Desmos Mastery

Desmos turns 90-second algebra into 15-second graphing and removes arithmetic error — but only if you know in 10 seconds whether to reach for it. A graphing calculator is available on the entire Math section in Bluebook. Top scorers use it to solve, verify, and bank time. The skill is two-sided: lightning Desmos workflows and the judgement to skip it when algebra is faster.

Sources: College Board calculator policy (Desmos on all Math); BWS Education Desmos tips; MySatCoach. Practise on the official build: desmos.com/testing/cb-digital-sat/graphing (the consumer app has extra features the test disables). Point convention: each Math item = 1 of ~44; Module-1 misses are ceiling-risk.

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#THE 10 CORE WORKFLOWS

1. Solve any equation by graphing. Type y = LHS and y = RHS; the x of the intersection is the solution. Works for linear, quadratic, rational, radical, absolute value. (e.g., |x−4|=9 → graph both → x=−5, 13.)
2. Systems by intersection. Type both equations; click the intersection dot for exact coordinates. Best for linear-quadratic / quadratic-quadratic. Watch for a restriction (x>0) or an "x+y" ask.
3. Roots / zeros. Type the expression; click the x-intercepts (grey dots). Beats the quadratic formula on messy quadratics built to bait it.
4. Vertex / min / max. Desmos auto-marks the vertex; click for exact coordinates — skip completing the square.
5. Sliders for unknown constants / "how many solutions." Type the equation with the unknown letter; accept "add slider"; drag until the condition holds (parallel = no solution; tangent = one solution / discriminant 0).
6. Regression for best-fit data. Open a table, enter points, then y₁ ~ m x₁ + b (linear), y₁ ~ a x₁² + b x₁ + c (quadratic), or y₁ ~ a·b^(x₁) (exponential). Use the tilde ~ and subscripts, or it won't run. Uses all points, no rounding error.
7. Graph circles directly. (x−h)²+(y−k)²=r² draws the circle — read centre/radius/intercepts. Pair with completing-the-square problems.
8. Inequalities / systems of inequalities. Graph each; the overlap (darker shade) is the solution set; test whether a point lies in it.
9. Statistics on a list. mean(...), median(...), and quartile/stdev functions for one-variable data.
10. Utility shortcuts. Click a decimal to toggle its fraction (handy for grid-in format); 20%700 computes 20% of 700; append {0<x<5} to restrict a domain.

Why (mechanism): each workflow replaces an error-prone hand computation with a read-off. On the hard Module 2 — messy quadratics, discriminant/tangency, conditional data — this both saves time and removes the arithmetic slips that cap an 800. [Time banked here is what lets you double-check the rest.]

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#WHEN NOT TO USE DESMOS

• Trivial one-step solves (3x+5=17 — 5 seconds by hand).
• "Equivalent expression" / "in terms of a, b" — Desmos can't answer; factor/expand or plug in a number.
• Simple percent/ratio/unit problems — setup is faster than typing.
• Anything where opening + typing + reading (~15–30 s) costs more than the mental solve.

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#DIAGNOSE YOUR ANSWER

• Graphed correctly but wrong answer? You misread the ask (x vs x+y, wrong intersection). Fix: re-read the ask after graphing.
• Regression didn't run? You used = not ~, or wrong subscripts. Fix: y₁ ~ … with table columns x₁, y₁.
• Slow on easy items? Over-using Desmos. Fix: drill tool-choice (below).
• Mode/format slip? Decimal vs fraction for grid-in. Fix: toggle to the cleanest accepted form.

#DRILLS (timed · self-marked · MERIDIAN-original)

Drill 1 — Tool choice (target 10/10, ≤2 min): for 10 items write "DESMOS" or "BY HAND" only. PASS: correct call on all 10. Drill 2 — Speed workflows (target: each <60 s): 10 systems by intersection; 6 messy quadratics by roots-dots; 4 "how many solutions" by slider; 3 best-fit by regression. PASS: correct + under time; re-enter any miss to find the mistype. Repetition: fail → repeat next day until each workflow is reflexive.

#TRANSFER

Abstract rule: if the answer is a graphable number, graph it; if it's structural, don't. Second context: the intersection method solves a finance break-even system and a physics two-equation motion problem identically. Constant: the 10 workflows + the when-not list. Changes: the equation's story.

#REFERENCE CARD — DESMOS

GRAPH IT: equation (y=LHS,y=RHS→intersection) · roots (x-ints) · vertex (auto dot) ·
  "how many solutions"/tangent (SLIDER) · best-fit (table + y₁~…) · circle eqn · inequality overlap · mean()/median()
SKIP IT: trivial solves · "equivalent expression"/"in terms of" (plug in) · simple %/ratio
Regression uses ~ and subscripts. Toggle decimal↔fraction for grid-ins.
Practise on desmos.com/testing/cb-digital-sat/graphing. Module-1 miss = ceiling risk.

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MERIDIAN · FORGE · DESMOS MASTERY | v1.0