Prep Effectively with a Mistakes Journal

If you’re preparing the SAT, ACT, ISEE, SSAT or any other standardized test, it’s essential that you don’t simply study hard, but study effectively. Two essential elements of effective studying are analyzing your mistakes in-depth, and then reviewing what you’ve learned from them. How can you make sure you’re systematically tracking, reflecting on, and learning from every mistake when you’re spending months studying for a sprawling exam? With a mistakes journal. 

A mistakes journal is a powerful tool for optimizing and organizing your studying. It is essentially a place where you systematically log every question you missed along with a record of where the question is located, why you missed the question, what type of question it was and how you could tell, and what lesson(s) you learned from reflecting on your mistake. You may have missed a question about triangles, for instance, because you didn’t know a certain rule in trigonometry, you didn’t pick up on the cue that this was a trigonometry question, or because you tried to solve the problem in your head without first labeling the diagram or writing out your work. Using a mistakes journal forces you to reflect on what exactly is making you miss questions and how you can avoid those mistakes in the future. The other great benefit of a mistakes journal is that it facilitates review by helping keep track of everything in one place—not always an easy task when you’re taking multiple practice tests from different books and websites. 

Learning science has revealed that we best learn new information through an iterative review process. This means that you must revisit your notes multiple times before they will move into your long-term memory. Specifically, you’re most likely to commit material to memory if you first review it within 24 hours after you first encounter it, while it’s still fresh. This means that you should review new entries in your mistakes journal the day after you write them, and then again every few days until the notes are in your long-term memory. Every so often, you should review the mistakes journal in its entirety to make sure you haven’t forgotten anything.

You should also attempt to resolve any missed problems a couple of days after you’ve entered them in your mistakes journal. To do this, first print a blank copy of the test so that you won’t see your old notes. Once you’ve successfully redone a problem, make of note of that in your mistakes journal. In another couple of days, use the mistake journal to identify the problems you haven’t been able to redo successfully, and attempt those again. Repeat the process as needed. Every so often, you should attempt to resolve all missed problems to make sure you haven’t forgotten anything. 

Lastly, remember that a mistakes journal can be as effective an aid in academic classes as it can be in test prep. Many students, seeing the benefits it brings to their test prep, start using the journal in school as well.

SAT and ACT Calculator Tips and Shortcuts

Both the SAT and ACT allow a calculator on the mathematics section, so it’s important to know how to get the most out of one come test day. Note, however, that the calculator is not allowed on any other sections—including ACT science.

What Type of Calculator Is Allowed?

The SAT and ACT place relatively few restrictions on calculator use. The ACT is somewhat stricter than the SAT, prohibiting calculators with CAS (“computer algebra system”) functionality, whereas these are generally allowed on the SAT. Most popular high school calculators, like the Texas TI-83 and TI-84, are permitted. Always make sure to check, however, that your model is kosher before you sit for the exam. You can find a complete list of permitted calculators for the ACT here and a similar list for the SAT here. The following graphing calculators are generally allowed on the SAT:

FX-6000 series
FX-6200 series
FX-6300 series
FX-6500 series
FX-7000 series
FX-7300 series
FX-7400 series
FX-7500 series
FX-7700 series
FX-7800 series
FX-8000 series
FX-8500 series
FX-8700 series
FX-8800 series
FX-9700 series
FX-9750 series
FX-9860 series
CFX-9800 series
CFX-9850 series
CFX-9950 series
CFX-9970 series
FX 1.0 series
Algebra FX 2.0 series
HP-28 series
HP-39 series
HP-40 series
HP-48 series
HP-49 series
HP-50 series
HP Prime


Radio Shack

EL-9200 series
EL-9300 series
EL-9600 series
EL-9900 series

Texas Instruments
TI-83/TI-83 Plus
TI-83 Plus Silver
TI-84 Plus
TI-84 Plus CE
TI-84 Plus Silver
TI-84 Plus C Silver
TI-89 Titanium
TI-Nspire/TI-Nspire CX
TI-Nspire CAS/TI-Nspire CX CAS
TI-Nspire CM-C/TI-Nspire CM-C CAS
TI-Nspire CX-C CAS


Datexx DS-883

What’s The Best Calculator To Use?

