# SAT / ACT Prep Online Guides and Tips If you're considering taking SAT Subject Tests and math is a strong subject for you, you'll need to decide which SAT Subject Test in math to take. There are two Math SAT Subject Tests: Math 1 and Math 2 (also written as Math Level 1 and Math Level 2, or Math I and Math II).

Math 2 is meant for students with more high school math coursework and covers a broader range of topics than Math 1 does. Other than that, the two tests are pretty similar: both have 50 multiple-choice questions and a 60-minute time limit.

In this article, I'll go over what's covered in Math 1, what's covered in Math 2, their similarities and differences, whether Math 1 is easier than Math 2, and how to choose which Subject Test to take.

Note: This article deals with the two Math SAT Subject Tests, not the Math section on the regular SAT. To learn more about the SAT Math section and how to do well on it, check out our ultimate SAT Math prep guide.

## What's Covered on SAT Math 1?

SAT Subject Test Math 1 covers the topics you learn in one year of geometry and two years of algebra. Here's what you can expect to see on the test:

 Topics and Subtopics % of Math 1 SAT Subject Test Approximate # of Questions Number and Operations 10-14% 5-7 Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences Algebra and Functions 38-42% 19-21 Expressions, equations, inequalities, representation and modeling, properties of functions (linear, polynomial, rational, exponential) Geometry and Measurement 38-42% 19-21 Plane Euclidean/Measurement 18-22% 9-11 Coordinate: Lines, parabolas, circles, symmetry, transformations 8-12% 4-6 Three-dimensional: solids, surface area and volume (cylinders, cones, pyramids, spheres, prisms) 4-6% 2-3 Trigonometry: right triangles and identities 6-8% 3-4 Data Analysis, Statistics, and Probability 8-12% 4-6 Mean, median, mode, range, interquartile range, graphs and plots, least-squares regression (linear), probability

Source: SAT Subject Tests Student Guide

As you can see, most of the questions will be about algebra, functions, or geometry. This means that when you are studying for Math 1, these are the main areas you should focus on.

There will also be a few questions (about five) on data analysis/statistics/probability. I'm calling this out because it's something many students haven't spent a lot of time on in class.

## What's Covered on SAT Math 2?

The SAT Subject Test Math 2 covers most of the same topics as Math 1—information that would be covered in one year of geometry and two years of algebra—plus precalculus and trigonometry.

However, the geometry concepts learned in a typical geometry class are only assessed indirectly through more advanced geometry topics such as coordinate and three-dimensional geometry.

Here is a chart with topics and percentage breakdowns:

 Topics and Subtopics % of Math 2 SAT Subject Test Approximate # of Questions Number and Operations 10-14% 5-7 Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences, series, vectors Algebra and Functions 48-52% 24-26 Expressions, equations, inequalities, representation and modeling, properties of functions (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, periodic, piecewise, recursive, parametric) Geometry and Measurement 28-32% 14-16 Coordinate: lines, parabolas, circles, ellipses, hyperbolas, symmetry, transformations, polar coordinates 10-14% 5-7 Three-dimensional: solids, surface area and volume (cylinders, cones, pyramids, spheres, prisms), coordinates in three dimensions 4-6% 2-3 Trigonometry: right triangles, identities, radian measure, law of cosines, law of sines, equations, double angle formula 12-16% 6-8 Data Analysis, Statistics, and Probability 8-12% 4-6 Mean, median, mode, range, interquartile range, standard deviation, graphs and plots, least squares regression (linear, quadratic, exponential), probability

Source: SAT Subject Tests Student Guide

It's worth noting that on the main College Board page for Math 2, they (incorrectly) state that the test is 48-52% geometry. But in the SAT Subject Tests Student Guide, you can see that the actual percentage is 28-32%. Let's all be glad that the questions on College Board tests are much more closely vetted than what goes on their website!

In terms of individual topics, the Math 2 test is, by far, weighted most heavily toward algebra and functions, with about half the questions in this area. You can also expect to see a sizable chunk of trigonometry.

