The rule in one line
You can use a calculator on every question of the Math section. The old split between a calculator module and a no calculator module is gone. Bluebook has a Desmos graphing calculator built in, and it is available from the first Math question to the last.
Calculators are not permitted during Reading and Writing, and you cannot open the built in one there either.
The graphs of the two linear equations in a system are shown as lines ℓ and k in the xy-plane. What is the solution (x, y) to the system?
The built in Desmos
The embedded calculator is a graphing calculator, not a four function one. You can type equations and see them plotted, enter a system and click the intersection point to read its coordinates, define a function and evaluate it, build a table of values, and add a slider for an unknown constant.
The single most useful move is graphing. If a question gives you two equations and asks where they meet, typing both and clicking the intersection is usually faster and safer than solving by substitution. The same goes for reading the roots or the vertex off a parabola.
It is worth practicing in the real Bluebook app rather than only on the Desmos website, because the panel is smaller on screen and the keyboard shortcuts take a little getting used to.
You are allowed to bring an approved calculator, and it is reasonable to do so as a backup and because muscle memory is fast.
Bringing your own
You are allowed to bring an approved calculator, and it is reasonable to do so as a backup and because muscle memory is fast. Most graphing and scientific calculators are approved. Phones, tablets, smartwatches, laptops, and anything with a QWERTY keyboard, internet access, or a camera are not.
If you bring one, bring fresh batteries. Proctors do not supply them, and a dead calculator is your problem, not the test center's. Check the current approved list on College Board's site before test day, since it is updated periodically.
When to reach for it and when not to
Use the calculator when the arithmetic is ugly, when a system of equations would take three lines of algebra, when you need a root or a vertex, or when you want to check an answer you already got by hand.
Skip it when the question is about structure rather than numbers. Questions asking which expression is equivalent to another, or what a coefficient means in context, or how many solutions an equation has, are usually faster to reason through than to compute. Reaching for the calculator by reflex on those questions costs time.
The common failure is spending 40 seconds typing a problem into Desmos that would have taken 15 seconds on paper. Decide first, then type.
Scratch paper
The test center provides scratch paper and you can use a pencil on it. This still matters on a digital test. Writing out a system, sketching a triangle, or listing what you know before you start is faster than holding it in your head.
Do not try to work entirely on screen. The annotator is for the reading passages, not for math scratch work.