Mathematics Level 1 Subject Test

beginning of content:

Introduction

The Mathematics Level 1 Subject Test assesses the knowledge you’ve gained from three years of college-preparatory mathematics, including two years of algebra and one year of geometry. If you’ve excelled in these courses, taking the test can support your high school grades, indicate an interest in pursuing math-based programs of study (science, technology, engineering, economics, etc.), and help you differentiate yourself in the admission process.

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Important:

Important Notes

• Offered in August, October, November, December, May, and June.
• Calculator use permitted. See calculator policy, including what calculators are acceptable.

Test Basics

Scoring, Timing, Number of Questions

Points Minutes Questions
200-800 60 50 (Multiple Choice)

• Number and operations
• Algebra and functions
• Geometry and measurement (plane Euclidean, coordinate, three-dimensional, and trigonometry)
• Data analysis, statistics, and probability
• At least three years of college-preparatory mathematics, including two years of algebra and one year of geometry
Content Approximate % of Test

Number and operations

• Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences
10%–14%

Algebra and functions

• Expressions, equations, inequalities, representation and modeling, properties of functions (linear, polynomial, rational, exponential)
38%–42%

Geometry and measurement

• Plane Euclidean
• Coordinate: Lines, parabolas, circles, symmetry, transformations
• Three-dimensional: Solids, surface area and volume (cylinders, cones, pyramids, spheres, prisms)
• Trigonometry: Right triangles, identities

38%–42%

18%–22%

8%–12%

4%–6%

6%–8%

Data analysis, statistics, and probability

• Mean, median, mode, range, interquartile range, graphs and plots, least squares regression (linear), probability
8%–12%

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The Official SAT Subject Test Study Guide in Mathematics Level 1

Get ready for the Mathematics Level 1 Subject Test with official tests from the test maker. This guide features:

• Four full-length, previously administered Mathematics Level 1 Subject Tests
• Detailed answer explanations for all test questions
• Exclusive test taking-tips and approaches, including information on calculator usage

The Official Study Guide for All SAT Subject Tests, Second Edition

Get the only study guide available for all 20 SAT Subject Tests.
Features include:

• 20 full-length, previously administered Subject Tests
• Detailed answer explanations for all test questions
• The most up-to-date tips and approaches on selecting which tests to take, the best time to take the tests, and how to best be ready for test day
• Detailed descriptions of every Subject Test, including topics covered and recommended course work
• Two audio CDs for all six Language with Listening Tests

Use the free Khan Academy® lessons in this playlist to study for Mathematics Subject Tests. View additional playlists here.

If you have taken trigonometry or elementary functions (precalculus) or both, received grades of B or better in these courses, and are comfortable knowing when and how to use a scientific or graphing calculator, you should select the Level 2 test. If you are sufficiently prepared to take Level 2, but elect to take Level 1 in hopes of receiving a higher score, you may not do as well as you expect. You may want to consider taking the test that covers the topics you learned most recently, since the material will be fresh in your mind. You should also consider the requirements of the colleges and programs you are interested in.

Areas of Overlap on Math Level 1 and Math Level 2

The content of Level 1 has some overlap with Level 2, especially in the following areas:

• Elementary algebra
• Three-dimensional geometry
• Coordinate geometry
• Statistics
• Basic trigonometry

How Test Content Differs

Although some questions may be appropriate for both tests, the emphasis for Level 2 is on more-advanced content. The tests differ significantly in the following areas:

• Number and Operations. Level 1 measures a more basic understanding of the topics than Level 2. For example, Level 1 covers the arithmetic of complex numbers, but Level 2 also covers graphical and other properties of complex numbers. Level 2 also includes series and vectors.
• Algebra and Functions. Level 1 contains mainly algebraic equations and functions, whereas Level 2 also contains more advanced equations and functions, such as exponential, logarithmic and trigonometric.
• Geometry and Measurement. A significant percentage of the questions on Level 1 is devoted to plane Euclidean geometry and measurement, which is not tested directly on Level 2. On Level 2, the concepts learned in plane geometry are applied in the questions on coordinate geometry and three-dimensional geometry. The trigonometry questions on Level 1 are primarily limited to right triangle trigonometry (sine, cosine, tangent) and the fundamental relationships among the trigonometric ratios. Level 2 includes questions about ellipses, hyperbolas, polar coordinates and coordinates in three dimensions. The trigonometry questions on Level 2 place more emphasis on the properties and graphs of trigonometric functions, the inverse trigonometric functions, trigonometric equations and identities, and the laws of sines and cosines.
• Data Analysis, Statistics and Probability. Both Level 1 and Level 2 include mean, median, mode, range, interquartile range, data interpretation and probability. Level 2 also includes standard deviation. Both include least-squares linear regression, but Level 2 also includes quadratic and exponential regression.

Seek advice from your high school math teacher if you are still unsure of which test to take. Keep in mind you can choose to take either test on test day, regardless of what test you registered for.

Please note that these tests reflect what is commonly taught in high school. Due to differences in high school classes, it’s likely that most students will find questions on topics they’re not familiar with. This is nothing to worry about. You do not have to get every question correct to receive the highest score (800) for the test. Many students do well despite not having studied every topic covered.

The following information is for your reference in answering some of the questions in this test:

Volume of a right circular cone with radius and height :

Volume of a sphere with radius :

Volume of a pyramid with base area and height :

Surface Area of a sphere with radius :

• Think about how you are going to solve the question before picking up your calculator. It may be that you only need the calculator for the final step or two and can do the rest in your test book or in your head. Don’t waste time by using the calculator more than necessary. For about half of the questions, there’s no advantage, or perhaps even a disadvantage, to using a calculator. For the other half of the questions, a calculator may be useful or necessary.
• Read the question carefully so that you know what you are being asked to do. Sometimes a result that you may get from your calculator is NOT the final answer. If an answer you get is not one of the choices in the question, it may be that you didn’t answer the question being asked. You should read the question again. It may also be that you rounded at an intermediate step in solving the problem, and that’s why your answer doesn’t match any of the choices in the question.
• The answer choices are often rounded, so the answer you get might not match the answer in the test book. Since the choices are rounded, plugging the choices into the problem might not produce an exact answer.
• Don’t round any intermediate calculations. For example, if you get a result from the calculator for the first step of a solution, keep the result in the calculator and use it for the second step. If you round the result from the first step and the answer choices are close to each other, you might have a problem.
• Bring a calculator that you are used to using. It may be a scientific or a graphing calculator, but if you’re comfortable with both, bring a graphing calculator. The most important consideration is your comfort level with the calculator. Test day is not the time to start learning how to use a new calculator, even if it has more capabilities.
• Verify that your calculator is in good working condition before you take the test. You may bring batteries and a backup calculator to the test center. Remember, no substitute calculators or batteries will be available at the test center. You can’t share calculators with other test takers.
• If you are taking the Mathematics Level 1 test, make sure your calculator is in degree mode ahead of time so you won’t have to worry about it during the test.
• If your calculator malfunctions at the test center, and you don’t have a backup calculator, you must tell your test coordinator when the malfunction occurs. You can choose to cancel your scores on the test.
• If you are using a calculator with large characters (one inch high or more) or a calculator with a raised display that might be visible to other test takers, you will be seated at the discretion of the test coordinator.
• You may not use your calculator for sharing or exchanging, or removing part of a test book or any notes relating to the test from the test room. Such action may be grounds for dismissal or cancellation of scores or both. You do not have to clear your calculator’s memory before or after taking the test.

Figures that accompany problems are intended to provide information useful in solving the problems. They are drawn as accurately as possible except when it is stated in a particular problem that the figure is not drawn to scale. Even when figures are not drawn to scale, the relative positions of points and angles may be assumed to be in the order shown. Also, line segments that extend through points and appear to lie on the same line may be assumed to be on the same line. The text “Note: Figure not drawn to scale.” is included on the figure when degree measures may not be accurately shown and specific lengths may not be drawn proportionally.