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SAT Subject Test Math 1 vs Math 2: Which Should I Take?

Posted by Ellen McCammon | Apr 2, 2016 8:30:00 AM

SAT Subject Tests

 

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If you are 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.

The College Board offers two Math SAT Subject Tests, aptly named “Math 1” and “Math 2.” (Sometimes these are also written out as Math I and Math II). Math 2 is meant for those with more high school math coursework and covers a broader range of mathematical topics than Math 1. Both are 50-question multiple-choice tests with 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 test to take.

 

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 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 modelling, properties of functions (linear, polynomial, rational, exponential)

Geometry and Measurement

38-42%

19-21

Plane geometry

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

 

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, those are areas to focus on. 

There will also be a few questions (around 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—so 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 like coordinate and three-dimensional geometry.

Here is a chart with topics and percentage breakdowns:

Topics and Subtopics

% of 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 modelling, 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, radians, 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



It’s worth noting that, on the main College Board page for Math 2, they [incorrectly] state that the test is 48-52% geometry. In the test booklet that the College Board puts out for all subject tests you can see that the actual percentage is 28-32%. Let’s all be glad that the questions on College-Board administered tests are much more closely vetted than what goes on their website. 

In terms of individual topics, this test is weighted, by far, most heavily towards “algebra and functions,” with about half of 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 this test; if you don’t know all of that backwards and forwards, there will be a lot of questions you simply don’t understand.

 

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Your friend the triangle. 

 

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 Exams

Numbers and Operations:
  • Operations: Basic multiplication, division, addition, 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? 3 cows for every 2 sheep? and so on.)

  • 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 and prime factors, and so on.

  • 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 this shape symmetrical? How long is this segment of this 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, basic trig identities like sine, cosine, tangent.

 

Algebra:

  • Expressions: Mathematical phrases with variables, numbers, and operators (like $x+3$ or $2x+9y−4$). You’ll need to understand 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 know how to solve these. You will 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, understand how they work, how they look when graphed, how to factor them, 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 $y = x^2 + 2x + 2$, but also functions like $y = x^5 + 4x$

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

    • Exponential: Functions in which x appears as an exponential power; i.e. $y = 3^(x+2)$

 

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; 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.

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 You could also skip standardized testing and go live alone in the desert.

 

Topics on Math 1 Only

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

 

Topics on Math 2 Only

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; polar coordinates.

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

  • Trigonometry: 

    • Radian Measure: An alternative way to measure angles in terms of π; 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; know the formulas and know 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, understand how they work, how they look when graphed, how to factor them, identify x- and y- intercepts, and any unique characteristics they may 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; i.e. $f(x) = sin (x)$

    • Inverse Trigonometric Functions: Graphs of the inverse of sine, cosine, tangent, and other trig identities; i.e. $f(x) = arcsin(x)$

    • 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:
  • 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 is a lot of overlap between the two exams. But 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. But even with that cut out, it still covers a much broader swathe of topics than Math 1. 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).

 

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A broad swathe.

 

Is Math 1 Easier Than Math 2?

Given that Math 2 covers more advanced topics than Math 1, you may think that Math 1 is going to be the easier exam. This is not necessarily true. Given that Math 1 is testing 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! 

Here’s an example of a “tricky” question you might see on the Math 1 exam. (Note: all practice problems in this article come from the College Board's free "Getting Ready for the SAT Subject Tests" booklet.)

 

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The above problem is testing fundamental plane Euclidean geometry concepts, but in a way that makes you apply those concepts in an interesting way. 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 x 12 = 60.

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 the diameter. But 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? Because since ABCD is an inscribed rectangle, angle $ABC$ is an inscribed right angle. 

So 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. 

$$5^2 + 12^2 = c^2$$

$$25 + 144 = c^2$$

$$169 = c^2$$

$$13 = c$$

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 answer is C!


The above problem didn’t test any difficult concepts, but it did make us combine a few different Euclidean geometry concepts (and three formulas!) in interesting ways to make a “tricky” problem. By contrast, problems on Math II tend to take fewer steps to solve and be more straightforward, high school math-test-type questions: identify the concept, plug in and go.

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

 

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Let’s walk through it.

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

We know the volume and we know that the diameter and height are equal. Since the radius is ½ the diameter, we can express the radius in terms of the height. This gives us the following equation:

$$h⋅π(1/2h)^2 = 2$$

Which can be simplified as

$$1/4h^3=2/π$$

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 (A).