While graphing calculators allow you to find solutions to some linear and quadratic problems, these problems are generally solved just as quickly (or more quickly) without a calculator. That said, popular graphing calculators like the TI-83 often contain handy shortcuts that standard or scientific calculators lack. For that reason I recommend using a graphing calculator, such as the TI-83 or TI-84, that features the types of added functionality described below.

No matter what type of calculator you’re using, make sure you’re familiar with it before test day. Know when to use parenthesis, for instance, and how your calculator processes the order of operations.

SAT and ACT Calculator Tips and Shortcuts

When Should I Use The Calculator?

Most, if not all, SAT and ACT math problems can be solved without the use of a calculator. That said, not using a calculator at all will take more time and can often lead to more careless mistakes. It’s important, then, to know when and when not to use the calculator.

In general, take a few moments to understand each question and plan your method of attack before picking up the calculator. Don’t rely on your calculator for the big picture problem-solving strategy—this part is up to you. You should be especially wary, for instance, of problems that look overtly complex. Many of these can be solved quickly with a simple shortcut, and thus should not be immediately plugged into the calculator.

Once you’ve figured out how you’re going to solve a problem, then you can use the calculator to quickly work through any arithmetic. Doing so is a good idea because it’s faster than solving on paper and less likely to lead to mistakes.

Beyond simple arithmetic, there are a couple of powerful shortcuts you should know about that can speed up your work on the SAT or ACT. Pretty much everything else, on the other hand, you can solve better without the calculator.

Calculator Shortcuts For The SAT and ACT

While these shortcuts are available on many graphing calculators, I’m going to explain how to access them on what are perhaps the most popular of all high school graphing calculators, the TI-83 and TI-84.

Decimal-Fraction Conversions: Did you solve a problem and end up with a decimal that you need to convert into a fraction, or vice-versa? Enter the value into your calculator and then hit “Math,” followed by “1:Frac” to turn a decimal into a fraction or “2:Dec” to turn a fraction into a decimal.

Least Common Multiple and Greatest Common Factor: Need to find one of these quickly? Don’t construct a time-consuming factor tree. Instead, hit “Math,” go to the “Num” menu, then go down to “8:lcm” for least common multiple or “9:gcd” for greatest common factor. Enter the two values, separated by a comma. If you’re trying to find the least common multiple or greatest common factor for more than two values, simply use this function to find the LCM or GCF of the first two values, then solve again for THAT result combined with the third term, then solve again for THAT result combined with the fourth term, and so on. Once you’ve worked through all your terms, you’ll end up with the LCM or GCF for the set as a whole.

Combinations: When finding out how many ways you can choose r number of selections from n number of things and the order they’re arranged in doesn’t matter, enter the total n number of objects, then hit “Math,” go to the “Prb” menu, then select “3:nCr,” then enter the number of r selections. Then press enter for your solution.

Calculator Shortcuts For The ACT Only

If you’re taking the ACT, you’ll also want to learn a few additional shortcuts.

Arc Functions: When given a sine, cosine or tangent value, you can solve for the initial angle by taking the arc function. Simply press “2nd,” then sin-1, cos-1 or tan-1, to find out the initial angle. The angle will either be in radians or degrees—you can choose which by using the “Mode” menu. Remember that arc functions result in only one of the possible angles that could produce the given sine/cosine/tangent value, so be careful here.

Radian-Degree Conversions: Need to convert radians to degrees or vice-versa? Hit “Mode” and then select radians or degrees to specify the type of value you’d like to end up with. Then enter the starting value and press “2nd,” then “angle,” then “1” if the angle is in degrees “3” if the angle is in radians. Press enter to see the converted value.

Logs: You can solve any log problem of the sort log base x of y by entering “log y” and then dividing that result by “log x.”


