If you’re looking at the SAT or PSAT for the first time, the questions can feel like a random mix of content: a smattering of topics from four years of math classes, a series of punctuation patterns you’ve never used, and an interrogation about arbitrary aspects of tiny reading passages. But there is a method to the apparent madness. The SAT contains four main types of questions for both the Reading/Writing and the Math sections, and then several subtypes within each type. For each type of question, there are patterns you can pick up on that help you do better the next time you face a question of that type. I’ve picked these up across a lot of time solving and teaching SAT problems. I am sharing pieces of the same reasoning I use under testing conditions.

Notice that the tips below are mostly not about “gaming the system”— they’re not about things that Collegeboard “doesn’t want you to know” about the SAT. They’re things that Collegeboard does want you to know, because they’re things colleges want you to know, or skills that colleges want you to have. I’ve simply distilled some important points here, to make them easier to digest, and most of them have some application outside of standardized tests. After all, good preparation for the SAT is primarily a matter of pulling together what you’ve learned in core classes in high school, and filling in gaps where necessary.

Let me add that—shameless plug—I would be happy to add more detail in a 1-on-1 tutoring session, in NYC or on Zoom. Even when the questions are broken down into this many types, still there are multiple possible types within each of the categories below, and practice is necessary to get a handle on each type of question.

Note: The example questions shown are from the sample questions in the Official Digital SAT Study Guide, not from any official Practice Tests, to avoid copyright infringement. Do check out Collegeboard’s official resources for the SAT! The testmakers write the best practice questions, and those are what I teach from. Note also that while some of the questions I picked out are particularly good fits for the tips I give, some of them are just for illustration of the general type of question. The tip is not necessarily applicable to every question of that type.

Reading/Writing

The Reading/Writing section has two areas that fall under “reading,” which together typically make up a little over half the section, and two areas that fall under “writing,” which make up the remainder of the section. We’ll look at the different types of questions within the reading areas, “Craft and Structure” and “Information and Ideas,” and then look at the writing areas, “Standard English Conventions” and “Expression of Ideas.”

Craft and Structure

Words in Context—This may seem cut-and-dried—either you know the word and how to use it, or you don’t. But you can improve here, and you don’t need to give your weekends over to flashcards to do so. Learning the basics of a word is easier than it has ever been. You can study for these questions with ChatGPT or another reliable LLM. Just, whenever you’re doing SAT practice or just reading anything, write down the words you don’t know. Then put the list into ChatGPT with the instructions “Give me example sentences that show the most common meanings of the following words in formal contexts: …” You’ll get example sentences that help you understand the word from the context, as well as a definition of the word. This takes much, much less mental fortitude than typing individual words into Google one at a time or flipping through a dictionary, and frees your brain up for learning. Flashcards can certainly help solidify what you’ve learned, but software like Anki can make review much easier.

Note that ChatGPT can get mixed up (which is related to why I can’t as strongly endorse using LLMs for practicing other types of question, or for generating practice questions; use them judiciously). But if you ask ChatGPT to focus on the meanings of words in formal contexts (as I did in my sample prompt above), and to consider multiple common meanings, you can minimize confusion.

Text Structure and Purpose—The correct answer for the “main purpose” or “overall structure” of a passage is typically described in somewhat abstract terms, in order to test a student’s ability to give a general description of a passage without reusing key terms from the passage itself. That means that for these questions, you shouldn’t expect the right answer to pop out at you, even if you fully understand the passage. Prune off the wrong answers one by one, and let your confidence in one answer grow as you go.

Example question for Text Structure and Purpose

Cross-Text Connections—It’s no surprise that on these questions, the passages often disagree. One pattern is that one passage represents “conventional wisdom” either of society or of a scholarly field, and the other presents a new finding that disputes the conventional wisdom. In this case, don’t fall into the trap of going for whichever answer seems to present the largest disagreement. In real academic controversy and on the SAT, the conventional wisdom is usually only partly disputed, and it’s important to pay attention to which part of it is being challenged.

Example question for Cross-Text Connections

Information and Ideas

Central Ideas and Details—The way to sum up the central idea of a passage is often (but not always) to name a contrast the passage emphasizes. Does the passage mention a difference between the past and the present? Consider whether the main idea involves change over time, and look for answer choices that express this. Does a character behave differently from how some other character expects? That difference may be the thing the author wanted to emphasize, and what made the test-makers pick the passage.

