# SAT Math 2 Subject Test

**Series Overview**

Welcome to the fourth post in our SAT Subject Test series. Previous posts in the series can be found below:

In this post, we will cover the SAT Math 2 Subject Test

**Specs**

- 60 minutes
- 50 questions
- Covers math topics from all years of high school
- Numbers and operations: 14% of questions
- Algebra and functions: 48-52%
- Geometry and measurement, including coordinate geometry, three-dimensional geometry, and trigonometry: 48-52%
- Data analysis, statistics, and probability: 8-12%

- Students may use a calculator (scientific or graphing) for all questions
- Students will be provided with select mathematical formulas, but they must memorize most of the ones they will use to solve problems
- Offered on the following SAT dates:
- May 2019
- June 2019
- August 2019
- October 2019
- November 2019
- December 2019
- May 2020
- June 2020

**Necessary Skills**

Students should consider a full-year course in precalculus and trigonometry to be a prerequisite to the SAT Math 2 Subject Test. There are plenty of questions on the exam pulled from courses taken earlier in high school (Geometry, Algebra 2), but a sizable number of questions will look familiar to students only if they have been through the precalc/trig circuit.

Additionally, students will need to feel comfortable parsing complicated questions to get at the math concepts that lie underneath. The SAT Math 2 Subject Test is, on a conceptual level, no more difficult than Honors or Advanced precalc/trig courses. What can make the exam more challenging is the way the SAT writes questions. The SAT Math 2 Subject Test is not just a reiteration of exams from math class; its questions demand more interpretation and analysis. In this regard, superficial familiarity with concepts will not be enough — students need to feel comfortable identifying their every use and application. On this exam, high scores are earned through adaptability, not rigidity.=

**Sample Test Content**

- What is the distance in space between the points with coordinates (-3, 6, 7) and (2, -1, 4)?

(A) 4.36

(B) 5.92

(C) 7.91

(D) 9.11

(E) 22.25 _

- In January 1990 the world’s population was 5.3 billion. Assuming a growth rate of 2 percent per year, the world’s population, in billions, for t years after 1990 can be modeled by the equation
*P*= 5.3(1.02)*t*. According to the model, the population growth from January 1995 to January 1996 was

(A) 106,000,000

(B) 114,700,000

(C) 117,000,000

(D) 445,600,000

(E) 562,700,000

- What is the measure of one of the larger angles of a parallelogram in the xy-plane that has vertices with coordinates (2,1), (5,1), (3,5), and (6,5)?

(A) 93.4°

(B) 96.8°

(C) 104.0°

(D) 108.3°

(E) 119.0°

- In a group of 10 people, 60 percent have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes?

(A) 0.13

(B) 0.16

(C) 0.25

(D) 0.36

(E) 0.64

*C* = -1.02*F* + 93.63

- The linear regression model above is based on an analysis of nutritional data from 14 varieties of cereal bars to relate the percent of calories from fat (
*F*) to the percent of calories from carbohydrates (*C*). Based on this model, which of the following statements must be true? - There is a positive correlation between C and F.
- When 20 percent of calories are from fat, the predicted percent of calories from carbohydrates is approximately 73.

III. The slope indicates that as F increases by 1, C decreases by 1.02.

(A) II only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

Author’s commentary:

Only one of the questions in this sample (#17) can be answered with the rote application of a formula. The rest of them will require formulas, of course, but to use those formulas correctly, students will first have to recognize several key features of the questions.

In #19, for example, students cannot simply apply the formula provided in the question once and expect an answer. This formula is written for the year 1990, but the question actually asks for population growth between 1995 and 1996. So students will first have to decide what values for *t* correspond to the years 1995 and 1996; once they have population values for both years, they then need to subtract 1995’s from 1996’s to find the growth between years. While not particularly difficult, this question illustrates the multi-step nature of SAT Math 2 Subject Test problems. Missing just one of these steps will, invariably, lead down the wrong path.

Where question #19 is mostly time-consuming, question #28 is both time-consuming *and* difficult, making it representative of the questions later on in the exam. The three statements provided in the question each challenge related but different domains of mathematical understanding (correlation, percents, and slope); to get the question right, students must feel comfortable interpreting and applying all three to the formula provided. This question demonstrates that formulas alone are virtually worthless — it’s facility with those formulas that will pay off.

Answers: D, C, C, A, D

**Who Should Take It?**

In our previous post on U.S. History, I said that good grades in U.S. History courses were not necessarily strong indicators of success on the SAT U.S. History Subject Test. That’s because the rigor of such courses can vary widely from school to school, so a high mark alone is really not enough to determine whether a student has seen the breadth and depth of information necessary for success.

Math curricula are far more standardized from school to school, meaning the rigor of such courses varies much less widely than it does for U.S. History. This is good news for high-performing math students: it means good grades actually are solid predictors of success on the SAT Math 2 Subject Test. There’s simply a much smaller chance that a high-performing student in a challenging math course will suffer a letdown on this exam. Students with straight As throughout their high school math career should consider this exam and, ideally, take a practice test to see how they might fare.

