How to Review for the Subject Area Math Test for Teacher Certificaton

If you're considering taking Sat Subject Tests and math is a strong bailiwick for you, yous'll demand to decide which SAT Subject Exam in math to accept. In that location are two Math Saturday Subject area Tests: Math 1 and Math 2 (too 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 take 50 multiple-option questions and a sixty-minute fourth dimension limit.

In this article, I'll become over what's covered in Math 1, what'southward covered in Math ii, their similarities and differences, whether Math 1 is easier than Math two, and how to cull which Subject Exam to accept.

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

Update: Sat Subject Tests No Longer Offered or Required

In January 2021, the College Board appear that, constructive immediately, no farther Saturday Subject field Tests will be offered in the United States (and that SAT Subject Tests would be offered internationally only through June 2021). It is now no longer possible to take SAT Subject Tests.

In the past several years, many schools accept dropped their Subject Test requirements, and by the time the College Lath fabricated their announcement, nearly no schools required them. With this news, no colleges volition require Subject Tests, even from students who could have hypothetically taken the exams a few years ago. Some schools may consider your Subject Test scores if y'all submit them, similar to how they consider AP scores, but you should contact the specific schools you're interested in to larn their exact policies.

Many students were understandably confused about why this announcement happened midyear and what this ways for higher applications going frontward. Read more well-nigh the details of what the end of SAT Subject Tests means for y'all and your college apps here.

What's Covered on SAT Math 1?

Sat Discipline Test Math 1 covers the topics you larn in 1 year of geometry and two years of algebra. Here's what you tin can await to see on the test:

Topics and Subtopics	% of Math 1 Sabbatum Subject Test	Approximate # of Questions
Number and Operations	ten-fourteen%	five-7
Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences
Algebra and Functions	38-42%	xix-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%	iv-half-dozen
3-dimensional: solids, surface area and book (cylinders, cones, pyramids, spheres, prisms)	4-6%	2-3
Trigonometry: right triangles and identities	6-eight%	iii-4
Information Analysis, Statistics, and Probability	8-12%	4-6
Mean, median, manner, 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 ways that when y'all are studying for Math 1, these are the main areas you should focus on.

There will besides be a few questions (about v) on data analysis/statistics/probability. I'm calling this out considering it'due south something many students haven't spent a lot of time on in course.

What's Covered on SAT Math two?

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

However, the geometry concepts learned in a typical geometry form are but assessed indirectly through more than advanced geometry topics such equally coordinate and 3-dimensional geometry.

Here is a nautical chart with topics and pct breakdowns:

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

In terms of individual topics, the Math two examination is, past far, weighted most heavily toward algebra and functions, with about half the questions in this surface area. You tin too expect to see a sizable chunk of trigonometry.

Knowing the backdrop of all different types of functions, including trigonometric functions, is the single most of import topic to study for the Math 2 exam. If you lot don't know all of that backwards and frontward, in that location volition be a lot of questions you simply don't understand.

Your friend, the triangle.

SAT Subject Examination Math 1 vs Math ii: Similarities and Differences

To give y'all an like shooting fish in a barrel-to-follow overview when you are comparison tests, I'll chop-chop go over which topics are covered on both exams and which you tin can expect to meet only on Math i and only on Math 2, respectively.

Topics on Both Math 1 and Math ii

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

Numbers and Operations

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

• Ratio and Proportion: Value comparisons and relationships between value comparisons. (Think: how many of one matter relative to another matter? 3 cows for every two sheep?)

• Complex Numbers: Numerical expressions that include imaginary numbers.

• Counting: How many combinations are possible given certain atmospheric condition. For example, if there are 8 chairs and eight guests, how many orders could the guests sit in?

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

• Matrices: Basic operations with number grids.

• Sequences: Number patterns.

Geometry

• Geometry on the coordinate plane, including questions nigh 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 backdrop of figures: is the shape symmetrical? How long is this segment of the line? So on.

• Iii-dimensional: Calculating the surface area and book of cylinders, cones, pyramids, spheres, and prisms.

• Trigonometry: Right triangles and the Pythagorean theorem every bit well as basic trig identities such as sine, cosine, and tangent.

Algebra

• Expressions: Mathematical phrases with variables, numbers, and operators (similar $x+three$ or $2x+9y−4$). You must know how to factor, expand, and dispense these expressions.

• Equations: An expression that is set to exist equal to something, like $ten+iii=10$. Y'all'll need to sympathise how to solve these. You'll besides need to be able to solve systems of equations.

• Inequalities: Expressions fix to be greater or less than a value, like $x+three<10$. Yous'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 lot'll need to know how to create and interpret these.

• Properties of Functions: You'll need to be able to identify the post-obit kinds of functions and understand how they work, how they look when graphed, and how to factor them. Yous should also know how to identify $ten$- and $y$-intercepts and any unique characteristics they may accept.

  • Linear: Directly-line functions, generally written as $f(10)=mx+b$ or $y=mx+b$

  • Polynomial: Functions in which variables are elevated to exponential powers. This includes quadratic functions like $y=x^2+2x+two$ as well every bit functions like $y=10^five+4x$.