Example question for Central Ideas. Details questions are, naturally, asking about a detail instead.

Command of Evidence—Naturally, when we make claims, we have to back them up. The trick on these questions is, figure out exactly which claim the evidence is supposed to be relevant to (which claim the evidence is supposed to support or weaken). Consider highlighting that claim, because every word of it matters. If the claim is a general one and the answer choices are presented as possible instances which would confirm the claim, the difference between the right answer and the trickiest wrong answer is typically that the wrong answer is an example of something slightly different. If the answer choices are supposed to present a counterexample that weakens the claim, the right answer may contradict only part of the claim—still enough to weaken it.

Bonus tip: Don’t dig too deeply into the graphs provided on some of these questions. Analyzing trends in data is for the math section. Just make sure that your answer choice says something that a) accurately reflects the graph and b) supports or undermines the claim at hand, depending on what the question asks you for.

Example question for Command of Evidence

Inferences—Here’s a simple fact that a lot of philosophers have tried hard to get around: valid logical inferences don’t introduce new information beyond what was contained in the premises.

Was that too academic? Ok, ignore that. The point is, when the test asks you to logically complete a sentence, they’re not looking for significant creativity on your part. They’re looking to see if you can recognize where the passage is going on the basis of the information already contained in the sentences you’re given. So if one of the answer choices is a dramatic-sounding claim or one that brings in a lot of new information, be suspicious of it. Expect the right answer to put a nice bow on the paragraph, drawing together existing elements.

Standard English Conventions

Boundaries—Treat each member of a list in parallel. If you see three members of a list, and the first two members are connected by semicolons, use a semicolon to connect the second and third. If the other members are connected by comma, use a comma.

Bonus tip: If you see two complete thoughts in a passage that can stand on their own as complete sentences—these are called “independent clauses”—there are only a handful of valid ways to connect them. There are four options to look out for. First, you can use a period, keeping the sentences separate. Second, you can use a semicolon. Third, with a comma followed an appropriate “coordinating conjunction” (for, and, nor, but, or, yet, so) that shows the relationship between the two . Fourth, you can use a semicolon followed by an appropriate “conjunctive adverb” (however, thus, moreover…), that shows the relationship between the two, followed by a comma.

The cat is on the mat. The hat is on the cat.
The cat is on the mat; the hat is on the cat.
The cat is on the mat, and the hat is on the cat.
The cat is on the mat; moreover, the hat is on the cat.

When a passage contains two independent clauses, the wrong answers reflect the most frequent ways that real writers sometimes wrongly combine them: with a comma, but no coordinating conjunction; with a coordinating conjunction, but no comma; or with neither a coordinating conjunction nor a comma.

(Note: it is ok to do what I just did, and use a coordinating conjunction, in this case “or,” after a semicolon. You might not find this pattern within some formal writing, but it is within the bounds of the Collegeboard’s sense of Standard English Conventions.)

Form, Structure, and Sense—These questions are ones that many students find they have no choice but to “feel out” and cross out the answers that seem wrong or “off.” Where do you use “was reading” instead of “have read,” and where do apostrophes go? If I have to give just one tip, I’d say to remember this (and adult writers need this tip as often as high school test-takers): very few plural words in English signify the plural by using an apostrophe. Apostrophes are primarily used for possessives (except for pronouns like “its”) and contractions (including “it’s” for “it is”). For the possessives of most plurals (but not some irregular plurals like “children’s” or “men’s”) the apostrophe moves after the “s”—for example, “The family’s games of Monopoly got heated. The parents’ perpetual alliance was the children’s greatest frustration.”

Example question for Form, Structure, and Sense

Expression of Ideas

Rhetorical Synthesis—One of the most important tags to pay attention for in these questions is the phrase “to an audience familiar with x” or “to an audience unfamiliar with x” (whether x is a person, artistic work, organization, or something else). If you see “unfamiliar with x,” expect the thing in place of “x” to get a few words of introduction in the right answer—if x is Mark Twain, then something like “American novelist Mark Twain” rather than just “Mark Twain.” If you see “familiar with,” expect the opposite. This isn’t typically enough to find the right answer, but it usually narrows it down to two options.

