SAT SUBJECT TEST MATH LEVEL 1
What You Need to Know About the Math Level 1 Test
• What Topics Are Covered on the Math Level 1 Test?
• How Many Questions Should You Answer?
• When Should You Guess?
• Should You Use a Calculator on the Math Level 1 Test?
There are two SAT Subject Tests in math: Level 1 and Level 2. Although there is some overlap in the material covered on the two tests, basically, the Level 1 material is less advanced than the Level 2 material. The Level 1 test is based on the math that most students learn in their first three years of high school, whereas many of the questions on the Level 2 test are on material normally taught in a fourth year of math (usually precalculus and trigonometry).
WHAT TOPICS ARE COVERED?
The Math 1 test consists of 50 multiple-choice questions. If you have completed three years of high school math, you have likely learned all the topics covered on the test. In fact, you almost surely have learned more than you need. At most, two or three questions, and possibly none, should seem completely unfamiliar to you. The following chart lists the topics included on the Math 1 test and indicates how many questions you should expect on each topic.
Topic |
Percent of Test |
Number of Questions |
Algebra |
30% |
15 |
Plane geometry |
20% |
10 |
Solid geometry |
6% |
3 |
Coordinate geometry |
12% |
6 |
Trigonometry |
8% |
4 |
Functions |
12% |
6 |
Statistics and sets |
6% |
3 |
Miscellaneous |
6% |
3 |
The information in this chart can help you guide your study. If you start your preparation early enough, you should plan on reviewing most, if not all, of the material in this book. If, however, your time is limited because you waited until right before your test date to start studying, you should concentrate on the topics that are heavily tested—algebra and plane geometry—and spend little or no time on solid geometry, statistics, and trigonometry.
The numbers in the chart above are approximations, because the percentages can vary slightly from test to test and also because some questions belong to more than one category. For example, you may need to solve an algebraic equation to answer a geometry question or you may need to use trigonometry to answer a question in coordinate geometry.
In the math review part of this book, you will specifically learn which facts you need to know for each topic. For example, you will learn that you do not need to know most of the trigonometry you were taught in school: only the most basic trigonometry is tested. The more advanced topics in trigonometry appear on the Math Level 2 test. You will also learn within each topic which facts are more heavily emphasized on the test. For example, to answer the 10 questions on plane geometry, you need to know several facts about triangles, quadrilaterals, and circles. However, some facts about circles are much more important than others, and more questions are asked about triangles than about quadrilaterals.
What Formulas Do You Have to Memorize?
You need to know well over a hundred facts and formulas to do well on the Math 1 test. However, many of them you have known for years, such as the formulas for the areas of rectangles, triangles, and circles. Others you learned more recently, such as the laws of exponents and the quadratic formula. In the math review chapters, each essential fact is referred to as a KEY FACT, and you should study and memorize each one that you do not already know.
If you have already taken the PSAT or SAT, you may recall that 12 facts about geometry are provided for you in a reference box on the first page of each math section. For the Math 1 test, you need to know these formulas (and many more), but they are not given to you.
There are five formulas, however, that you do not have to memorize. They are provided for you in a reference box on the first page of the test. All five concern solid geometry and are explained in Chapter 12. It is unlikely that more than one of the 50 questions on any Math 1 test would require you to use one of these formulas, and it is possible that none of them will. So don’t worry if you are not familiar with them. The five formulas appear in the box below.
FORMULAS WORTH MEMORIZING
Here are formulas for the volumes of three solids and the areas of two of them. Although they will be provided on the test itself, memorizing them can save you time.
For a sphere with radius r :
For a right circular cone with radius r, circumference c, height h, and slant height l:
For a pyramid with base area B and height h:
HOW MANY QUESTIONS SHOULD YOU ANSWER?
This seems like a strange question. Most students, especially good students, try to answer all the questions on a test. Occasionally, they might have to leave out a question because they get stuck, but they never start a test planning to pace themselves in such a way as to omit 10, 15, or 20 percent of the questions intentionally. Surprisingly, this is precisely what many students should do on the Math 1 test. The biggest mistake most students make when taking this test is trying to answer too many questions. It is far better to go slowly, answering fewer questions and getting most of them right than to rush through the test answering all the questions but getting many of them wrong.
Because nothing lowers one’s score more than making careless mistakes on easy questions and because a major cause of careless errors is rushing to finish, take the test slowly enough to be accurate, even if you don’t get to finish.
So exactly how many questions should you answer? Obviously, the answer to this question depends on your goal. If you are an outstanding math student and your goal is to get an 800, then not only do you have to answer all 50 questions, you have to get all of them right. If, on the other hand, your goal is to earn a 650, then, as you can see from the SAMPLE MATH 1 CONVERSION CHART, you could answer fewer than 40 questions and even miss a few.
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The best way to increase your score is to answer fewer questions.