Knowing the properties of all different types of functions, including trigonometric functions, is the single most important topic to study for the Math 2 test. If you don't know all of that backwards and forwards, there will be a lot of questions you simply don't understand. ## SAT Subject Test Math 1 vs Math 2: Similarities and Differences

To give you an easy-to-follow overview when you are comparing tests, I'll quickly go over which topics are covered on both exams and which you can expect to see only on Math 1 and only on Math 2, respectively.

### Topics on Both Math 1 and Math 2

We'll start by looking at the general topics that are present on both Math Subject Tests.

#### Numbers and Operations

• Operations: Basic multiplication, division, addition, and subtraction. Remember the proper order of operations!

• Ratio and Proportion: Value comparisons and relationships between value comparisons. (Think: how many of one thing relative to another thing? Three cows for every two sheep?)

• Complex Numbers: Numerical expressions that include imaginary numbers.

• Counting: How many combinations are possible given certain conditions. For example, if there are eight chairs and eight guests, how many orders could the guests sit in?

• Elementary Number Theory: Properties of integers, factorization, prime factors, etc.

• Matrices: Basic operations with number grids.

• Sequences: Number patterns.

#### Geometry

• Geometry on the coordinate plane, including questions about lines, parabolas, circles (and circle equations), symmetry, and transformations. With the exception of circles, coordinate geometry is less concerned with the actual functions making the figures and more with the properties of figures: is the shape symmetrical? How long is this segment of the line? And so on.
• Three-dimensional: Calculating the surface area and volume of cylinders, cones, pyramids, spheres, and prisms.
• Trigonometry: Right triangles and the Pythagorean theorem as well as basic trig identities such as sine, cosine, and tangent.

#### Algebra

• Expressions: Mathematical phrases with variables, numbers, and operators (like \$x+3\$ or \$2x+9y−4\$). You must know how to factor, expand, and manipulate these expressions.
• Equations: An expression that is set to be equal to something, like \$x+3=10\$. You'll need to understand how to solve these. You'll also need to be able to solve systems of equations.
• Inequalities: Expressions set to be greater or less than a value, like \$x+3<10\$. You'll need to know how to solve these, and how to solve systems of inequalities.
• Representation and Modeling: Creating equations that model a given scenario. You'll need to know how to create and interpret these.
• Properties of Functions: You'll need to be able to identify the following kinds of functions and understand how they work, how they look when graphed, and how to factor them. You should also know how to identify \$x\$- and \$y\$-intercepts and any unique characteristics they may have.

• Linear: Straight-line functions, generally written as \$f(x)=mx+b\$ or \$y=mx+b\$

• Polynomial: Functions in which variables are elevated to exponential powers. This includes quadratic functions like \$y=x^2+2x+2\$ as well as functions like \$y=x^5+4x\$.

• Rational: Functions in which polynomial expressions appear in the numerator and the denominator of a fraction. For example: \$\$y=(x^2+4)/(x^3+x^2+9)\$\$

• Exponential: Functions in which \$x\$ appears as an exponential power. Here's an example: \$\$y=3^(x+2)\$\$

#### Data Analysis, Statistics, and Probability

• Mean, Median, Mode, Range: Basic properties of data sets.
• Interquartile Range: A measure of a data set variability based on the range between data quartiles 3 and 1.
• Graphs and Plots: Creating and interpreting visual representations of data sets.
• Least Squares Regression (Linear): How closely correlated two variables are, and how much a data set resembles a straight line.
• Probability: Mathematical determinations of how likely a certain outcome is to occur; you'll need to be able to create and interpret these. You could also skip standardized testing and go live alone in the desert.

### Topics on Math 1 Only

The only topic on Math 1 that's not directly addressed at all on Math 2 is plane geometry, which is a fairly significant 20% of Math 1. Note that plane geometry concepts are addressed on Math 2 via coordinate and 3-D geometry.

### Topics on Math 2 Only

Math 2 contains a fairly large number of topics that aren't tested on Math 1.