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

  • Exponential: Functions in which $x$ appears every bit an exponential ability. Here's an example: $$y=iii^(ten+2)$$

Data Analysis, Statistics, and Probability

• Mean, Median, Mode, Range: Basic backdrop of data sets.

• Interquartile Range: A measure of a data set variability based on the range between information quartiles 3 and 1.

• Graphs and Plots: Creating and interpreting visual representations of data sets.

• To the lowest degree Squares Regression (Linear): How closely correlated 2 variables are, and how much a data set resembles a straight line.

• Probability: Mathematical determinations of how likely a sure issue is to occur; you lot'll need to be able to create and interpret these.

You could as well skip standardized testing and go live lonely in the desert.

Topics on Math 1 Only

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

Topics on Math ii Only

Math two contains a fairly large number of topics that aren't tested on Math i.

Numbers and Operations

• Series: The sum of a sequence.

• Vectors: Geometric objects with size (length) and direction; you'll need to exist able to do basic operations with vectors.

Geometry

• Coordinate: Equations and backdrop 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 fashion to measure out angles in terms of π. You must know how to catechumen 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 i of the angles and two of the sides are known. You'll need to know the formulas and how to utilize them.

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

  • Double Bending Formulas: Formulas that allow yous to find information on an angle twice every bit big every bit the given angle measure.

Algebra

• Properties of Functions: Y'all'll need to exist able to place the following kinds of functions and understand how they work, how they wait when graphed, and how to factor them. Y'all should also be able to identify $ten$- and $y$-intercepts and whatever 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 instance: $f(ten)=sin(x)$

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

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

  • Piecewise: A function that is defined by a unlike equation for dissimilar 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.

    $10=cos(t)$
    $y=sin(t)$

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

Information Analysis, Statistics and Probability

• Standard Deviation: How shut together or spread out the points of a data fix is around the mean.
• Least Squares Regression (quadratic, exponential): How well the points of a information fix correspond to a quadratic or exponential shape.

As you tin come across, there's a lot of overlap between the two Math Saturday Subject Tests.

Nonetheless, Math ii too tests more advanced versions of the topics tested on Math ane. It leaves off directly testing plane Euclidean geometry, though the concepts are indirectly tested through coordinate and iii-D geometry topics.

Math 2 as well covers a much broader swath of topics than Math 1 does. This ways that question styles for Math 2 and Math 1 can be pretty different, even though many of the same topics are addressed (come across the adjacent section for elaboration on this).

A wide swath.

Is Math ane Easier Than Math 2?

Given that Math two covers more advanced topics than Math i does, you might think that Math 1 is going to be the easier exam. Merely this is not necessarily truthful. Since Math 1 tests fewer concepts, you tin expect more abstract and multi-footstep problems to test the same core math concepts in a variety of means. The College Board needs to fill up l questions, subsequently all!

Below is an example of a tricky question you might run into on the Math i test. (Notation that all practice bug in this article come up from the official SAT Subject area Tests Student Guide.)

The in a higher place problem is testing fundamental plane Euclidean geometry concepts just in a way that makes you apply these concepts differently than yous might wait to. Allow's walk through it.

To effigy 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. And so that would be $5*12 = half dozen$0.

Now, nosotros'll demand to find the area of that circle. $πr^2$ is the formula for a circle'due south expanse, but we don't take the radius or diameter. Nevertheless, nosotros can find the diameter with the assist of our friend, the Pythagorean theorem.

Nosotros know that $\ov{Ac}$ is going to exist the same length as the bore. How do nosotros know this? Since ABCD is an inscribed rectangle, angle ∠ABC is an inscribed correct angle.

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

$$5^2+12^2=c^2$$ $$25+144=c^2$$ $$169=c^2$$ $$thirteen=c$$

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

$$π(half dozen.5)^two=132.73$$

Expanse of the circumvolve minus area of the rectangle:

$$132.73−threescore=72.73$$

The answer is C!

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

On the other hand, problems on Math Ii tend to have fewer steps to solve and are more straightforward, loftier-school-math-test-type questions: place the concept, plug in, and become.

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

22. The diameter and elevation of a right round cylinder are equal. If the volume of the cylinder is 2, what is the top of the cylinder?

(A) ane.37
(B) one.08
(C) 0.86
(D) 0.80
(E) 0.68

Allow'south walk through information technology.

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

We know the book; nosotros besides know that the diameter and height are equal. Since the radius is equal to half the bore, nosotros can express the radius in terms of the height. This gives usa the post-obit equation: $$h*π(1/2 h)^2=2$$

which tin can be simplified as

$$(πh^iii)/four=2$$
$$(h^three)/4=2/π$$

and so

$$h^3=eight/π$$

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 unmarried-variable algebra trouble that only uses i formula.These two problems showcase the divergence betwixt trouble types on Math 1 and Math two.

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

Essentially, Math 1 is the easier exam simply if you lot don't know the advanced topics tested on Math 2. If you do know the Math 2 concepts, you'll observe it easier than Math 1 considering the material will be fresher in your mind, the questions are more straightforward, and the curve is kinder.

