, for instance, in a given equation that, at first glance, features both “x” and an undefined constant. So now what??!! Well, just continue reading the question and typically you’ll find something like, “What is the value of x . . . IF k = 7!!” Well, how convenient. So once you substitute 7 for k, then the equation looks just like all the ’Solving for X’ problems that you’ve practiced in school time and time again. But if you haven’t prepped for this quirky SAT presentation, you might be thrown off your game!
OK, getting back to basics, here’s our Golden Rule commandment—Do unto one side (of the equation) as you do unto the other! Specifically, you can add or subtract or divide or multiply etc. by anything you want, AS LONG AS you perform the identical operation on the other side of the equation. And yes, seeking to isolate that which is requested is generally the appropriate strategy. To unerringly manipulate algebraic equations toward an eventual solution, you will need to be fluent with PEMDAS—
- Parentheses
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
PEMDAS is the order of operations that must be observed when simplifying algebraic expressions. And part and parcel of PEMDAS is the distributive property, which in and of itself is not overly complicated. However, the SAT loves to concoct expressions that mix a variety of terms and multiple “+” and “-” signs (along with at least one term requiring distribution) just to see if you can keep everything straight! For instance, check out the expression below—
Which of the following is equivalent to the above expression?
If you have any doubt as to which of the above answers is correct (BTW—it’s the second one), than you absolutely need to access our curriculum, which kicks off with a review of Arithmetic, PEMDAS, etc. We cover these basic topics, and also look at the ways in which the SAT attempts to throw a monkey wrench into even something as seemingly straightforward as basic Arithmetic!
OK, that’s it for our introduction to Algebraic Manipulation. There are more complex algebraic challenges that you will encounter on the SAT MATH exam (e.g., solving equations that contain radical terms, transforming rational expressions, manipulating fractions, etc.). And these are all addressed in subsequent modules in our SmashingTheSAT curriculum, as is the SAT’s penchant for ‘like term’ problems, the strategic reworking of quadratics, binomials, linear equations, circle formulas, measures of angles, and so much more!
So, do you want to attempt to laboriously read your way through all of these topics OR do you want to master this subject matter via a cutting-edge INTERACTIVE VIDEO approach! I think we both know the answer! Click below to begin your learning adventure—