#### Numbers and Operations

• Series: The sum of a sequence.
• Vectors: Geometric objects with size (length) and direction; you'll need to be able to do basic operations with vectors.

#### Geometry

• Coordinate: Equations and properties of ellipses and hyperbolas in the coordinate plane and polar coordinates.

• Three-Dimensional: Plotting lines and determining distances between points in three dimensions.

• Trigonometry:

• Radian Measure: An alternative way to measure angles in terms of π. You must know how to convert to and from degrees.

• Law of Cosines and Law of Sines: Trigonometric formulas that allow you to determine the length of a triangle side when one of the angles and two of the sides are known. You'll need to know the formulas and how to use them.

• Equations: Know how to identify and solve algebraic equations involving trigonometric identities, like \$10=cos(x+8)\$.

• Double Angle Formulas: Formulas that allow you to find information on an angle twice as large as the given angle measure.

#### Algebra

• Properties of Functions: You'll need to be able to identify the following kinds of functions and understand how they work, how they look when graphed, and how to factor them. You should also be able to identify \$x\$- and \$y\$-intercepts and any unique characteristics they might have.

• Logarithmic: Functions that involve taking the log of a variable. For example: \$f(x)=log(x)\$

• Trigonometric Functions: Graphs of sine, cosine, tangent, etc. For example: \$f(x)=sin(x)\$

• Inverse Trigonometric Functions: Graphs of the inverse of sine, cosine, tangent, and other trig identities. For example: \$f(x)=arcsin(x)\$ or \$f(x)=sin\$-1\$(x)\$

• Periodic: Any function that repeats its values over an interval; trigonometric functions are periodic.

• Piecewise: A function that is defined by a different equation for different ranges of \$x\$.

• Recursive: A function defined in terms of other functions.

• Parametric: Equations of curves in which x and \$y\$ are defined via some third variable, normally t.

\$x=cos(t)\$
\$y=sin(t)\$

is the equation for the unit circle, a parametric equation.

#### Data Analysis, Statistics and Probability

• Standard Deviation: How close together or spread out the points of a data set is around the mean.

• Least Squares Regression (quadratic, exponential): How well the points of a data set correspond to a quadratic or exponential shape.

As you can see, there's a lot of overlap between the two Math SAT Subject Tests.

However, Math 2 also tests more advanced versions of the topics tested on Math 1. It leaves off directly testing plane Euclidean geometry, though the concepts are indirectly tested through coordinate and 3-D geometry topics.

Math 2 also covers a much broader swath of topics than Math 1 does. This means that question styles for Math 2 and Math 1 can be pretty different, even though many of the same topics are addressed (see the next section for elaboration on this). ## Is Math 1 Easier Than Math 2?

Given that Math 2 covers more advanced topics than Math 1 does, you might think that Math 1 is going to be the easier exam. But this is not necessarily true. Since Math 1 tests fewer concepts, you can expect more abstract and multi-step problems to test the same core math concepts in a variety of ways. The College Board needs to fill up 50 questions, after all!

Below is an example of a tricky question you might see on the Math 1 test. (Note that all practice problems in this article come from the official SAT Subject Tests Student Guide.) The above problem is testing fundamental plane Euclidean geometry concepts but in a way that makes you apply these concepts differently than you might expect to. Let's walk through it.

To figure out the area of the shaded region, we'll need to subtract the area of the rectangle from the area of the circle. The area of the rectangle is pretty straightforward—\$\ov{AB}\$ is 5 and side \$\ov{BC}\$ is 12. So that would be \$5*12 = 6\$0.

Now, we'll need to find the area of that circle. \$πr^2\$ is the formula for a circle's area, but we don't have the radius or diameter. However, we can find the diameter with the help of our friend, the Pythagorean theorem.

We know that \$\ov{AC}\$ is going to be the same length as the diameter. How do we know this? Since ABCD is an inscribed rectangle, angle ∠ABC is an inscribed right angle.