That said, there’s a slight catch: straight A students *who tend to lose most of their points on math tests because of sloppy calculations* should be mindful of their weaknesses. Math classes offer partial credit; the SAT Math 2 Subject Test does not. One small error in calculation is often the difference between right and wrong. Put enough of these minor errors together and scores can come crashing down.

Of course, this is not to suggest that these students should second-guess their decisions to take this test. In fact, the exam’s scoring framework may represent an opportunity in disguise: students may find that a slight change in approach — that is, a greater attention to detail — can yield big score improvements in short order. As long as they’re willing to cultivate their focus and accuracy, students with a history of imprecision in their calculations will find themselves well-positioned for good performance. Put another way, work ethic matters, too!

**Materials**

The College Board’s SAT Subject Test Student Guide contains sample questions for this exam (the above selection can be found there). The College Board also publishes a preparatory book specific to this exam titled *The Official SAT Subject Test in Mathematics Level 2 Study Guide*. This book contains four full-length practice exams, making it a must for anyone studying for this exam.

Also indispensable to a well-designed study strategy is the Barron’s prep book for SAT Math 2 Subject Test. As with many other Barron’s books, the material found in this one is, frankly, harder than the real thing — by a lot. Even with the mismatched difficulty level in mind, Barron’s would be worth it for the review material alone. Students who take their time combing through this material will feel comfortable with every last concept they need to know for the exam. Additionally, the practice exams, while difficult, examine the exact same concepts as the real thing. Essentially, then, students are cutting their teeth on harder versions of the same questions they will face on test day, which can make the real thing seem easy by comparison.

Finally, students may want to explore formula programs for their calculators. These programs can be written into the calculator manually (example here), or downloaded directly from the internet (example here). These programs, if well-understood, can shave time off the calculation process, which is crucial for exam that leaves many feeling short on time.

It should be stressed, however, that these programs are *no guarantee* of a good score. After all, students can’t simply feed the calculator a question and expect it to spit out the right answer. These programs are useful supplements — nothing more. And even then, they are only useful if students spend time learning how to use them properly.

**Study Approach**

Students who succeed on this exam first review the conceptual material available in the Barron’s book, taking diligent notes as they go. Depending on the curriculum of their math courses, students may encounter a concept or two that they’ve not seen before. Given the quality of Barron’s instructional material, this is fine — students will likely find these concepts easy to understand. Students should also pay special attention to areas in which they know they have struggled in the past — because of its breadth of material, the SAT Math 2 Subject Test is rather adept at exposing weaknesses!

Once students have finished their conceptual review, they can move onto practice exams. Barron’s exams should be taken first — better to build confidence by starting with more difficult material and scaling down over time than to do the opposite. Additionally, as the real exam approaches, students will want to accurately calibrate their expectations, which will be easy to do if the exams they’ve taken most recently were written by the College Board. If students are intent on using calculator programs on test day, then they should absolutely use them on *all* practice exams.

Good scores become great scores through mistake review, so students should devote as much time as possible to checking their errors after they finish a test. Reviewing questions (especially the hardest ones) four or five times is a good idea. SAT exams are difficult, sure, but their material is not original — there’s a 0% chance students see some new domain of math on the actual exam. Students who memorize their past errors, then, are essentially eliminating their weaknesses, which makes the path to a high score that much easier.

**Author’s Take **

In our previous posts on SAT Subject Tests, it’s become clear that, to a large degree, these exams are “self-selecting.” That is, only the students who know they’re really good at a particular subject are likely to take its SAT Subject Test. This makes sense, of course, but it leads us back to that eternal conundrum of SAT Subject Tests: the best of the best are taking the exam, which means pretty much everyone who takes it does really, really well. The SAT Math 2 Subject Test happens to be the most extreme demonstration of this phenomenon: a perfect 800 puts a student in — I’m not making this up — the 79th percentile. Roughly a fifth of those who take this exam get the highest possible score.

This being our fourth post in this series, we’ve now covered 2 Math/Science exams and 2 Humanities exams. At this point, we have enough of a backlog to point out a clear trend among SAT Subject Tests: “objective” disciplines like Science and Math are easier to perfect than “subjective” disciplines like English and History. That’s because subjective disciplines do not lend themselves to total mastery the way objective ones do. A great reader may, from time to time, come across a piece whose theme they simply do not understand — offer a dirge to someone who has never experienced the loss of a loved one before and they may miss some signals. By contrast, one’s intellectual limits can only be stretched so much by, say, triangles.

This raises an important and potentially thorny question: why take an exam like the SAT Math 2 Subject Test at all? The simple answer is, of course, about students’ relative strengths and weaknesses. A future engineer is likely to find math easier and more enjoyable than, say, U.S. History, and should thus take the SAT Math 2 Subject Test. And, for the record, they should not feel ambivalent about doing so. The point of these subject tests is, after all, to demonstrate mastery, not to game the percentiles. Show universities what you *can* do, not what you think they want you to be able to do. If you think an 800 on this exam is a cinch, do it and don’t look back.

So, long story short: take the SAT Math 2 Subject Test if you strongly believe you can ace it. If you don’t think you can, consider your other options — you may be better served taking an exam with a better risk/reward profile. Just as confident students should feel fine about taking the SAT Math 2 Subject Test, other, less confident students should feel fine about *not* taking it. Don’t force yourself into an ill-fitting box!