There are certain topics on the SAT that are more common than others. Efficient studying for the SAT involves starting with subjects that are more likely to appear, and then working your way through less frequent ones.
Today we'll look into what exactly the most frequent subjects are.
The most important topics on the math section
The following topics are listed in order of importance, according to my experience:
2. Word problems
3. Ratios / Percentages
5. Sets of equations
6. Quadratic equations: standard equations
7. Quadratic equations: vertex equations
8. Imaginary numbers
Lines This is the single most important topic on the SAT. There are questions on the conceptual representation of lines, questions on line parameters, questions on the interpretation of line graphs, etc. SAT writers enjoy this topic because there's a wide variety of questions that can be asked. And since you're expected to know linear equations well, they can dig in.
Linear equations is a simple topic compared to other subjects on the math section. It doesn't take a lot of energy and time to understand them well, and you'll be rewarded with many correct answers on the SAT.
To get a start on line questions, try the following articles:
This topic is a hefty one, and many skills are required to solve word problems correctly.
When I say word problems, what I actually mean is the ability to translate verbal language into math. Solving the equations you've written may require a whole slew of skills - the ability to manipulate variables or to solve ratios and percentages, just to name a few. But that initial ability to maneuver verbal description to mathematical equations is a fundamental and very important skill. (And not just on the SAT.)
Ratios / Percentages
These two topics pop up most often in word problems. The majority of word problems involve a ratio or percentage at some point, so it would be difficult to carry the problem to its end and obtain a correct answer if you don't have these skills. Other topics can involve ratios / percentages; they sometimes come up on the SAT in the topic of data science, for example.
Studying one of these things (ratios or percentages) will help you understand the other, as the two are conceptually related.
The topic of exponents is a popular one on the SAT, because it's possible to formulate threatening-looking questions on their foundation. Nevertheless, these questions can be solved quickly by people who know the rules of exponents well. This allows the SAT to filter mathematically adept students from those who are less adept.
Exponents also come with a long list of rules, which can confuse students who haven't practiced them enough. The good news is that these rules are technical, rather than conceptually difficult. This means that if you simply do enough problems, you should have exponents down pat- which will help substantially with your SAT score.
Sets of equations
Algebra is an important topic on the SAT, and after linear equations, the most important algebraic topics are sets of equations and quadratic equations. Quadratic equations is an extensive topic which contains a wide range of material, whereas each set of equations usually involves the same series of steps. Investing just a little time in sets of equations will allow you to solve these questions correctly.
Quadratic equations: standard equations
Since quadratic equations is a large topic, and much of it can be complicated, it's best to divide it into smaller topics. The most important topic in quadratic equations is familiarity with the basic standard equation. A standard quadratic equation looks as follows:
ax² + bx + c
Familiarity with the standard quadratic equation involves:
familiarity with the quadratic formula
a conceptual understanding of the radical in the quadratic formula
the ability to factor the equation
an understanding of the graphical significance of roots / the equation's zeros
a basic knowledge of the graph's appearance. (y intercepts, x intercepts or lack thereof, whether the graph is "rightside up" or "upside down")
Quadratic equations: vertex equations
Vertex equations appear fairly frequently on the SAT, though they're less common than standard equations. When I say that they "appear", I mean that the equation is either imperative or helpful in solving the question; it doesn't necessarily manifest in the body of question itself. These questions can sometimes be solved with a standard equation, but are more quickly and naturally handled with a vertex equation.
The vertex equation appears as such: a * (x - h)² + k
With vertex equations, you are expected to know:
the graphical significance of the numbers in place of h and k
the parabola's vertex and axis of symmetry
the graphical counterpart of the equation
The good news is that you probably won't have to transform from standard to vertex form, or vice versa, probably one of the more confusing operations in quadratic equations.
Imaginary numbers aren't that common on the SAT. But they're on the list for the same reason that sets of equations are higher on this list than quadratic equations are. Sets of equations are less common than quadratic equations, but they're also an easier topic. Just a little studying will help you perform better.
The same with imaginary numbers! SAT questions on this topic look scary but are usually simple. Familiarizing yourself with them shouldn't take long, and the result will be an easy right answer.
To learn about how to approach imaginary numbers on the test, see here.
A few last words
If you've just started studying for the SAT and are unsure where to start, or you're wondering what to tackle next, try addressing one of the topics on this list. Studying any one of these items should lead to a rapid improvement in your test score.
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