A kind (and mathematical!) bend.

How to Determine Which Math Subject Test to Take

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

Which Math Courses Take You Taken?

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

Downward-testing (i.eastward., taking Math 1 when you take the coursework for Math 2) is probable to backfire due to the fact that the material won't be every bit fresh for y'all and the curve for Math 1 is so unforgiving.

If you're in the middle of precalculus/trigonometry, things are a fiddling more complicated. If information technology'south the starting time or heart of the year, take Math ane. If you lot endeavor to take Math 2 too early, there volition be material on the exam you haven't covered even so, so y'all'll either have to learn information technology or accept that you won't get those points (which is a risky motility I don't recommend at all!).

If yous're close to the end of the twelvemonth and y'all'd like to take Math 2, I'd advise you to just wait to accept the test until you've completed the requisite coursework.

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

In contempo years, many schools such every bit Caltech and Harvey Mudd, which had required Sabbatum Subject Test scores, peculiarly in Math, have dropped those requirements. Though many institutions still recommend SAT Subject Test scores, very few schools require at present them. (And, equally a consequence of the coronavirus pandemic, most all these schools have dropped their Saturday Subject area Test score requirement, at least temporarily.) However, submitting Field of study Test scores tin can still boost your application, especially if you scored well and the school recommends Field of study Test scores, such as gost institutions in the University of California system which strongly recommend Math two for applied science and science applicants.

If you know that you have your eye on a programme that requires or recommends the Math two Subject Exam, plan alee to take the necessary math coursework. Programs that require or prefer the Math 2 Subject Examination oft 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, endeavor to go far the coursework necessary to be able to have and practice well on the Math 2 Field of study Examination. If you don't plan alee, y'all might terminate up in a situation in which you lot are set to go into precalculus your senior year. In this case, you should aim to have precalculus the summertime afterwards your junior year and the Math 2 Subject Test in the fall of your senior yr.

Some loftier schools don't offer an advanced enough math track for you lot to be able to go through precalculus by your senior year. It's not super fair if you're in this state of affairs, but you can make upwards for it past taking a math class over the summertime or at a local customs higher.

On the other manus, some engineering programs and schools volition accept either Math Field of study Test (i.eastward., they accept no preference). If your program accepts Math one or Math ii, take them at their word and opt for the test that amend aligns with your regular coursework.

The reason the College Board offers 2 levels of math isn't to advise that those who accept Math 2 are somehow improve at math, but rather that they sympathise not all loftier schools will offering the same math classes. High schools with fewer resource oftentimes practice non offering every bit much advanced math coursework, and the colleges that accept either math exam do so for this exact reason.

Annotation: In general, colleges volition not have Math 1 and Math 2 as two dissever Discipline Tests considering at that place's and then much overlap between the material. This doesn't mean yous can't have both—just that they won't count equally ii split up Field of study Tests in the optics of the college you're applying to.

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

If you're still at a loss (or even if y'all just want to validate your choice before you register for one of the two Math tests), answer some exercise questions for each Math Subject area Examination and compare how you exercise on them. If you score a lot higher on one exam, choose that i. You tin can find practise 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'southward no rule that if you lot take one of the math tests that you can't then accept the other one if you experience equally though you didn't choose the better exam for you the kickoff fourth dimension around.

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

You should also double-cheque that you actually have to have a Math Subject Test for the programs you're applying to since many schools volition accept a scientific discipline Subject Test instead.

Choose your exam carefully, like this intrepid soul choosing which rocks to pace on.

SAT Discipline Test Math i vs Math 2: The Final Give-and-take

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

In general, you lot should accept the Math Discipline Examination that best corresponds to the coursework you've completed. Taking Math one 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 test.

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

And remember, if yous end up taking both Math Bailiwick Tests, almost programs volition simply take ane toward your full of required or recommended Subject area Tests.

What's Next?

Ready to exam out your ratio and proportions skills? Try calculating how many seconds there are in a twenty-four hours, week, and year, then compare the event to our guide.

Planning to take the Math 2 Subject exam but a petty shaky on your coordinate geometry? Make sure to review our articles on graph quadrants and how to complete the foursquare then that you're not defenseless unaware on test day.

Desire some more specific advice on when to take the Math ii Subject Examination? Read our guide to learn how to choose the all-time test date for y'all. You might also desire to check out our guide to SAT Subject Exam scores for the Ivy League to learn how loftier to aim on test day.

If you're taking AP tests and Sabbatum Subject Tests, y'all might exist wondering which exams are more than important. In this guide, we explicate which tests to prioritize for your higher applications.

Taking the regular SAT, besides? Let united states of america walk y'all through the format of the SAT Math section.

Want to ameliorate your Sabbatum score past 160 points or your Deed score by 4 points? Nosotros've written a guide for each examination nearly the height 5 strategies you must be using to have a shot at improving your score. Download it for free now:

Have friends who also demand aid with examination prep? Share this article!

About the Author

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

polksquir1979.blogspot.com

Source: https://blog.prepscholar.com/sat-subject-test-math-1-vs-math-2

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