Why Being a Good Math Student Doesn't Always Equal High SAT/ACT Math Scores

SAT/ACT Math is Harder Than Typical High School Math

SAT and ACT math is deceiving in that it “only” covers topics up to and including typical Algebra 2 content. The ACT and new SAT do include trigonometry (which may or may not be covered in Algebra 2), but trig makes up a tiny percentage of the material on both tests.

Assuming students have taken Algebra 1, Geometry, and Algebra 2, they’ve covered all or almost all of the math on the SAT and ACT. So why is SAT/ACT math so hard?

The issue isn’t that the content is harder, per se; instead, the way SAT/ACT questions are formulated, the time pressure, the inclusion of questions requiring numbers theory, logic, and imaginary symbols most students don’t have experience with, and the mixing of concepts across different math topics make the SAT and ACT math sections more difficult than the typical high school math content.

Question Formulation

Here are some examples illustrating why the same content can seem much more difficult on the SAT/ACT.

See the difference? The same content is required for both sets of questions, but the way the SAT/ACT questions are formulated is much more challenging.

Time Pressure

While students have undoubtedly dealt with time pressure before on tests, quizzes, and final exams, the time pressure of the SAT/ACT math sections is even more difficult to manage. The ACT gives just one minute per math question, while the SAT gives one minute 15 seconds on the no calculator section and one minute 26 seconds on the calculator section. This requires much faster and more intense work by students than what they’ve typically been required to do in math class.

Inclusion of Numbers Logic/Theory/Imaginary Symbols Questions

The SAT in particular (ACT to a lesser extent) will give questions on topics that are completely unfamiliar to the majority of students. They either involve topics students have seen many years ago (but haven’t been required to think deeply about), such as long division remainders, or rules that students work with but don’t explicitly know. There are also questions that involve imaginary symbols and operations. Chances are, students have the content knowledge and skill to answer them, but are often so thrown off by these unusual questions that they pose a challenge. Here are some examples:

• a @ b = (a + b)(2a + 2b). What is x @ 4y?

• For the equation c = b^3, which of the following statements are true?

  • c can never be negative

  • c > b

  • if b is positive, c is positive

• What is the greatest possible remainder when any odd number is divided by 4?

Mixing of Concepts Across Different Math Topics

In the typical Algebra or Geometry curriculum there’s a bit of cross course material, but not very much and it’s highly teacher/course dependent. The SAT and ACT often mix algebra, geometry, and other areas of math both in the same question and throughout the test, requiring students to be well versed in what content knowledge to apply and when.

For Students: How to Handle SAT/ACT Math

There are two general approaches that I think work well for students to prepare for SAT/ACT math. One is to start by doing a math content review of the topics tested, and then doing practice questions regularly (every day if possible, even if only a few questions per day). I think this works best for students who perhaps have forgotten or never fully grasped a number of areas of math content. These students will need to fill in some content areas first in order to make doing practice questions more meaningful.

The other approach is to get into a routine of doing practice questions and fill in any missing content areas as needed. I think this works best for students who already have a good grasp on most of the test content areas.

I recommend that all students build a formula/rule sheet as they work through practice questions, and review that sheet periodically. If students realize in doing a particular practice question that they don’t know or have forgotten the content necessary to answer it, they should address it by reviewing that topic and adding to their formula/rule sheet as necessary.

For Math Teachers: Incorporate SAT/ACT Questions When Possible

Having kids do SAT and ACT questions in class can be a great way to add rigor and challenge to your math class. If kids can do SAT/ACT style questions on a particular topic, typically they will have achieved a deeper level of mastery and understanding of the topic due to the additional challenges that these questions entail.

When I’ve worked with small groups of students, I’ve found that having them verbalize (or write down) their approaches and solutions (giving guidance when necessary) helps them internalize the analytical process they’ll need to do well on the SAT/ACT math sections. Here are some ideas for how to incorporate SAT/ACT questions into your math class:

1. Give SAT/ACT questions as challenges at the end of class. Have students who get them correct use the board to explain/show how they did them and give guidance as needed.

2. Include topic relevant SAT/ACT type questions as a bonus on quizzes or tests.

3. Have an SAT/ACT question of the day up on the board for students to try to solve during class.

4. Use as early finisher assignments.

5. Assign each student one SAT/ACT math question to solve and create a small presentation/diagram/step by step outline explaining how to solve it.

6. Have students discuss alternate methods of solving SAT/ACT questions (often there are at least 2 different ways of doing a problem), determine which method is most expedient and least prone to error, and explain why that method is the best.

The College Board website has a ton of free SAT practice questions, and the ACT website does as well. I’ve also created this free SAT/ACT math formula sheet and this set of 100 practice questions divided by subject area.