The number-crunching in this might be a little ugly, but it’s pretty simple conceptually: a single-variable algebra problem that only used 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 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 will 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.

 

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A kind (and mathematical!) curve.

 

How to Choose Which Math Subject Test to Take

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

 

Which Math Courses You Have Taken?

In general, if you are going to take a Math Subject Test, you should take the one that most closely aligns with the math coursework you have 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 in 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 you won’t be as fresh on the material and because 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 that I don’t recommend at all. If you are close to the end of the year, and you would like to take Math 2, I would advise you to simply wait to take the test until you’ve completed the requisite coursework.

 

Which Test Do the Programs You Are Applying to Recommend or Require?

While many institutions that recommend or require subject tests give you flexibility in what subjects you send, others have more stringent requirements—particularly engineering or medicine-based programs.

Some notable programs and institutions that require Math level 2 include:

  1. Boston University - select programs require Math 2
  2. CalTech - requires Math 2 from all applicants
  3. Harvey Mudd - requires Math 2 from all applicants.
  4. Johns Hopkins - requires Math 2 for engineering applicants.
  5. Northwestern - select programs require Math 2
  6. Most institutions in the University of California system require Math 2 for engineering applicants.

 

If you know that you have your eye on a program that requires the Math 2 Subject Test, you will need to 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.

If you know you might be applying to a program that requires the Math 2 Subject Test, try to get in the coursework necessary to be able to take Math 2 and do well.  If you don’t plan ahead enough, you might end up in a situation where 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 instead, and take the Math 2 Subject Test your senior fall.

Some high schools don’t really 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 should try to take a math class over the summer or through a local community college to get the necessary math coursework in time if you’re in this situation.

On the other hand, some engineering programs and schools state that they accept either Math exam (i.e. they have no preference).  If your programs of choice accept either Math 1 or Math 2, I would take them at their word and take the one that best aligns with your regular coursework.

The reason why the College Board offers two levels of math isn’t to suggest that those who take Math 2 are “better” at math, but because they understand that not all high schools offer the same math classes. High schools with less resources often do not offer as much advanced math coursework. Those schools that accept either math exam do so for that exact reason.

In fact, the colleges and programs that require Math 2 are unfortunately penalizing underprivileged students, even if they are doing so because their introductory math coursework starts at too high a level to accept a less-advanced Math test.

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 are applying to.

 

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

If you are still at a loss (or even if you just want to validate your choice before you register) then answer some practice questions for each exam and compare how you do. If you score appreciably higher on one test than the other, take that one. You can find practice questions for both exams in the College Board’s “Getting Ready for the SAT Subject Tests” booklet. 

Don’t forget that you can also retake subject tests, and there’s no rule that if you take one of the Math Subject Tests you can’t then take the other one if you feel like you didn’t choose the best test for you the first time around. I don’t recommend taking both tests as a first-line strategy because you’ll waste time prepping for both exams when you really don’t need to, and you already have enough to study and prepare for when you apply to college. But 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 are applying for since many schools will accept a science instead.

 

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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 different SAT Subject Tests in math: Math 1 and Math 2.

Math 1 is designed for those who have taken two years of algebra and one year of geometry while Math 2 is meant for those who have also taken precalculus/trigonometry. While they cover many of the same topics, Math 1 involves more “tricky” applications of math concepts because the scope of the exam is narrow.

In general, you should take the exam that best corresponds to the coursework you have completed. Taking Math 1 when you have the coursework for Math 2 may backfire given Math 1’s steeper curve. Taking Math 2 without the requisite coursework will leave you completely lost for much of the exam.

If you are applying to programs that require 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 exams, most programs will only accept one towards your total of required or recommended Subject Tests.

 

What's Next?

Want some more specific advice on when to take the Math 2 subject test?

Reaching for the stars? See our guide to SAT Subject Test scores for the Ivy League.

If you're taking APs and SAT Subject Tests, you might be wondering which exams are more important

Taking the SAT? Let us walk you through the recent changes to 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:

Get eBook: 5 Tips for 160+ Points

Raise Your ACT Score by 4 Points (Free Download)

 

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Ellen McCammon
About the Author

Ellen has extensive education mentorship experience and is deeply committed to helping students succeed in all areas of life. She received a BA from Harvard in Folklore and Mythology and is currently pursuing graduate studies at Columbia University.



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