Therefore, AC, the diameter, is the hypotenuse of right triangle △ABC. The Pythagorean theorem states that \$a^2+b^2=c^2\$ and we know a and b are 5 and 12, respectively. Therefore,

\$\$5^2+12^2=c^2\$\$ \$\$25+144=c^2\$\$ \$\$169=c^2\$\$ \$\$13=c\$\$

With a diameter of 13, the radius is 6.5. The area of the circle =

\$\$π(6.5)^2=132.73\$\$

Area of the circle minus area of the rectangle:

\$\$132.73−60=72.73\$\$

The above problem didn't test any difficult concepts, but it did make us combine a few Euclidean geometry concepts (and three formulas!) in interesting ways to make the problem appear tricky.

On the other hand, problems on Math II tend to take fewer steps to solve and are more straightforward, high-school-math-test-type questions: identify the concept, plug in, and go.

For example, see this pretty straightforward plug-in-and-go 3-D volume/basic algebra question:

22. The diameter and height of a right circular cylinder are equal. If the volume of the cylinder is 2, what is the height of the cylinder?

(A) 1.37
(B) 1.08
(C) 0.86
(D) 0.80
(E) 0.68

Let's walk through it.

The volume of a right circular cylinder is \$h*π(1/2 d)^2\$

We know the volume; we also know that the diameter and height are equal. Since the radius is equal to half the diameter, we can express the radius in terms of the height. This gives us the following equation: \$\$h*π(1/2 h)^2=2\$\$

which can be simplified as

\$\$(πh^3)/4=2\$\$
\$\$(h^3)/4=2/π\$\$

and then

\$\$h^3=8/π\$\$

All of a sudden, we've got a pretty simple single-variable algebra problem. Plug and go to get 1.37, or answer choice A.

The number-crunching in this problem might be a little ugly, but it's pretty simple conceptually: a single-variable algebra problem that only uses one formula.These two problems showcase the difference between problem types on Math 1 and Math 2.

Additionally, the curve is much steeper for Math 1 than it is for Math 2. Getting one question wrong on Math 1 is enough to knock you from that 800, but you can get seven or eight questions wrong and still potentially get an 800 on Math 2.

Essentially, Math 1 is the easier exam only if you don't know the advanced topics tested on Math 2. If you do know the Math 2 concepts, you'll find it easier than Math 1 because the material will be fresher in your mind, the questions are more straightforward, and the curve is kinder. A kind (and mathematical!) curve.

## How to Decide Which Math Subject Test to Take

There are, in general, two factors to consider when deciding between Math 1 and Math 2: (1) what math coursework you have completed and (2) what the colleges you're applying to recommend or require.

### Which Math Courses Have You Taken?

In general, if you're going to take a Math Subject Test, you should take the one that most closely aligns with the math coursework you've completed. If you've taken one year of geometry and two years of algebra, go with Math 1. If you've taken that plus precalculus and trigonometry (which is taught as one yearlong math class at most high schools), then take Math 2.

Down-testing (i.e., taking Math 1 when you have the coursework for Math 2) is likely to backfire due to the fact that the material won't be as fresh for you and the curve for Math 1 is so unforgiving.

If you're in the middle of precalculus/trigonometry, things are a little more complicated. If it's the beginning or middle of the year, take Math 1. If you try to take Math 2 too early, there will be material on the exam you haven't covered yet, so you'll either have to learn it or accept that you won't get those points (which is a risky move I don't recommend at all!).

If you're close to the end of the year and you'd like to take Math 2, I'd advise you to simply wait to take the test until you've completed the requisite coursework.

### Which Test Do the Colleges You're Applying to Recommend or Require?

In recent years, many schools such as Caltech and Harvey Mudd, which had required SAT Subject Test scores, particularly in Math, have dropped those requirements. Though many institutions still recommend SAT Subject Test scores, very few schools require now them. (And, as a result of the coronavirus pandemic, nearly all these schools have dropped their SAT Subject Test score requirement, at least temporarily.) However, submitting Subject Test scores can still boost your application, especially if you scored well and the school recommends Subject Test scores, such as most institutions in the University of California system which strongly recommend Math 2 for engineering and science applicants.