Example question for Rhetorical Synthesis

Transitions—These questions ask for the right conjunctive adverb or adverb phrase to connect two sentences. There are a lot of these, a lot more than I mentioned above, so it can be hard to be familiar with all of them (the Collegeboard provides a helpful, but not exhaustive, list in the Official Digital SAT Study Guide). But one trick if you’re stuck is to think of a word not present in the answer choices that would connect the sentences well, and see if there is a similar word among the answer choices. So if two sentences feel like they could be connected by a “but,” that contrasting relationship might be illustrated well by “however” or “nevertheless.” If they feel like they could be connected by a “so,” then a word or phrase like “thus” or “as a result” could work. Do the sentences want to be connected by an “and,” almost with a capital “A,” because they’re piling on evidence or examples? “Moreover” or “in addition” might be a good fit. If none of these feels right, you may want an adverb that shows that the later sentence emphasizes or illustrates a point made in an earlier sentence, like “in fact” or “indeed.” Or you may want one that expresses a parallel between two sentences, like “similarly.” The options go on. The key is always to pay attention to the details already in the text.

Example question for Transitions. The numbers on the sentences are training wheels and won’t be on the actual test.

Math

You’ll notice below that the title headings under “Algebra” get very long, and that there a lot of different subtypes listed under “Advanced Math.” These two facts are related: the two areas form the core of the math section (about 70% of the questions), and pack in most of the mathematical skills and content Collegeboard wants to test. Out of an interest in transparency, they are being careful about identifying all the combinations of skills and content that may go into a given problem.

The other two areas, “Problem-Solving and Data Analysis” and “Geometry and Trigonometry,” only take up about 15% each of any given test. The “Geometry and Trigonometry” questions stand out the most from the other questions because they introduce mathematical content absent from other questions. On the other hand, the “Problem-Solving and Data Analysis” questions, though they introduce some new content, have similarities to the Reading/Writing questions with graphs, and to the word problems in the main Math sections, emphasizing that the test is concerned with skill in analyzing real-world problems, arguments, and evidence.

Note that some math questions are not multiple-choice and require you to put in your own answer (Student-Produced Response questions). For these, you can put in as your answer: an integer; an exact decimal; a rounded decimal that uses all five characters available (six if the answer is negative); or any exact fraction (it doesn’t need to be in simplest form) that fits within that same character limit (five for positive numbers, six for negative numbers).

Algebra

Linear Equations, Linear Inequalities, and Linear Functions in Context—A lot (but not all) of the questions in this category that seem simple really are. Just be careful, when translating from the verbal description of a linear relationship to a function, to make sure you’ve correctly identified which item in the description is the slope—identifying a rate of change of a quantity relative to some other changing quantity (often a speed or price per unit)—and which item is the y-intercept— identifying the amount of that quantity at some fixed point treated as zero (often a starting time or base price).

Example question for Linear Equations, Linear Inequalities, and Linear Functions in Context

Systems of Linear Equations and Inequalities in Context—If you know you need to find two equations or inequalities in a context, but one seems puzzling, start with the one that you feel more confident in. Getting one equation or inequality figured out will eliminate some answer choices and give you some clues to work with.

Bonus tip: Paying attention to units can help you here. For an equation or inequality to model some part of a real-world problem, each term on each side of the equation or inequality has to have the same units on it (you can’t add miles to hours, but you can add miles to miles, or compare miles to miles, for example).

Example question for Systems of Linear Equations and Inequalities in Context

Fluency in Solving Linear Equations, Linear Inequalities, and Systems of Linear Equations—DESMOS can often be very helpful for solving these problems more quickly, so make sure you are fluent with it before you take the test. If you use DESMOS, also be sure to check your work by plugging your solution back into the equations.

Bonus tip: Collegeboard is aware that they are giving you a powerful tool by making DESMOS (or other approved calculators) available for all math questions (which hasn’t always been the case). That is part of the reason why they emphasize context in many questions, to test your ability to understand the math through your ability to interpret and apply it. But they can also put a check on the power of DESMOS by including wrong answer choices that are easily arrived at by mistakes in operating the calculator. Even if you are very fluent with DESMOS and prefer to work with it whenever possible, it can be good when practicing to often solve a question without it, to confirm that you know what the calculator is doing.

Example question for Fluency in Solving Linear Equations, Linear Inequalities, and Systems of Linear Equations

The Relationships among Linear Equations, Lines in the Coordinate Plane, and the Contexts They Describe—Questions relating an equation and a graph often require you to check slope the old-fashioned way, by dividing the rise (change in y) by the run (change in x). Unlike most geometry questions, coordinate planes are drawn to scale, so this can be done reliably (although not everything about these graphs can be eyeballed—sometimes the points on a graph that are labeled, or that clearly have integer values for both x and y, must be used to calculate the position of another point).

