Summary of "How I got an 800 on SAT Math with ONLY Desmos"

High-level summary

• Claim: You can use Desmos to solve essentially every SAT Math question (both math modules). The video demonstrates this by solving many representative problems while showing specific Desmos techniques and shortcuts.
• Main takeaway: Learn a handful of Desmos tricks (plotting, regression, sliders, rearranging equations, using tables, forcing constraints) and you can quickly test answer choices, find roots/intercepts, model proportions/percent problems, visualize geometry, and compute numeric answers during the SAT.

Learn a handful of Desmos tricks (plotting, regression, sliders, rearranging equations, using tables, forcing constraints) and you can quickly test answer choices, find roots/intercepts, model proportions/percent problems, visualize geometry, and compute numeric answers during the SAT.

General approach

• For multiple-choice questions: graph the given expression or situation and graph each answer choice; the correct choice will match visually.
• For equations: rearrange to eliminate the equals sign (put everything on one side so the expression equals 0) so Desmos plots it as a curve/line and you can inspect intersections/zeros.
• Use regression and tables to derive linear models from two or more points instead of algebraic manipulation.
• Use sliders to represent unknown parameters and adjust them until constraints are satisfied (make lines intersect, force a point to lie on a curve, etc.).
• Use substitutions or arbitrary positive values when the problem restricts variable signs (e.g., “positive numbers”) to test equivalence.
• Use inequalities in Desmos (>, <) to enforce domain constraints.

Types of problems and how Desmos helps

Linear, slope, and line equations

• Plot a line using slope and a point, or enter two points into a table and use Desmos’ linear regression output.

Polynomial / expression equivalence

• Graph the given polynomial and each answer option; visually check which graph overlaps exactly.

Proportions and scaling

• Use regression or set up a proportion (e.g., 16/20 = x/400) and let Desmos compute x.

Simple algebra and linear solving

• Rearrange equations (move everything to one side) and compare resulting graphs for equivalence or intersections.

Parameterized expressions with positivity constraints

• Replace symbolic constants with positive variables or placeholders, or enforce inequalities like a > 0.

Percent change and exponential growth/decay

• Model percent increases as multiplication by (1 + rate) (e.g., 3% → ×1.03) and test candidate functions.

Word problems (units, time, percent)

• Assign variables and use Desmos to compute or solve systems directly.

Projectile motion and physics

• Treat quadratic height functions as y(t); use domain restrictions (t ≥ 0) and read initial height at t = 0.

Quadratics and roots

• Use graphs to determine whether a quadratic has real solutions and to locate zeros.

Domain, range, and positive differences

• Read min/max or difference directly from plotted data points or functions.

Geometry (area, volume, similar triangles, transformations)

• Use algebraic formulas and Desmos plotting to find areas, volumes, and missing dimensions.
• For similar triangles and ratios, set up proportional equations in Desmos.
• Test translated circles by entering candidate equations and comparing positions.

Trigonometry

• Compute trig ratios (e.g., cosine = adjacent/hypotenuse) numerically in Desmos.

Systems of equations and constraints

• Input systems using commas/brackets (e.g., { [equation1, equation2] }) and include inequalities to enforce domain conditions.

Probability and counting

• Use table counts and direct arithmetic or Desmos expressions to compute conditional probabilities.

Detailed Desmos methodology & step-by-step techniques

Basic graphing and matching answers

1. Type the given expression/function into Desmos exactly as presented.
2. For algebraic equivalence questions, graph the original expression and each answer; choose the option whose graph exactly overlaps.

Removing the equals sign

• Move everything to one side so the expression equals 0 (e.g., convert 2x = 16 to 2x - 16 = 0). Desmos will draw the resulting curve and show intersection points/zeros.

Linear regression from two (or more) points

• Create a table (type “table”) and enter (x,y) pairs.
• Click the regression button (or use the linear model output) to get an equation in slope-intercept form.
• Use this to infer slope/intercept, extrapolate, or convert proportions into larger-population estimates.

Using sliders for unknown parameters

• Create sliders for letters (a, b, p, t, etc.) and drag them until the graph satisfies constraints (passes through a point, becomes parallel, etc.).

Creating and solving small systems

• Use comma/parentheses/brackets to enter multiple equations and inequalities together.
• Enforce positivity or other domain constraints (e.g., b > 0) inside the system.

Testing options quickly

• Enter each answer choice on its own line for quick visual comparison.
• Use the “delete all” or clear function to restart quickly between attempts.

Tables and function interplay

• If g(x) = f(x)/(x + 3) and g is given as table values, create a table for g and use regression or algebraic reconstruction to find f(x).

Geometry and distance tools

• Plot circles with (x - h)^2 + (y - k)^2 = r^2.
• Place points and use distance formulas or built-in distance() expressions to compute lengths and verify relationships.

Numeric checks and rounding

• Use Desmos’ numeric evaluation for decimal answers; minor rounding differences are usually acceptable for College Board-style grading.

Practical tips and small tricks

• Use x as the primary variable if Desmos has trouble with other letters.
• When a problem states “positive numbers,” you can often substitute arbitrary positive placeholders or add inequalities to the system.
• If you don’t want to zoom/pan, use regression or sliders to find points of interest.
• Create temporary variables (e.g., m for missing) to compute intermediate values quickly.
• Familiarize yourself with tables, regression, sliders, and rearranging equations so you can execute these actions under time pressure.

Representative problem types demonstrated

• Find slope and equation of a line from slope + point.
• Identify equivalent polynomial/expression via graph matching.
• Solve for a missing number given a sum or unit conversion.
• Convert sample proportions to population estimates (scaling).
• Solve linear equations by rearrangement and graph comparison.
• Test algebraic forms under “positive numbers” constraints.
• Model percentage increases as multiplicative factors.
• Interpret projectile motion quadratics (initial height, domain).
• Determine number of real solutions for quadratics.
• Compute ranges and positive differences from datasets.
• Derive cube height from area and volume constraints.
• Identify exponential models of the form a · b^x.
• Compute trig ratios numerically.
• Find roots and factor polynomials graphically.
• Solve similar-triangle ratio problems.
• Find parameters that make lines parallel (no intersection).
• Compute conditional probabilities from tables.
• Use special triangles (30-60-90) to relate rectangle diagonals and circle diameters.
• Solve percentage-based systems (e.g., A = 224% of (B + C), B = 83% of C).
• Find parameters for quadratics given roots and integral constraints.

Practical exam-focused lessons

• Desmos is often faster and less error-prone than long algebra for verifying multiple-choice options.
• Practice a small set of Desmos operations (tables, regression, sliders, rearrangement) so you can execute them rapidly during the SAT.
• For SAT-style problems: enter expressions exactly as written, use sliders to satisfy constraints, and confirm choices with graphical overlap or numeric checks.
• Use Desmos’ precision judiciously—minor rounding is acceptable when working with decimal outputs.

Speakers and sources mentioned

• Michael — video presenter and demonstrator (primary speaker).
• Desmos — the graphing tool used for demonstrations.
• College Board — referenced as the SAT test maker/grader.
• AP Physics — referenced for projectile-motion context.
• Jeremy Fragrance — brief pop-culture reference.
• Chemtutor — referenced for learning geometry concepts (vertical angles).
• Casual mentions: Chipotle (not technical).

Category

Educational

---

Share this summary

Share on X/Twitter Share on Facebook Share on LinkedIn Share on Reddit Share on WhatsApp Share on Telegram

---

Is the summary off?

If you think the summary is inaccurate, you can reprocess it with the latest model.

Reprocess summary

Video