To see why this is so, consider the following situation. Suppose Bob took the Math 1 test, answered all 50 questions, and got 34 right and 16 wrong. Then his raw score would be 30 (34 points for the 34 right answers minus points for the 16 wrong answers), and his scaled score would be 600. Probably among the 16 questions he missed were a few that he just didn’t know how to solve. It is also likely that several of his mistakes were careless. Especially during the last 10 or 15 minutes, he probably went too fast trying to finish and missed questions he could have gotten right had he worked more slowly and more carefully. A likely scenario is that in the first 30 questions, when he was not rushing, he got about 26 right and 4 wrong. On the last 20 questions, in contrast, when he was going too fast, he got about 8 right and 12 wrong.
What if he had worked as slowly and as accurately at the end of the test as he had at the beginning of the test? He would have run out of time. However, his score would have been higher. Suppose in the last 20 questions he omitted 8, answering only 12, but getting 10 right and 2 wrong. Then in total he would have had 36 right answers and 6 wrong ones. His raw score would have been 35 and his scaled score a 650. By slowing down and answering fewer questions, his score would have increased by 50 points!
SAMPLE MATH 1 CONVERSION CHART
Which Questions Should You Answer?
Every question has the same raw score value, 1 point. You get the same 1 point for a correct answer to the easiest question on the test, which you could answer in less than 30 seconds, as you do for a correct answer to the hardest question, which might take you more than three minutes to answer. Therefore, if you are not going to answer all the questions, then you should answer the easy and moderately difficult ones and leave out the hardest ones.
Of course, to follow this advice, you need to know which questions are easy and which ones are hard. Fortunately, that is not a problem. The first ones are the easiest, the last ones are the hardest. In general, the questions on the Math 1 test go in order from easy to difficult.
On a recent actual Math 1 test, on questions 1–10, the average percentage of students answering a question correctly was 82 percent, and on questions 41–50 the average percentage of students answering a question correctly was 28 percent. Of questions 1–27, every question was answered correctly by more than 60 percent of the students taking the test; of questions 28–50, not one question was answered correctly by at least 60 percent of the students.
You may not find question 30 to be harder than question 26—especially if you are better in algebra than geometry and question 30 is on algebra and question 26 is on geometry. However, you will definitely find questions 10–19 to be easier than questions 20–29, which in turn will be significantly easier than questions 30–39.
SHOULD YOU GUESS ON THE MATH 1 TEST?
The simple answer is “YES.” In general, it pays to guess. To be fair, however, that answer was a little too simple. There are really two types of guessing—wild guessing and educated guessing—and they should be handled separately.
How Does Wild Guessing Affect Your Score?
Suppose that when you take the Math 1 test you work slowly and carefully and answer only 40 of the 50 questions but get them all right. First of all, is that good or bad? Well, probably on a math test in school that would not be very good—you probably wouldn’t be happy with a grade of 80. On the Math 1 test, however, those 40 right answers give you 40 raw score points, which convert to a very respectable 700!
Now comes the big question. Should you take your last 10 seconds and quickly bubble in an answer to the last 10 questions without even looking at them? In other words, should you make 10 wild guesses? The answer is that it probably won’t matter. Since there are 5 answer choices to each question, the most likely outcome is that you will get of them right. So if you guess on those last 10 questions, you will probably get 2 right and 8 wrong. For the 2 right answers you will earn 2 points and for the 8 wrong answers you will lose points.
If that happens, your score remains the same—your raw score is still 40 and your scaled score is still 700. Of course, you might be unlucky and get only 1 right answer or really unlucky and get none correct, in which case your score would drop to 690 or 680. On the other hand, you might be lucky and get 3 or 4 right, in which case your score would increase to 710 or even 730. On average, however, wild guessing does not affect your score, so whether you make wild guesses or not is completely up to you.
How Does Educated Guessing Affect Your Score?
Educated guessing is very different from wild guessing. Sometimes, even though you don’t know how to solve a problem, you are sure that some of the answer choices are wrong. When that occurs, you eliminate everything you know is wrong and guess among the remaining choices. This use of the process of elimination is called educated guessing and, unlike wild guessing, can increase your score significantly.
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Educated guessing can increase your score dramatically.
To see why educated guessing is so important, consider a scenario slightly different from the one in our discussion of wild guessing. Suppose now that you have time to answer all 50 questions, but you are sure of only 40 of them. On the other 10 you are able to eliminate 3 choices, say A, B, and C, but have no idea whether D or E is the correct answer. Should you guess at these 10 questions and risk getting some wrong, or should you leave them out? If you omit these questions, your raw score will remain at 40 and your scaled score will still be 700. Now, however, if you guess, since you have a 50-50 chance of guessing correctly, you will probably get about 5 right and 5 wrong. How will that affect your score? For the 5 you get right, you will earn 5 points; for the 5 you get wrong, you will lose points. This is a net gain of 3.75 points. Your raw score would go from 40 to 43.75, which would get rounded up to 44, and your scaled score would go from 700 to 740, which is a tremendous improvement. You cannot afford to give up those 40 points because you are afraid to guess.
