Desmos, and when not to solve

The Desmos graphing calculator is built into Bluebook and permitted on every math question. Students who treat it as a four-function calculator leave real time on the table.

Practise in it before test day — in Bluebook itself, or at desmos.com/calculator, which is the same engine.

#What it does that matters

• Graph anything you type. Two equations → the intersection is a clickable point with exact coordinates.
• Solve a single equation by typing it in and reading where the curve crosses zero, or by graphing both sides.
• Systems, instantly. Type both lines; click the intersection.
• Regressions — type y₁ ~ mx₁ + b with a table for a line of best fit.
• Sliders. Type an equation with a letter in it and Desmos offers a slider; drag it to see what that parameter does. Genuinely useful for "for what value of k..." questions.
• Tables. Enter a table of values and see it plotted.

#Technique 1 — graph instead of solving

2x² − 5x − 3 = 0 can be factored, or you can type it and read the two x-intercepts. For anything with awkward numbers, graphing is faster and less error-prone.

Anything of the form "how many solutions does this have" is a graphing question: count the intersections.

#Technique 2 — plug in the answers

Multiple choice with four numeric options and a messy equation: try them. Start with B or C — the choices are usually ordered, so if B is too small you've eliminated A as well.

This turns an algebra problem into four arithmetic checks, and arithmetic checks can be done in Desmos.

#Technique 3 — pick a number

When the answer choices are expressions in a variable rather than numbers, invent a value. Let x = 2, compute what the question asks for, then evaluate all four choices at x = 2 and keep the one that matches.

Rules: avoid 0 and 1 (too many things coincide), avoid numbers already in the problem, and if two choices survive, try a second value.

#When to just do the algebra

• The question asks for an expression or a proof-like relationship, not a number.
• It's a two-step linear solve — typing it takes longer than doing it.
• The question is about form ("which equation displays the vertex as constants") — that's reading, not computing.

#The failure mode

Reaching for Desmos on a question that needed ten seconds of thought. The calculator is a tool for avoiding messy algebra, not a substitute for reading the question. Decide what you want before you start typing.