Example question for The Relationships among Linear Equations, Lines in the Coordinate Plane, and the Contexts They Describe

Advanced Math

Note: The Collegeboard doesn’t expect you to think about complex numbers, or more specifically, complex solutions of equations, on the SAT. So, for example, a function with no x-intercepts has no solutions we need to worry about. Breathe easy.

Operations with Polynomials and Rewriting Expressions—Remember the rules for combining like terms—only terms with the same variables raised to the same degree can be combined (by adding or subtracting their coefficients). Remember also that multiplication distributes over addition—a factor outside parentheses is multiplied by each term within the parentheses. Most students will remember FOIL also, which reminds you that two binomials multiplied together give four terms, two of which can often be combined—this is a more complicated application of the distributive property. Similarly, a trinomial (three-term polynomial) multiplied by a binomial (two-term polynomial) will yield six terms, some of which can usually (certainly on the SAT, as in your math classes) be combined. In general (and unfortunately the general statement is hard to digest) two polynomials multiplied together yield a polynomial with a number of terms (before any like terms are combined) equal to the product of the numbers of terms of the two polynomials that are being multiplied together.

Example questions for Operations with Polynomials and Rewriting Expressions

Quadratic Functions and Equations—When it comes to question about quadratic functions, finding the zeroes is frequently the first half of finding the answer. Then one must often either pick one of the zeroes, or add them together, or sometimes perform a more complicated operation, to get the answer. So if you don’t know what a question is asking, consider whether finding the zeroes of a given function could be the first step.

Bonus tip: The zeroes are most directly represented in factored form of a quadratic, y = a (x-l)(x-m) , where l and m are the zeroes. For the hardest questions on quadratics—and there are some hard quadratics questions on every test—you need to understand the relationship between factored form, standard form, and vertex form of a quadratic, as well as the graph of the function. It takes real work to build the mental muscle to translate, but it is key to cracking some of the hardest questions on the test. Look out soon for another post entirely on this topic, and if you want to be notified when it comes out, you can subscribe here.

Example question for Quadratic Functions and Equations

Exponential Functions, Equations, and Expressions and Radicals—Questions about exponential functions can be disorienting. It helps to remember that there are only four general arrangements of a basic exponential function like you’ll find on the SAT. If it’s exponentially decaying (settling towards a horizontal asymptote as x increases), then it can be coming toward that asymptote from positive or negative infinity (that is, as x decreases y can approach positive or negative infinity). Similarly, if it’s exponentially growing (getting further from a horizontal asymptote as x increases), then as x increases y can approach negative or positive infinity. And which of those four it is is determined only by whether the coefficient at the start is positive or negative, and (assuming the coefficient on the independent variable is positive) whether the base (the number being raised to a variable power) is greater or less than one.

Example question for Exponential Functions, Equations, and Expressions and Radicals

Solving Rational Equations—When these questions come up, remember two things: 1) division by 0 is undefined, so certain values are excluded from the domain; 2) polynomials are much nicer to deal with, so whenever you can, multiply both sides by the denominators in order to get the variables out of the denominator. Actually, remember a third thing as well: DESMOS can also help here, but be sure to type in the equation correctly, and be sure you know what you are looking for.

Example question for Solving Rational Equations

Systems of Equations—These questions often involve finding an intersection between a linear function and a quadratic function. One way to find intersections, regardless of whether the nonlinear function in the problem is a quadratic or something else, is first (if needed) solve for y in each case, then subtract one function from the other, and then find the zeroes of the resulting function. My next post will also be relevant to these problems.

Example question for Systems of Equations

Relationships between Algebraic and Graphical Representations of Functions—My upcoming post on quadratics will also be relevant here. But more generally than quadratics, these questions test your ability to find the intercepts of a given function (x-intercepts are found by setting y or f(x) to 0, and vice-versa); the domain and range; what happens when you translate the graph (transform it by shifting it up, down, right, left, or diagonally, without stretching, rotating, or flipping it); where the function is at a maximum or minimum; where it is increasing or decreasing; and what it does as x approaches infinity or negative infinity. Like the Algebra questions about graphing lines in the coordinate plane above, these often require using your eyes to identify where a function passes through an identifiable point where both the x and y coordinates are integers.

