How to Self Study for the Digital SAT

The strategies I teach to my students aren’t secret: they’re just not widely known. So here’s what I’d do if I were a student studying on my own:

Section 1 — What to Practice With

Use official questions only. No third-party material, no random prep books. College Board publishes the questions that actually appear on the SAT, and someone on Reddit compiled the question bank into PDFs sorted by topic. This is your primary study material.

SAT Question Bank PDFs (sorted by topic) reddit.com/r/Sat — community-compiled from official College Board questions

Supplement with full-length practice tests in the Bluebook app. Do not use third-party tests — they don’t match the real exam’s style, difficulty, or scoring.

Bluebook — Official Digital SAT Practice bluebook.collegeboard.org

The Review Cycle

Here’s the habit that actually moves your score: spend as much time reviewing a practice test as you spent taking it. For every question you missed, watch a YouTube video explaining it — then find a second YouTuber explaining the same question. Keep track of which teachers you like best. A few days later, go back and try those questions again from scratch. No notes, no help. If you can nail it, you’re improving.

Take a practice test Review every miss Retry from scratch Test again

Then take another practice test and see how much your score has grown. Repeat the cycle.

Section 2 — Learning New Topics & Relearning Old Ones

Reading & Writing

Most people wonder what to focus on when prepping. More importantly, here’s what not to focus on: reading.

Wait, really? Don’t focus on reading for the reading score?

This is not your parent’s SAT. There are typically 20 or 21 reading questions — roughly 38% of the verbal section. That means about two-thirds of the test is vocabulary, grammar, transitions, and student notes.

Grammar is the most reliable way to improve your overall Reading & Writing score. You need to learn some grammatical rules, and this is true for everyone I’ve ever tutored. No one ever comes in knowing what a dangling modifier is, but that’s going to show up on your SAT. Or that a semicolon is used interchangeably with a period — or as a separator in a complex list.

SAT Grammar Course (YouTube) A solid free primer covering the major grammar rules tested Complete SAT Grammar Rules thecriticalreader.com — a thorough reference list of nearly everything tested

For vocabulary, start cramming. Many reading questions are really just testing whether you know a word. I go over and over a question with students that basically boils down to whether they know that the secondary definition of the word “novel” is “new.”

Official SAT Vocabulary Lists mrjohnstestprep.com Roots to Words — SAT/ACT Vocabulary roots2words.com

You should also work on transitions and student notes questions, then practice all of these using the question bank sorted by topic.

Math

The single best way to improve your math score is learning how to use Desmos. The graphing calculator is built right into the digital SAT, and most students barely touch it. That’s a mistake. Let me show you why.

Example 1 — System of Equations
$$\begin{align*} \frac{2}{7}x – \frac{3}{5}y &= -13 \\[6pt] \frac{15}{7}x + \frac{18}{5}y &= 24 \end{align*}$$

The solution to the given system is \((x, y)\). What is the value of \(y\)?

Doing this by hand means clearing fractions, lining up coefficients, and doing a lot of arithmetic where one slip kills you:

✏️ The Algebra Way
Clear the fractions (multiply both equations by 35)
$$\begin{align*} 10x – 21y &= -455 \\[4pt] 75x + 126y &= 840 \end{align*}$$
Multiply the first equation by 7.5
$$75x – 157.5y = -3412.5$$
Subtract from the second equation
$$\begin{align*} (75x + 126y) – (75x – 157.5y) &= 840 – (-3412.5) \\[4pt] 283.5y &= 4252.5 \end{align*}$$
Solve
$$y = \frac{4252.5}{283.5} = 15$$

(And pray you didn’t make an arithmetic mistake along the way)

Or you type both equations into Desmos and read the intersection point:

📊 The Desmos Way
At least 2 mins by hand ~15 secs in Desmos Same answer: y = 15

Same answer either way. One of them lets you spend your time on harder problems.

Here’s a harder question — the kind of problem where becoming a Desmos power user really pays off:

Example 2 — Infinitely Many Solutions
$$\begin{align*} \frac{5}{3}x – \frac{1}{2}y &= 24 \\[6pt] ax – by &= 2 \end{align*}$$

In the given system of equations, \(a\) and \(b\) are constants. The system has infinitely many solutions. What is the value of \(\frac{a}{b}\)?

The algebra approach requires you to recognize that “infinitely many solutions” means the equations describe the same line, then find a scalar, apply it to each coefficient, and compute a compound fraction:

✏️ The Algebra Way
Find the scalar k such that k · 24 = 2
$$k = \frac{2}{24} = \frac{1}{12}$$
Apply k to each coefficient
$$a = \frac{1}{12} \cdot \frac{5}{3} = \frac{5}{36} \qquad b = \frac{1}{12} \cdot \frac{1}{2} = \frac{1}{24}$$
Compute the ratio
$$\frac{a}{b} = \frac{\;\frac{5}{36}\;}{\;\frac{1}{24}\;} = \frac{5}{36} \cdot \frac{24}{1} = \frac{120}{36} = \frac{10}{3}$$

Alternatively, you can learn how to type the following and Desmos will find the answer for you:

📊 The Desmos Way
a/b = 3.333… = 10/3

Type it in, read the answer. That’s it.

The point isn’t that algebra should always be avoided. It’s that using Desmos is often the best way: Desmos will give you more time for questions that require algebra, improve your accuracy, catch mistakes, make the unsolvable solvable, and improve your score.

Fill In the Gaps

Beyond Desmos, it’s important to review concepts you’ve forgotten since you last took geometry — or to fill in gaps your school district doesn’t teach. A few topics that I often need to cover with students: standard deviation, Vieta’s formulas, margin of error, and cofunction identities, among others. Let your practice tests guide which topics you should work on. If you keep getting a certain type wrong, that’s the universe telling you to go learn it.