While calculators can’t do the big picture thinking the SAT and ACT require for you, they can help minimize errors and speed up your work. Look for an approved graphing calculator with the above functionality for the exam, become familiar with it, and then use it to your advantage on test day!

Want a Free List of All the Math Topics That Have Recently Appeared on the SAT or ACT?

For a free list of all the math topics that have recently appeared on the SAT or ACT, and/or for answers to any other questions, you can reach me at or 212-658-0834.

How To Solve Direct and Inverse Variation Problems On The SAT and ACT

Here’s an explanation of direct and inverse variation and how to solve problems asking about them on the SAT and ACT.

Want a Free List of All the Math Topics That Have Recently Appeared on the SAT or ACT?

For a free list of all the math topics that have recently appeared on the SAT or ACT, and/or for answers to any other questions, you can reach me at or 212-658-0834.

How To Write The New (Redesigned) SAT Essay

Essays Changes and Basic Features

The new (or “redesigned”) SAT essay, debuting in March of 2016 as an optional section on the new SAT, looks radically different than the earlier version of the essay. Instead of coming up with your own argument, you’ll now be required to analyze someone else’s argument. This argument takes the form of a 650-750 word article, and you’ll be given a total of 50 minutes, instead of 25, to read and respond to it.

In short, the SAT asks you to describe how the article in question persuades the reader of its point. In particular, you’re asked to consider its use of evidence, reasoning and/or stylistic and persuasive elements.

How To Write the New (Redesigned) SAT Essay

Scoring has also changed. Instead of receiving a cumulative score of 2-12, you’ll now receive three cumulative scores of 2-8 in three separate categories (with 2 being the lowest score and 8 the highest). Two separate graders will read your work and each will rank it on a scale of 1-4 for each category. When they’re finished, their scores will be combined into your three cumulative scores. The three categories are writing (how well write, i.e. your grammar and style), reading (how well you understood the article) and analysis (how well you assessed the writer’s persuasive techniques). It’s possible to do very strongly in one category but very poorly in another, and there is no overall single score for the essay as a whole.

Even though each essay will feature a different passage, the essay question itself—show how the author persuades the reader of her argument—will never change. For this reason it’s completely possible to prepare for the essay in advance.

Should You Take The New (Redesigned) Essay?

Unlike the old SAT essay, the new version is optional. Some colleges will require the essay, some will recommend it, and others will neither require nor recommend it. In the Ivy League, for instance, the essay is currently required by Harvard, Yale, Princeton and Dartmouth, whereas Columbia, Penn, Brown and Cornell are not requiring it. You can find an official list of each college’s policy here.

Because a number of colleges do require or recommend you submit essay scores, I recommend anyone sitting for the SAT also sit for the essay. Even if you’re not currently planning on applying to a college that asks for the essay, you might later decide to apply to a school that does. College lists change frequently and you never know where you might want ultimately apply. The last thing you want is to have to retake the entire exam, or, worse yet, not be able to apply to a particular college, just because you took the exam without the essay.

How To Write A High Scoring Essay

Before you begin writing your essay, you’ll want to make sure you read the passage carefully. It’s important to read actively, always keeping in mind the author’s main point and how the various parts of her argument relate to that point.

Before you start reading, look at the question that follows the passage. This question tells you the main point of the passage, so you don’t have to figure it out on your own. For example, one official question reads “write an essay in which you explain how Paul Bogard builds an argument to persuade his audience that natural darkness should be preserved.” This means that the main point or argument of the passage is that natural darkness should be preserved.

After you’ve ascertained the main point from the question, keep it in mind as you read the passage. Ask yourself how the author uses evidence, reasoning and/or stylistic and persuasive elements to convince the reader of this main point, as well as how the various parts of her argument relate to the main point. Everything should lead back to the main point in some way.

