FULL SAT DESMOS GUIDEFULL SAT DESMOS GUIDE

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Desmos Complete Guide

The full course: every tool, every question type, every trap

What this guide is. It follows the whole Desmos course in order, from the first tour through the hardest "must be true" questions. Every chapter has the rule, the reason, a worked example, and the trap. Screenshots are the real SAT Desmos calculator. Work each example yourself as you read. 0. The system that never breaks

The course's main idea: hard problems are easy if you follow the same routine every time. Never abandon it.

1. Know what you are solving for. Read the question and say it out loud: "I am solving for ___." 2. Predict your tool before you type. Decide "graph", "table + regression", "list", or "sliders" first. Typing blindly is how Desmos problems get missed.

3. Fulfill every condition. If it says x > 5, k is positive, r is an integer, or h(5) = 7, Desmos must be told. Breaking a condition gives a wrong answer even when the math looks right.

4. Verify two ways. Spend the extra 20 seconds. Optimize for accuracy, not speed. One silly mistake costs 20 to 30 points.

Default tool: graph first. Graphing should be your answer to a question about four times as often as regression. Do not spam the tilde (~). Use ~ only when a plan says you need it.

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1. The tour: everything Desmos can do The SAT Desmos screen

1 + adds an expression or a table.

2 Undo / redo.

3 Gear: list-edit mode.

4 « hides the list for a bigger graph. 5 Wrench: zoom, grid, and degrees/radians. 6 Expression row.

7 The graph. Gray dots are clickable. The keyboard tab at the bottom left lists every function (abs, statistics, trig). If you forget a command, open it. Typing the name also works. SAT Math · Desmos 2 of 20

Graphing: gray dots

y = x² − 6x + 5, clicked at the bottom

Type an equation and Desmos graphs it and marks the

x-intercepts, the y-intercept, and the minimum or

maximum (the vertex of a parabola). Click a dot to

see its coordinates. If an equation is x² − 100, the

intercepts are x = −10 and x = 10.

Vertex (3, −4). Zeros x = 1, 5. y-intercept (0, 5).

Intercept is not a solution. For two lines like 5x

+ 10 and −2x + 7, the solution is only where the

two lines cross, not any other gray dot. Gray dots

also mark intercepts. Do not mix them up.

Tables

Click + then Table, or just type table . Use it any time you are given multiple points. Enter the points, then add a regression (linear, quadratic, exponential from the drop-down) or a custom regression (Chapters 9 and 10). In the SAT you cannot copy and paste, so retype equations or use function notation. x and y versus constants

Desmos graphs only x and y. Any other letter (c, a, k) is a constant and will not graph until it has a value. So c² = 100 will not graph.

If an equation has x or y, finish the equation. Something like x²y has to be set equal to a number to graph. Pick a number like 100. Do not pick 0 or 1, because they are unreliable.

Typing y = in front of an expression is only a name for the graph. It is fine and good practice. f(x) = is better when you want to use it as a function.

Sliders

A blue "add slider" box sometimes appears for an undefined constant. It does not always appear (for example, when the equation is set equal to 100). So practice typing it yourself: on a new line type c = 1 . A slider just assigns that number to the letter everywhere it appears.

Boundaries. The default range is −10 to 10. Click either end number and change it (for example 1000). SAT Math · Desmos 3 of 20

Step. Default is decimals. If the question says the constant is an integer, set the step to 1 so it can only land on whole numbers.

Statistics and number functions

Type What it does

mean(L) median(L) Average and median of a list, such as [1,2,3,4,5]

stdev(L) Standard deviation. Very hard by hand, so use Desmos every time.

gcd(4,40,60) Greatest common divisor (factor) = 4. Also gcd(2,4,6) = 2. Great for

factoring problems.

lcm(4,6) Least common multiple. Rare on the SAT, but possible in factoring.

mod(50,4) Remainder = 2. mod(50,5) = 0. 5 ÷ 2 leaves 1. Handy for unit-circle

questions like 478π/4, where you go around by 2π again and again.

Typing shortcuts

cbrt sqrt nthroot Cube root, square root, and nth root. Type the word and the symbol appears. Everything lives on the keyboard tab if you forget.

10^5 Exponent: Shift + 6 gives ^. If the exponent has more than one thing, use

parentheses: 10^(x+1) . Without them the +1 slides down.

Divide a long expression Highlight the whole expression, then press / .

distance((1,1),(2,5)) Distance between points. midpoint(...) gives the middle and plots both. a ~ 50% of 100 Percentages: solve for a with ~ . For "percent more" multiply by 1 + p. For "percent less" multiply by 1 − p. Lists (Chapter 10) are best for chains of

percentages.

x ≥ 0 Constraints. Type x≥0 after an equation (in curly braces) to see only that part. Optional, but good if you want to see it.

Functions

Type f(x) = 10x + 3000 . Now f(100) returns the value. Do any math: (f(10) + f(3)) / f(1000) , or mix two functions with f(30)/g(2) . The name must match: if you defined g(x) , then f(100) means nothing. The name (f, g, h) does not change the function.

Trig

Desmos starts in radians. For degrees, open the wrench and choose Degrees. In degree mode sin(10) = cos(80) , because angles that add to 90° are complementary and sin of one equals cos of the other.

2. One-variable equations

An equation with one unknown, like 5x + 100 = 5000. It is the base of everything else on Desmos, and if you cannot do these you cannot do systems, equivalent expressions, or anything else.

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x² − 2x − 3 = 0 draws vertical lines

Type the whole equation. The vertical lines are the

solutions. Click where a line meets the x-axis for the

value.

x = −1 and x = 3. Graph without the = 0 and you

get the parabola. Add = 0 and the solutions

become vertical lines.

One variable gives vertical lines. A system gives

an intersection point. This is the big difference.