How Frequently Do Math Question Types Appear In Different Parts of the ACT?
Calculating the frequency of question types, grouped by difficulty.
I tagged every question from the last 10 ACTs (through June 2023), then used a python script to see how frequently each question type appeared in four parts of the test: 1 - 15, 16 - 30, 31 - 45, and 46 - 60. Because the ACT questions get harder as you move through the test, these four groups serve as a rough proxy1 for difficulty.
Here is what I found:
Observations
Fractions are everywhere. You see fractions very frequently throughout the test, whether it’s through mixed numbers, common denominators, or abstract questions with variables. You can’t outsource this work to your calculator – you need to be very comfortable with fractions in order to do well on the ACT.
Exponents, slope, and probability also make the top 10 in every part of the test. Slope is a bit of a surprise, but it’s always hovered near the top 10 in previous versions of this analysis. The other two (and fractions) are versatile – they can be difficult in their own right or they can be combined with other question types.
The ‘average sum trick’ has been showing up a lot in the 16 - 30 range of the test. That’s the problem type that says something like, “Bobby’s average on the first 5 test was 84. After the 6th test, his average was 86. What did he score on the 6th test?” Of the 13 averages that appeared in this portion of the test, 6 of them were average sum tricks.
The ‘tails’ get longer towards the end of the test. You can see that the most common questions show up more frequently at the beginning of the test than they do towards the end. The most frequent question in the 1 - 15 group appears 15 times; the most frequent question in the 46 - 60 group appears only 10 times. There are so many possible question types on the ACT, especially towards the end of the test, where you can see anything from the Law of Cosines to logarithms to vectors to matrices to dozens of other types.
What am I not seeing here? Function shifts and probability with two events were a little less common in the last 15 questions. Conversions appeared to be less common in the 31 - 45 range. (Decimals and functions dropped out too, but they were lurking near the top 10.) Ratios and percents dropped out of the top 10 in the first 15 questions, but they were both still quite common.
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You will occasionally see a hard question early (or an easy one surprisingly late), but on average, a question in the third group (31 - 45) is going to be easier than a question in the last part of the test.