Bonus tip: Note also, given what we said about exponential functions above, that no real number can be their maximum or minimum, because they approach infinity on one end, and come closer and closer to a horizontal asymptote on the other.

Example question for Relationships between Algebraic and Graphical Representations of Functions

Function Notation—These are good questions to write out on your scratch paper and use substitution to write the function you need to evaluate solely in terms of x. Once written out, they are often quite manageable, even when they are a headache to stare at.

Interpreting and Analyzing More Complex Equations in Context—These questions require a lot of flexibility because there are a lot of things they could throw at you and it is usually not easy to get help from DESMOS, but they are usually not too many steps, so don’t be intimidated. The test-makers just want to see you evaluate nonlinear relationships among a range of real-world variables. For example, if c divided by d is the square root of b, b is c squared divided by d squared. To take another case, if e varies with the square of f, tripling f multiplies e by 9. You may have encountered this way of manipulating equations in your science classes.

Example Question for Interpreting and Analyzing More Complex Equations in Context

Problem-Solving and Data Analysis

Ratios, Proportions, Units, and Percentages—Percentages can be tricky. To get from 40 to 50, you increase 40 by 25%. But to get from 50 to 40, you decrease 50 by 20%! Where did the 5% go? The trick is to keep track of what you’re taking a percentage of: 10 is 20% of 50, and 25% of 40.

Bonus tip: You know that increasing a quantity by 100% means doubling it, multiplying it by two. Yet somehow we easily get confused when we hear that a quantity is being increased by 400%, and we think it means the quantity is being multiplied by 4. Increasing by 100% means multiplying by two, increasing by 200% means multiplying by 3, increasing by 300% means multiplying by 4, and increasing by 400% means multiplying by 5.

Example question for Ratios, Proportions, Units, and Percentages

Interpreting Relationships Presented in Scatterplots, Graphs, Tables, and Equations—Confirm the scale of any graphs presented, whether it can be found on the axes of the graph or in the wording of the question. You don’t want your answer to be off by a factor of 1000, and sometimes wrong answers choices will be lying in wait if you do.

Example question for Interpreting Relationships Presented in Scatterplots, Graphs, Tables, and Equations

More Data and Statistics—Be sure to remember the difference between mean and median. Mean is the average value of all the values in the data set, median is the one in the middle if all the values are lined up in order. The mean gets affected easily by outliers in a data set, whereas the median—like the median on a highway—is hard to move.

Example question for More Data and Statistics

Geometry and Trigonometry

Geometry—There is a lot of material that can be tested in these questions, and there aren’t that many of them on the test, so trying to prepare for them can be frustrating if remembering formulas doesn’t come easily to you. But remember always that you have 11 figures available to you with formulas at the top right of your testing screen, under “reference,” as well as three further facts. These 14 references are your friends, so don’t forget about them. Studying that reference ahead of time, especially the special right triangles (45-45-90 and 30-60-90), can also be helpful, so that even if you don’t remember a formula you know by reflex exactly where to look.

Example question for Geometry—probably the hardest of the sample questions I’ve included, but doable with 4 facts from the reference guide

Coordinate Geometry—For questions about the formula for a circle, using DESMOS can be very helpful to give you an idea of what you’re looking at, and sometimes is all you need. But remembering the meaning of the formula (x - h)² + (y - k)² = r² is even more important (this one is not in the reference at the start of the section). When an equation is in this form, (h,k) is the center of the circle, and r is the radius. That means all points on the circle (that is, all points on its circumference) will be r units away from (h,k).

Example question for Coordinate Geometry

Trigonometry and Radians—You may find you need the Pythagorean theorem for these problems or you may not. Just knowing the meaning of SOH CAH TOA will get you many of these problems. For one of the acute angles in a right triangle, its Sine is the length of the Opposite leg, divided by the length of the Hypotenuse; its Cosine is the length of the Adjacent leg, divided by the length of the Hypotenuse; and its Tangent is the length of the Opposite leg, divided by the length of the Adjacent leg . Be sure to sketch out triangles on your scratch paper, labeling points that are named in the problem. And remember that sine, cosine, and tangent can be negative when the angle in question is not between 0 and π/2 radians (between 0 and 90 degrees).

Example question for Trigonometry and Radians

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