What's the difference between ACT and SAT? Part 2: Math

Math is usually the part of a test when you really feel like things are easy or hard.  The answers aren't subjective: you either know how to do them or you don't.

So, many people choose SAT or ACT based on how they feel about the math sections.

And there may be something to the notion that the ACT math is easier (well, at least there are more easy questions).  But, just the feeling that something is easier doesn't mean that it's giving you a comparatively higher score.

Before we get into the details, let's do the basic breakdown:

Basic SAT v. ACT Comparison
54 Questions 60 Questions
 3 Sections (each with 15-20 questions)  One long section
 44 multiple choice questions; 10 grid-in questions  All multiple choice questions
 Guessing penalty (lose .25 points for each wrong answer) on multiple choice  No guessing penalty
 Goes through geometry and algebra (mostly middle school geometry and Algebra I content)  Goes through basic trigonometry (mostly middle school geometry and Algebra I content with some Algebra II content)
 Provides geometry formulas at the beginning of each math section  Sometimes provides formulas in questions but mostly wants students to know them
 Calculator allowed  Calculator allowed
 Each section goes from easy to hard  The math problems go from easy to hard
70 minutes total (1.3 minutes per problem) 60 minutes (1 minute per problem)
 Getting 50% of questions correct = 500 (45th percentile)  Getting 50% of the questions correct = 19 ( 46th percentile)

 25% of questions = 390 (13th percentile);

75% of questions = 620 (80th percentile)

  25% of questions = 15 (14th percentile);

75% of questions = 28 (91th percentile)

From a test-taking perspective there are three critical differences between the SAT and the ACT math.

  1. The ACT math is one long section, whereas the SAT math is broken into three sections.  Sixty math problems in a row feels like a lot.  For students who get bored easily, SAT may be the way to go.  For students who hate having their concentration broken up, ACT is probably a better bet. 
  2. ACT is a faster test.  Students need to complete about a minute per problem.  If time is an issue, SAT may be a better option.
  3. SAT is a bit more logic based and tricky.  ACT is a bit more straightforward but requires students to know more.  Students who have not taken trig will encounter problems that they have no idea how to do on the ACT (whereas students who have completed Algebra I have most of the skills that they need for SAT -- even though they will probably find many of the problems quite challenging).  

This tricky v. hard issue is the aspect of the tests that we'll talk discuss further.

You'll hear lots of generalizations about SAT and ACT.  We often hear "ACT is easier than SAT" or "ACT is better for hardworking students while SAT is better for smart [or lazy or lucky] students" or "ACT is better for minority students."  We think that a lot of these generalizations come from the math section.  The math on ACT feels a little easier (of course, there are 6 extra questions, and simply making them all easy could skew someone's feeling of the the section being easier overall.  The ACT also goes farther in terms of learning, so a student with fewer math skills and more math common sense does better on the SAT.  A student who "knows more" stands to do better on the ACT (although for a great ACT score, one really needs a lot of good logic and math sense too).  

Part of the differences between the two tests is historical.  The SAT used to be called the Scholastic Aptitude Test.  By design, the test tried to measure students' thinking skills, not their actual specific math knowledge.  That's why there are so many logic questions and why the math content does not go much past what many students learn in middle school.  SAT developed the subject tests, which, by the way, used to be called Achievement Tests, to test how much kids know.  The SAT was supposed to test how well kids thought.  That approach has come under fire from those who consider the test biased (against cultural and economic minorities) and has tried to more into more "achievement" type areas (and it dropped the whole "aptitude" part of the name (now, according to the offical website, SAT doesn't stand for anything).  But, when you take the test you can feel the remnants of that idea: the test, especially the math section, kind of wants you to get creative with basic skills in order to solve some hard problems.   ACT has been more curriculum aligned from its inception.

Of course, to the test taker, the history doesn't matter.  But, the way a test feels does matter, so what's the break down?

Looking at a a recent ACT math section, here's what we found:

  • 46 of the questions on the ACT could easily show up on an SAT
  • 4 of the questions on the ACT were too simple to show up on an SAT (although with one extra twist they could easily show up on an SAT)
  • 10 of the questions on the ACT would not show up on SAT because they required trigonometry or advanced algebra (e.g., sine, cosine, tangent, imaginary numbers, formula for circles, matrices).  Some of those problems could be solved without that specialized knowledge, but only a very good test taker would know how -- and feel confident enough -- to try.

Look at a set of recent SAT math sections (3 sections, one test), here's what we found:

  • 42 of the questions on the SAT could easily show up on an ACT.
  • 12 of the questions on the SAT were significantly more complicated that problems that test similar skills on the ACT.  

So, ACT has an easy end, which SAT seems to avoid by simply having fewer questions (and, it has more time per question precisely because its questions are a bit more complicated).

Both tests have a "hard side" -- although they are hard for different reasons.  A student who has hard time intuitively understanding how to approach a problem, might be able to learn all of the trig rules faster and do beter on the ACT.  A student without a strong trig background or who does not memorize well, might do better learning strategies for working through SAT problems. 

Either way, both sections draw heavily on pre-algebra (especially proportions and basic statistics and data analysis), basic geometry (area, perimeter, triangles, parallel lines, circles -- although SAT gives you formulas and ACT doesn't!), and basic algebra (lots of variable manipulation, graphing on coordinate planes, linear and quadratic equations/inequalities and systems).  

And, even testing similar skills in similar ways, SAT is more likely to be a little extra tricky (e.g., "which of the following could NOT be a solution") while ACT tends to be clearer about what it wants.

Finally, in the end, the differences may not matter all that much.  Overall, we find that most students score about the same (nationally, SAT and ACT scores are correlated  about .9, which is to say that on average the scores are about 90% the same).

Bottom line: doing very well on the math section of either test takes strong math skills, the willingness to dig into a problem (even if you're not sure how to do it), and prep.  Doing a few sections for practice -- on either test -- will help a student get used to the timing, format, tricks, and types of problems.  And, knowing what to expect is half off the game.

I call these sections a draw.  Students should take both, see what feels better (make sure to use a timer as time is such a big difference!), and then prep for that test.