Has the ACT Math changed?
I analyzed two sets of 10 tests, each roughly three years apart.
Has the math changed much on the ACT over the past few years? If you look at big categories, it really hasn’t. But if you look at individual categories, you do see a lot of movement. For those of us trying to help students earn that last point, these individual changes matter quite a bit.
But before I dive into the numbers, I should describe where I got them. I took two batches of 10 tests. One batch started with December 2017 (A10) and ended with July 2020 (C01). The other started with April 2021 (D05) and ended with June 2023 (F12). I tagged every question, ran the tags through a number of python scripts, and then looked for fun patterns.
Every question had at least one of the nine tags that serve as x-axis labels in this chart:
I was surprised to see General Skills1 drop a bit. So did Difficult Equations2 and Advanced Topics3. Exponents were up, and so were Angles and Trig. But on the whole, these big categories did not change too much. I was much more interested in the more specific problem types mentioned below.
Why Should We Care About Small Movements In Small Categories?
You might wonder why these frequencies matter – if something showed up 2 times in 10 tests from 2018 - 2020, but it showed up 5 times from 2021 - 2023, should we care? I would argue…yes!!
On the most recent test (F12), 51/60 came out to a 30. But 56/60 was a 35. In that part of the curve, every question was worth a point. There’s no way to predict which questions will appear, of course. But let’s say you can find 50 question types with these attributes 1) they have a 10% chance of appearing on the test 2) the student would almost certainly get wrong today and 3) the student could learn fairly easily. On average, the student would get five more of these questions right – there’s your 35!
This hypothetical scenario is unrealistically simple, but I think it illustrates the right way to think about how to direct students’ efforts in homework and tutoring sessions.
Suppose you’ve assigned test form C03, and you realize that your student has missed both the logarithm question (#36) and the matrix multiplication question (#43). Both are difficult topics for many students, but logarithms showed up 10 times in the last 10 tests, while matrix multiplication only appeared once.
Now let’s get into the changes…
Even More Of These
Exponents and triangle area were both already on the ‘Guaranteed To Show Up’ portion of the Top 75 list, but they showed up even more on recent tests. I’m not sure that this changes how I teach students, but I thought it was interesting.
Fewer Of These
Fractions appeared much less frequently (from 52 down to 384)...but they are still one of the most common topics on the test, appearing at every level of difficulty.
Graph translations also dropped significantly (fewer than half as many). I couldn’t attribute this drop to any particular subcategory…there were just fewer ellipses, circle equations, and other equations or graphs that required vertical/horizontal shifts.
Medians dropped from 14 to 6. This really surprised me…you used to be able to count on medians to appear in every test, but that’s no longer the case.
Matrices (10 down to 6) and Circle Equations (6 down to 3) were also somewhat less common. Matrix multiplication only appeared once, as did completing the square for a circle equation. These are both so time consuming – I probably won’t teach them at all unless the student is very advanced or I start seeing more of them again.
Interesting Increases
Undefined rational expressions went from “Should I cover this?” (1 appearance) to “Worth Knowing” (4 appearances). Algebraic lowest common denominators (3 to 6) and given sine, find cosine were in this group too. Some others that appeared more frequently: geometric sequences (2 to 6), logarithms (6 to 10), and remainders (7 to 10).
Staples
It’s also worth pointing out how incredibly stable the test is as a whole. When I looked at all of my tags, more than half of them either appeared exactly the same number of times or within one of that number. Here are just a handful of very specific types that appeared the same number of times in the two sets: Pythagorean Theorem, Systems of Equations, the average sum trick, composite functions, factoring, midpoint, and 30:60:90.
These are all skills developed by 6th grade, including fractions, decimals, factors, multiples, basic chart reading, and many others. They aren’t necessarily easy questions, but every 6th grader would have encountered them at some point.
These include quadratic equations, cubic equations, conics…pretty much any equation that is more advanced than a linear equation.
These include matrices, vectors, imaginary numbers, function notation, absolute value…I’ll admit it’s a bit of a grab-bag.
On my ACT frequencies post, I found 43 questions in the past 10 tests…that is because I decided to use a different test this time (D05 instead of Z04, both from the same month). Z04 had even more fractions that usual! But the trend would still be there.