SAT vs. ACT: Math

 Probably the biggest different between the SAT and the ACT is in the math sections. 

When people talk about SAT and ACT being different, this is usually what they are talking about.  Not only do the sections vary in content, but they also seem to test different types of thinking skills. It's in the math section that one might say that SAT is easier for people who are naturally good at puzzles and word problems.  ACT seems a better fit for those who have strong math skills and can execute problems through trigonometry. 

But, let's start with the organization, format, and timing. 

SAT has two math sections.  The first section gives students 25 minutes for 20 question, 15 multiple choice and 5 grid-ins, and there is no calculator allowed.  The second section is gives students 55 minutes for 38 questions (30 are multiple choice and 8 are grid-ins).  There are usually several quite easy "grid-ins" on each math section, but grid-ins are harder in that you can't guess on them or plug in the multiple choice answers.  These can be rough.

ACT has one math section.  It gives you 60 minutes for 60 multiple-choice questions.  You can use a calculator for the entire section.  Because it's all multiple choice -- if you guess on any problem, you have a 20% change of guessing correctly.  And, by the way, ACT offers 5 choices for each question. SAT offers only 4. 

Timing is an obvious difference.  ACT clocks in at a minute a question.  SAT gives students 1.25 minutes per question on the no calculator section and 1.44 minutes per question on the calculator section. 

So, then it comes down to content. What kinds of problems are on SAT and ACT?

We analyzed the released SAT and ACT exams and broke the math sections into categories (note, there's some overlap in these categories -- in those cases we coded into the category that we emphasize when we teach a student how to do a problem). Overall, the ACT is a breadth test.  It tests far more math concepts, across more math fields.  SAT focuses much more on Algebra (with a secondary focus on statistics), and is more likely to go in-depth in those areas.

Computation (usually fractions) 0% 2%
Pre-Algebra (ratios, proportions, percents) 7% 18%
Algebra (mostly linear and quadratic) 63% 39%
Statistics (reading charts and graphs, measures of central tendency, probability) 18% 9%
Trigonometry (sin, cosine, tangent) 2% 6%
Geometry (2d and 3d figures) 7% 27%

Clearly the SAT is algebra heavy.  And, ACT has a much stronger emphasis on geometry.  Also, note that SAT provides geometry formulae and rules while ACT does not.  So, ACT really does want students to know their geometry well. 

We also coded questions into "easy" or "hard" categories.  These coding decisions are obviously subjective, but generally, we considered questions "easy" if they were the types of problems that students learn in school.  "Hard" problems were problems that even strong math students tend to get stuck on -- these are what we consider "test prep" questions.  They are the types of questions that require several steps and/or  have an "ah-ha!" moment that students need to discover in order to solve the question. 

By that coding scheme, SAT not only has more algebra, but more "hard" algebra.  About half of the algebra questions on SAT tests are "hard."  Students often get them with just a few tips, but on their face, they are a little strange or difficult.  In contrast, only about a third of the algebra problems on ACT are "hard."

But, it's important to note that ACT always includes at least one problem with a matrix and one hard trigonometry problem (something more than just knowing SOHCAHTOA).  SAT does not include matrices or trigonometry that involves more than basic knowledge of sin, cosine, and tangent. 

And then what about the statistics?  ACT asks students to read graphs and charts, calculate some statistical measures, and do a bit of probability, but almost all of the questions are clear and straightforward, the type of statistics that most students learn in middle school. SAT, on the other hand has more difficult questions, often asking students to calculate statistical measures or probability using data pulled from a graph or chart (and the graphs and charts are not always organized intuitively).  Students are also expected to know basics about research, including sampling and research design. Although sampling is part of middle school curriculum, it's rarely covered well, and we find that most students need a lesson in sampling and research design in order to get these questions right (but once they get it, it's pretty easy).  About two thirds of the statistics questions on the SAT are "hard" -- which meant that they require more than most students seem to know from school. 

What's the bottom line?  As ever, you should take an ACT and an SAT and see what you do better one!  But, if you know a lot of math, ACT might be easier.  The questions are, on average, a bit easier. But, if you've forgotten some math (including all of those geometry formulae), there's much less material to review for the SAT.  The SAT requires a crash-course in statistics and some more critical thinking,  but far fewer concepts. 

Which is a better fit for you?