As you read, annotate or note whenever you come across a device the author uses to persuade you of her argument. If you don’t understand something, go back and reread it. You have ample time to make sure you understand the passage, and it’s important you do so in order to get the highest “reading” category score possible. Confusing moments are often easier to make sense of after you’ve read the entire passage and understand the full context.

Once you’ve read the passage and identified key persuasive devices, it’s time to make a brief outline for your essay. A powerful way to structure your essay is to have an opening paragraph that states the thesis, followed by two or three paragraphs, each devoted to arguing one part of the thesis, followed by a conclusion that restates the thesis (although in slightly different language than in the opening paragraph).

The thesis should make a central claim that the entire essay then sets out to prove. You might argue, for example, that “the author uses statistical evidence, ironic language and emotional appeals to persuade the reader that natural darkness should be preserved.” The next paragraph would then provide concrete examples of how the author uses statistical evidence to persuade the reader, the following paragraph would discuss examples of ironic language, and the next paragraph would discuss specific examples of emotional appeals. The concluding paragraph would wrap things up by restating the thesis. Here’s an example of what your outline might look like:

P1: Thesis – author uses statistical evidence, ironic language and emotional appeals to persuade reader natural darkness should be preserved
P2: Statistical evidence examples
P3: Ironic language examples
P4: Emotional appeals examples
P5: Conclusion (restate thesis)

After you’ve completed this brief outline, you’re ready to write. Keep an eye on the clock and make sure to leave a couple minutes at the end so that you can review what you’ve written. This will give you a chance to correct any grammatical, spelling or stylistic mistakes before you hand in the essay.

Key Pointers and Mistakes To Avoid


When you’re coming up with your thesis, make sure to focus on what the author does to persuade the reader, rather than on what the author fails to do. Even if there are some shortcomings in the author’s argument, your task is to analyze what devices are used in order to persuade the reader, not what shortcomings might exist in the argument.

New Redesigned SAT Essay 2

Similarly, make sure that your thesis explains what persuasive devices the author uses rather than whether her argument is right or wrong. Even if you personally agree or disagree with the argument, it’s important to stay neutral. Think of yourself as an impartial outside observer, confined to commenting on how the author constructs her argument, not on the merits of the argument itself.


When you write about your examples of persuasive elements, always make sure to tie those examples back to your central argument about persuasion. It’s easy to get so caught up in the details that you forget to state what those details are actually doing—attempting to persuade the reader of something—but it’s important to make this connection clear.

When you choose your examples, look for those examples that are most important to persuading the reader of the author’s argument. Avoid marginal and insignificant details that don’t play a big role in persuading the reader of the main point.

While the SAT asks you to consider the author’s use of “evidence, reasoning, and stylistic and persuasive devices,” you’re not required to discuss all three. In fact, it’s better to go into more detail on just two than to try to address all three and use less detail in the process.

As you discuss specific persuasive elements, try to elaborate on how and why they work to persuade the reader of the main point. It’s not enough to simply mention a detail from the essay in one sentence. Try instead to really flesh out why a specific detail works persuasively—devote a number of sentences to explaining the different ways it functions. The highest scoring essays always go into great detail about a few select moments in the passage, rather than trying to briefly mention every persuasive moment in passing.

When discussing examples, avoid making broad claims that you can’t back up, such as “by discussing tragedy, the author moves the reader.” Instead, get into specifics: “when the author discusses tragedy, she chooses specific examples aimed at resonating with her audience. Since her audience is American, for example, she discusses the American tragedy of September 11th.”

You should also mention how key details and ideas interrelate to one another and the author’s main argument. Showing how everything “fits together” in the passage is critical for earning the highest score possible according to the SAT’s scoring rubric.

In citing specific examples, avoid lengthy direct quotations from the text. You should mainly reserve direct quotes for when you want to draw attention to the specific language or structure of the writing the author is using. Otherwise, it’s usually best to paraphrase what the author is saying. This is not only good writing practice, but it also demonstrates to the grader that you have understood the passage, which is critical to earning a high “reading” category score.