When Should You Guess?
You should be able to make an educated guess on most of the questions you attempt. As you will see in the next chapter on tactics for taking the Math 1 test, there are strategies for dealing with almost all of the questions on the Math 1 test that you do not know how to do or get stuck on. Incredibly, when properly used, some of these tactics are guaranteed to get you the right answer. Others will enable you to eliminate choices. Whenever you can eliminate one or more choices, you must guess.
Basically, if you attempt a question, you should almost always answer it: either you will know how to do it or you should be able to make an educated guess. Certainly, you should omit very few, if any, of the first 25 questions, which make up the easier half of the test.
When Should You Omit Questions?
There are two reasons for omitting a question on the Math 1 test:
• You absolutely do not understand what the question is asking. You do not know how to answer it and have no basis for making a guess.
• You do not get to that question. Most students who pace themselves properly, going slowly enough to avoid careless errors, do not have enough time to answer every question. If you run out of time, you may omit the remaining questions—or, if you like, you can make a few wild guesses.
SHOULD YOU USE A CALCULATOR ON THE MATH 1 TEST?
On the PSAT and SAT, using a calculator is optional. Although almost all students bring one to the test and use it on at least a few questions, there isn’t a single question that requires the use of a calculator. On the Math 1 test, the situation is very different. At least 20 percent of the questions on the Math 1 test require the use of a calculator (to evaluate sin 40°, , log 17, or (1.08)^{20}, for example). On another 20–30 percent of the questions, a calculator might be helpful. So it is absolutely mandatory that you bring a calculator with you when you take the test.
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You must bring your own calculator to the test. None will be available at the test center, and you are absolutely forbidden from sharing a calculator with a friend.
What Calculator Should You Use?
Basically, you have two options—a scientific calculator or a graphing calculator. The decision is really quite simple: you should bring a calculator with which you are very comfortable. This is probably the calculator you are currently using in your math class.
Do not go out and buy a new calculator right before you take the Math 1 test. If, for any reason, you want a new calculator, get it now, become familiar with it, and use it as you go through this book and especially as you do all the model tests.
The College Board recommends that if you are comfortable with both a scientific calculator and a graphing calculator, you bring a graphing calculator. This is perfectly good advice because there is no disadvantage to having a graphing calculator, but the advantages are small.
One advantage is that in the larger window of a graphing calculator, you can see the answers to your last few calculations, so you may not have to write down the results of intermediate steps in a problem whose solution requires a few steps.
Suppose, for example, that you are asked to find the area of ABC in the figure below.
The straightforward way to answer this question is to use the area formula . The area of Δ. Now make three calculations.
Step 1:
On most scientific calculators, the value will disappear as soon as you start your next calculation, so you would have to write 7.66 in your exam booklet. On a graphing calculator, “10 cos40° = 7.66” remains visible in the screen when you do step 2:
On a graphing calculator, both values are still there when you need to do step 3:
A second advantage of a graphing calculator is the obvious one—it can graph. However, this is not as big an advantage as you might think. As you will see in the next chapter, occasionally if you get stuck on a question and cannot come up with the correct mathematical solution, looking at a graph may help you to get the right answer or at least make an educated guess. However, this is not a common situation, and no question on the Math 1 test requires the use of a graphing calculator.
To summarize, there is absolutely no reason not to use a graphing calculator if you own one and are comfortable with it, but the advantages of using it are small and do not warrant buying one just for this test.
By the way, you may bring two calculators and use whichever you prefer on any question. In fact, the College Board recommends that you bring batteries and/or a backup calculator to the test center. Remember, if your calculator fails during the test, you may not borrow or share anyone else’s and the test center won’t have any to lend you.
What Else Do I Need to Know About Calculators?
In Chapter 1, you will receive very important advice about when to use and when not to use your calculator. Be sure to read that chapter—it is critical for learning good test-taking skills.
This discussion of calculators concludes with a few miscellaneous bits of advice.
• As you will see in Chapter 14, all angles on the Math 1 test are measured in degrees. You do not have to know anything about radians, so keep your calculator in degree mode.
• If you are using a graphing calculator, you do not have to clear its memory. Therefore, you can store any formulas you like and even program your calculator, if you know how. You should know, however, that this is usually not advisable. If you have a program to solve quadratic equations, for example, you may very well spend more time searching for it and running it than it would take just to solve the equation in your test booklet.
• If your calculator fails during the test and you do not have a backup and if you immediately tell the proctor, you may cancel your math test without canceling any other SAT Subject Tests you are taking that day. (Normally, if you want to cancel a test, you must cancel all the tests you take that day.)