The SAT Prep Black Book(95)
Ignore The So-Called “Order Of Difficulty”
Test-takers are often encouraged to believe that the questions on the SAT Math section get harder as the section goes on. But I would recommend ignoring that idea.
It’s true that the College Board assigns difficulty-level rankings of 1 through 5 to each question, and that we’ll typically see that the earliest questions in an SAT Math section are ranked 1 or 2, while the last questions are 4’s and 5’s.
But that shouldn’t mean anything to us, as trained test-takers. Let me explain why.
The difficulty ranking is simply an indication of the percentage of the test-taking population who miss a particular question. In other words, if a question has a difficulty ranking of 1, then the vast majority of people who see it will get it right; if it has a difficulty ranking of 5, then the vast majority of people who see it will answer it incorrectly.
The difficulty ranking has nothing to do with the number or type of math concepts that appear in a particular question. Sometimes a question that’s based on the definition of the word “even” might be ranked as a 1, and sometimes it’s ranked as a 5. The deciding factor is simply the percentage of test-takers who get it right or wrong.
And here’s the important thing to keep in mind: the vast majority of SAT-takers have no idea at all of how to take the test. They do almost everything wrong. If you’re familiar with the concepts in this Black Book, you’ll be looking at SAT Math questions the right way, and the percentage of regular test-takers who get a question right has nothing to do with whether you, yourself, will get that question right.
We’ll generally find that questions near the end of an SAT Math section tend to be more abstract or conceptual, while questions towards the beginning of a section tend to be a little more similar to the kinds of things you might be asked about in school. But that doesn’t mean the later questions are always harder. In fact, we’ll often find that questions towards the end of a section are more likely to be things you can solve without actually doing any calculations (because they’ll rely on things like properties and definitions of terms). This can often mean that we can answer later questions much more quickly than earlier questions, if we’re approaching them correctly.
But this cuts both ways. Just as we shouldn’t be intimidated by later questions, we also shouldn’t take earlier questions for granted. Remember that doing well on SAT Math is a question of reading carefully and thinking carefully, and that wrong answer choices are often designed to attract students who make small mistakes. This means that we have to be alert to possible mistakes at all times, even when a question might seem extremely easy.
In fact, when I work with students who are trying to score a perfect 800 on the SAT Math section but who might be missing one or two questions per test, I find that they nearly always miss questions in the first half of the section because of small mistakes—usually because they’ve been incorrectly taught that those questions are always “easy” and that they don’t have to pay full attention to them.
So here’s the bottom line: you should ignore the idea of an order of difficulty, because it serves no purpose. Instead, treat each question as a separate event. Don’t be afraid of any questions, and don’t take them for granted either.
The Math Path In Action
To demonstrate how this approach to SAT Math questions works, and to help you improve your understanding and execution of that approach, we’ll go through an SAT Math section from the second edition of the College Board’s Blue Book, The Official SAT Study Guide. (Remember, the Blue Book is the only book I recommend for practice questions, because it’s the only book whose questions are totally guaranteed to play by the College Board’s rules.) I’ve chosen the first practice-test section that includes both Multiple Choice problems and Student-Produced Response problems. It starts on page 413 of the Blue Book.
Page 413, Question 1
You really have to be careful on a problem like this—it’s the kind of thing that most test-takers will feel they can’t possibly miss because it seems so simple. But it’s very easy to overlook a couple of small details on this question and end up with a wrong answer.
The question asks us to figure out how many new houses were built from 1961 to 1990. To answer that question, we have to look at the relevant years on the chart. The first row shows the houses built from 1961 to 1970; the next row shows the houses from 1971 to 1980; the third row shows us the houses from 1981 to 1990. There are 2 house icons in the first row, 4 in the second row, and 8 in the third row. That makes a total of 14 house icons.