Adaptive Digital SAT Math Deep Dive

How does it compare to the current SAT’s math? What’s on it? What’s not?

The closer you look, the more differences you notice

After taking my first adaptive SAT, I thought I might not have to change the Mathchops question base all that much. Almost every question felt familiar. But after taking all of the tests (four adaptive and four linear), tagging every question multiple ways, and then running the tags through different python scripts, I do think the math on the digital adaptive SAT is significantly different from the current SAT’s math.

It’s more about the balance than anything else. Some questions show up much more frequently now, others are gone, and the overall mix is quite different. If students had infinite time and infinite motivation to do infinite practice problems, these changes of emphasis wouldn’t matter – they’d get to everything eventually. But the reality is that students will only answer a limited number of questions, and we need those questions to target the skills that are most likely to raise their scores. So I’ve ended up making a lot of changes to the question base: adding some new types, removing others, and altering the frequencies of important problem types to make sure they reflect what’s on the test.

In this post, I’ll take you through what I found: Big Categories, Five Types On the Rise, Five Types On the Decline, Module Comparisons¹, and General Observations. Unless otherwise noted, the categories are the same ones we use in Mathchops. The stats² are based on all released versions of the new test.

Big Categories

I’ll start with the categories the College Board uses in their technical manual. Big picture: the general categories of Algebra and Advanced Math are slightly smaller, but Proportions and Stats are a lot smaller, and Geometry and Trigonometry are a lot higher.

• Problem Solving and Data Analysis (15%). These are basically what I’d call Proportions and Stats. They are down a lot…there are 30% fewer of these.

• Algebra (35%) – I think this means “Algebra up to Quadratic Equations”. In the chart below, it refers to Algebra Moves³ (down a bit) , Linear Equations (also down a bit), and Systems (slightly up). Overall, this category covers about 5% less than it used to.

• Advanced Math (35%) – They call this “an understanding of absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations.” These are up quite a bit. In my chart, they’re called Quadratic Equations, Advanced Equations, and Exponents. There are 20% more of these questions than there were before.

• Geometry and Trig (15%) – These are way up…there are 40% more of these. I just refer to these questions as Geometry.

This chart compares the topic coverage of the two tests, using Mathchops categories⁴:

Five Types On The Rise

Exponential growth: lots of y intercepts, identifying the graph.

Triangles: Pythagorean Theorem, SOHCAHTOA, Special right triangles, angle chasing.

Rectangles: perimeter, area, volume of rectangular prism. It’s also used in conjunction with other types (like quadratics).

Quadratic shortcuts:  -b/2a, discriminant, -b/a, factor by grouping…I even saw one that directly tested product of roots = c/a.

Cubic equations: function shifts, finding roots, working with graphs.

Five Types On The Decline

Median: dropped more than 50%.

Table probability: The current SAT has one of these every test, but it did not even show up on half of the new tests.

Ratios: this one surprised me…I wonder if this was a sample-size issue. But it was down about 60%.

Line of best fit: another one that dropped by more than 50%.

Answer is not x: This the kind that has you solve for x, but then asks for 2x + 3.

Module 1 vs Module 2E vs Module 2H

As expected, Algebra Moves are more common on Mod 1 and Mod 2E than they are on Mod 2H. They account for 21% of 2E’s questions, but only 13% of 2H’s.

Interestingly, Advanced Equations appear on both 2E and 2H, but they are much less common on Module 1.

Quadratics are a ‘hard’ type. They account for 19% of 2H’s questions, but only 5% of 2E’s.

Linear Equations and Systems were pretty stable throughout.

Exponents were more of a mod 1 type, for some reason.

The Linear versions of the SAT math sections were pretty similar to the adaptive SAT math sections, but there were some minor differences. There were more basic Algebra questions on the adaptive tests, but more proportions on the linear tests.

General Observations 

- Shorter questions – I was pleased to see that a lot of them felt like Mathchops questions, with very little text and a lot of ‘nice numbers’ for answers.

- More linear equations that are hard – Linear equations are rarely used to discriminate in the 700+ region of the current test, but there were a lot of hard linear equations on the adaptive SAT math.

- Hard questions are harder – There were some really crazy questions…I always tell students that questions can be answered in under one minute (if not much faster), but there were some that needed at least 90 seconds, even if you took the perfect approach.

- Lots of questions can be solved with Desmos. I didn’t track this, but I might in the future (when I have a better sense for how students are using it). You can now just plug some systems into Desmos, for example.

If you have any questions, please post them in the comments below!

1. Every adaptive test taker gets module one, but you either get an easy second module (2E) or a hard second module (2H). So there are only two potential paths through the test: 1 + 2E or 1 + 2H. There is also a linear version of the new test – everyone gets the same version of that. These stats include all of the questions (from all adaptive and linear tests).

2. Also, I hope I don’t give anyone a sense of false precision with some of the numbers I throw out here. They are the ones I came up with, but there aren’t that many questions to work with, and (as always) it’s possible I made some errors when tagging questions.

3. Things like combining like terms, distributing a negative, isolating a variable.

4. One note on the totals: the percents add up to more than 100 because the categories sometimes overlap. Percents (part of proportions) will often play a minor role in a question that primarily targets some other skill, for example. But I tried to keep the categories as distinct as possible. Any question with a primary tag of ‘Systems’ was not labeled as a Linear Equation, for example, even though they do contain linear equations.