If you know that you have your eye on a program that requires or recommends the Math 2 Subject Test, plan ahead to take the necessary math coursework. Programs that require or prefer the Math 2 Subject Test often have required introductory math coursework for first-year students that necessitates a certain background level in math, which is why they require Math 2.

Therefore, try to get in the coursework necessary to be able to take and do well on the Math 2 Subject Test. If you don't plan ahead, you might end up in a situation in which you are set to go into precalculus your senior year. In this case, you should aim to take precalculus the summer after your junior year and the Math 2 Subject Test in the fall of your senior year.

Some high schools don't offer an advanced enough math track for you to be able to get through precalculus by your senior year. It's not super fair if you're in this situation, but you can make up for it by taking a math class over the summer or at a local community college.

On the other hand, some engineering programs and schools will accept either Math Subject Test (i.e., they have no preference). If your program accepts Math 1 or Math 2, take them at their word and opt for the test that better aligns with your regular coursework.

The reason the College Board offers two levels of math isn't to suggest that those who take Math 2 are somehow better at math, but rather that they understand not all high schools will offer the same math classes. High schools with fewer resources often do not offer as much advanced math coursework, and the colleges that accept either math exam do so for this exact reason.

Note: In general, colleges will not accept Math 1 and Math 2 as two separate Subject Tests because there's so much overlap between the material. This doesn't mean you can't take both—just that they won't count as two separate Subject Tests in the eyes of the college you're applying to.

### What If You Still Can't Decide Which Math Subject Test to Take?

If you're still at a loss (or even if you just want to validate your choice before you register for one of the two Math tests), answer some practice questions for each Math Subject Test and compare how you do on them. If you score a lot higher on one test, choose that one. You can find practice questions for both exams in the College Board's SAT Subject Tests Student Guide.

Don't forget that you can also retake Subject Tests, and there's no rule that if you take one of the math tests that you can't then take the other one if you feel as though you didn't choose the better test for you the first time around.

I don't recommend taking both Math Subject Tests as a first-line strategy because you'll waste time prepping for both when you don't need to, and you already have enough to study and prepare for when you apply to college. However, it's something to keep in mind.

You should also double-check that you actually have to take a Math Subject Test for the programs you're applying to since many schools will accept a science Subject Test instead. Choose your exam carefully, like this intrepid soul choosing which rocks to step on.

## SAT Subject Test Math 1 vs Math 2: The Final Word

The College Board offers two SAT Subject Tests in math: Math 1 and Math 2. Math 1 is designed for those who've taken two years of algebra and one year of geometry, while Math 2 targets those who've also taken precalculus/trigonometry. Although they cover many of the same topics, Math 1 involves more tricky applications of math concepts since the scope of the exam is narrower.

In general, you should take the Math Subject Test that best corresponds to the coursework you've completed. Taking Math 1 when you have the coursework for Math 2 might backfire given Math 1's steeper curve. By contrast, taking Math 2 without the requisite coursework will leave you completely lost for much of the exam.

If you're applying to programs that require or strongly recommend Math 2, plan ahead so that you can complete the necessary coursework before you take the exam.

And remember, if you end up taking both Math Subject Tests, most programs will only accept one toward your total of required or recommended Subject Tests.

## What's Next?

Ready to test out your ratio and proportions skills? Try calculating how many seconds there are in a day, week, and year, then compare the result to our guide.

Planning to take the Math 2 Subject test but a little shaky on your coordinate geometry? Make sure to review our articles on graph quadrants and how to complete the square so that you're not caught unaware on test day.

Want some more specific advice on when to take the Math 2 Subject Test? Read our guide to learn how to choose the best test date for you. You might also want to check out our guide to SAT Subject Test scores for the Ivy League to learn how high to aim on test day.

If you're taking AP tests and SAT Subject Tests, you might be wondering which exams are more important. In this guide, we explain which tests to prioritize for your college applications.

Taking the regular SAT, too? Let us walk you through the format of the SAT Math section.

Want to improve your SAT score by 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:   