In order to earn a high “reading” score, it’s also important that you write a substantial amount. Essays earning the highest reading scores are usually among the longest, and this is because the more you write about the text, the clearer it is that you understand the text as a whole. Plan on using the full 50 minutes to write as much as possible when you’re not reading the passage or planning and reviewing your essay.

Common Persuasive Elements

There are an unlimited number of persuasive elements that an author can use to make a point, and each passage will feature different ones. That said, here are some common persuasive elements that you might see on any given passage:

Historical Facts

Applying a general rule to a specific case
Deducing a general rule from specific cases
Using logic to rule a possibility in or out

Stylistic or Persuasive Elements
The author tries to sound like the reader
Word choice
Irony or sarcasm

Grammar and Style Tips

Because your essay will receive a “writing” score, it’s important to use good grammar and style. Since you should already be studying grammar for the Writing and Language section of the redesigned SAT, try to apply the same rules you’re learning to your own writing on the essay.

New Redesigned SAT 3

To pick up as many “writing” points as possible, make sure that your writing flows smoothly from one idea to the next. Use strong and clear transitions at the start of each new paragraph. You might begin a new paragraph, for example, by saying “Similar to her use of historical evidence, the author employs statistical evidence to argue that the economy is strong.” You should also connect separate clauses with words and phrases that show the specific nature of their relationship, such as “thus,” “therefore,” “nevertheless,” “for example” and “in contrast.”

It’s also important to vary the structure of your sentences. Instead of writing “John is hungry. John is tired. John is not having a good day,” write “John is feeling hungry and tired. As you might guess, he is not having a good day.” Avoid starting consecutive sentences and paragraphs with the same word. One trick to help mix up sentence structure is to throw in an occasional rhetorical question, such as “How would the early Monicaros have felt if they too lacked freedom?”

Whenever possible, forgo passive sentences for active ones. Instead of writing “The apple was eaten by the boy,” for instance, write “The boy ate the apple.” What you’re essentially doing is replacing any “to be” verb forms (“was”) with a verb that represents the action actually taking place in the sentence (eating, or “ate”).

The SAT also expects you to write formally. This means avoiding contractions like “it’s” or “that’s” in favor of “it is” or “that is,” as well as avoiding the first person (I, we, me, etc.). You should also avoid clichés or any expressions that sound too colloquial. Try to emulate the type of formal writing you find in many academic essays and school textbooks. This also means aiming to use advanced vocabulary when appropriate. Just make sure you’re using any advanced word correctly—when in doubt, leave it out.

Practice Makes Perfect

Now that you’re armed with the knowledge of what to do on the essay, it’s essential to practice. You’ll ideally want to write a couple of practice essays before you sit for the real thing.

It’s best to practice with official College Board essay prompts, since prompts written by test prep companies might not always represent what you’ll see on test day as accurately. Fortunately, College Board has already released a number of prompts. You can find two prompts, including scored sample responses with College Board commentary, here. There are also another four included with the four released practice tests here, as well as an additional two in the new Official SAT Study Guide.

If you’ve exhausted these eight practice prompts, you can also practice with old AP English Language and Composition free response questions, available here. The second question in each free response asks you to compete essentially the same task as the SAT essay question.

Make sure to adhere to the 50 minute time limit when practicing!


The new (or “redesigned”) SAT features a very different type of essay question than the prior SAT did. Although this essay is optional, it’s a good idea to take it so as not to close the door on any colleges you might be eventually wish to apply to. You can make sure you’re prepared on test day by combining the advice in this article with writing multiple, timed practice essays. Because the assignment and scoring criteria never change, preparing should leave you with no surprises and a high set of scores.

Solving Percent Problems Quickly On SAT and ACT Math

Most SAT and ACT percent problems can be solved in a matter of seconds. Here’s how:

Percents SAT ACT Math

Want a Free List of All the Math Topics That Have Recently Appeared on the SAT or ACT?

For a free list of all the math topics that have recently appeared on the SAT or ACT, and/or for answers to any other questions, you can reach me at or 212-658-0834.