The Desmos SAT Guide: 21 tricks for a higher Math score

21 tricks · about 3 min each · Updated October 2026

These are 21 patterns top scorers use to solve SAT Math questions in seconds instead of minutes. Every trick comes with a real question. Press Next step and the calculator next to it does exactly what the text says.

Why bother: about 80% of SAT Math can be solved with Desmos, it saves 2 to 3 minutes per question on average, and 750+ is a realistic score once you know it well.

YekoMath 580740

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“This course helped me with my math a lot because in September I only had 580, and 580 to 740 is an insane improvement.”

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Practice tests, from our Telegram channel

“Math part was amazing, I finally understood how to use Desmos properly.”

Before you start: typing in Desmos

Tilde ~ is Shift plus the key left of 1. On a Russian or Kazakh layout that key is Ё, so switch to English first.
Subscript x₁: type x_1, then press the right arrow to leave the subscript.
Slider: type a line with a new letter, like y = 2x + k, and click the “k” button Desmos shows under it.
Tilde lines also print statistics and residuals. Ignore them and read only the values of your letters.
Exponent with a sum: after ^ type ( first. Otherwise the + or - jumps out of the exponent.
Fraction with several terms on top: select the whole top part, then press /.
Skip the keypad: typing sqrt, cbrt, nthroot or pi turns into the symbol.
No copy and paste in Bluebook. Type a long expression once as f(x) = ... and reuse f(2), f(x+3) and so on.
Ugly decimal = check again. SAT answers are almost always whole numbers or clean fractions. A result like 3.71829 usually means a typo or a missed condition.
Test numbers: when you pick values for letters, never use 0 or 1. They hide mistakes, because 1² = 1 and 0 · anything = 0.

Systems of Equations: Click the Intersection

Graph two lines, click where they cross, compute the answer. By hand: about 2 min.

Question

\begin{cases} \frac{5}{4}x + 2y = 17 \\[6pt] \frac{3}{4}x + 2y = 15 \end{cases}

The solution to the system above is

(x, y)

. What is the value of

\frac{11}{4}x + 6y

A. $4$
B. $6$
C. $32$
D. $47$

what we knowwhat we need

Solving it in Desmos

1.Type the first equation exactly as written. No need to solve for $y$ first: Desmos graphs it as is.

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

Inequalities: Test Points in the Shaded Region

Desmos shades the double-overlap region. Just check which point falls inside it. By hand: about 2 min.

Question

\begin{cases} y \leq x + 8 \\ y \geq -3x - 8 \end{cases}

Which of the points

(0,-9)

(0,9)

(-5,0)

(5,0)

is a solution to the system of inequalities above?

A. $(0,-9)$
B. $(0,9)$
C. $(-5,0)$
D. $(5,0)$

what we knowwhat we need

Solving it in Desmos

1.Type $y \le x + 8$ . Desmos shades everything below the line.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Vertex Form: Read the Minimum Off the Graph

Click the lowest point, plug it into vertex form, and check by graphing. By hand: about 1.5 min.

Question

The function

f

is defined by

f(x) = x^2 - 4x - 780

. Write

f

in an equivalent form that displays the minimum value as a constant.

A. $f(x) = x^2 - 4x + 195$
B. $f(x) = (x-2)^2 - 784$
C. $f(x) = x(x-4) - 780$
D. $f(x) = (x+26)(x-30)$

what we knowwhat we need

Solving it in Desmos

1.Graph the original, $y = x^2 - 4x - 780$ . The parabola dips far below the axis.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

No Real Solutions: The Slider Trick

Drag a slider and watch the graphs cross, touch, or separate. The boundary is your answer. By hand: about 2 min.

Question

-(3x-7)^2 = p+17

, where

p

is an integer constant. If the equation has no real solutions, what is the least possible value of

p

A. $-18$
B. $-17$
C. $-16$
D. $-15$

what we knowwhat we need

Solving it in Desmos

1.Split the equation into two graphs. The left side, $y = -(3x-7)^2$ , is a parabola opening down. Its highest point is at $y = 0$ .

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

Exactly One Intersection: Slide Until It Touches

A line and a parabola meet once only when the line just touches. A slider finds that moment. By hand: about 2 min.

Question

In the

xy

-plane, the line

y = 2x + k

intersects the parabola

y = x^2 + 4x + 7

at exactly one point. What is the value of

k

A. $3$
B. $6$
C. $7$
D. $8$

what we knowwhat we need

Solving it in Desmos

1.Graph the parabola $y = x^2 + 4x + 7$ .

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Infinitely Many Solutions: Make the Lines Overlap

Infinitely many solutions means the same line twice. Slide the unknown coefficient until they merge. By hand: about 1.5 min.

Question

The system of equations

\frac{3}{5}x + ky = 2

and

1.8x + 4.5y = 6

has infinitely many solutions. What is the value of

k

A. $0.5$
B. $1.5$
C. $2.5$
D. $4.5$

what we knowwhat we need

Solving it in Desmos

1.Graph $1.8x + 4.5y = 6$ exactly as written.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

No Solution: Two Graphs, Then Zoom In

Put each side of the equation on its own line. On one line, no solution and infinitely many solutions look exactly the same. By hand: about 1.5 min.

Question

\frac{8cx + 7}{5} = 4x - 7

. In the given equation,

c

is a constant. If the equation has no solution, what is the value of

c

A. $\frac{1}{5}$
B. $2$
C. $\frac{5}{4}$
D. $\frac{5}{2}$

what we knowwhat we need

Solving it in Desmos

1.Split at the equals sign. Type the left side as $y = \frac{8cx + 7}{5}$ and the right side as $y = 4x - 7$ . Typing it all on one line would show nothing for both no solution and infinitely many solutions, so you couldn't tell them apart. The first line waits until $c$ has a value.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Let Desmos Solve the Equation with ~

Swap the variable for x₁ and the equals sign for a tilde. Desmos solves it, fractions and all. By hand: about 1 min.

Question

\frac{2x + 5}{3} - \frac{x - 1}{4} = 6

, what is the value of

x + 1

A. $9.8$
B. $10.8$
C. $11$
D. $49$

what we knowwhat we need

Solving it in Desmos

1.Desmos keeps $x$ and $y$ for graphing, so call the unknown $x_1$ and swap $=$ for $\sim$ . The tilde tells Desmos: find the $x_1$ that makes both sides equal.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Sum of the Solutions: Graph, Don't Tilde

The tilde stops after one answer. For a sum, the greatest solution, or how many there are, graph the equation and read every line. By hand: about 2 min.

Question

2|4x - 1| = 4x + 9

. What is the sum of the solutions to the given equation?

what we knowwhat we need

Solving it in Desmos

1.The trap first. Type it with a tilde: $2|4x_1 - 1| \sim 4x_1 + 9$ . Desmos says $x_1 = 2.75$ and stops. That is only one of the solutions.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Percent Changes with a Tilde

Write the whole percent story as one expression and let Desmos solve for the unknown percent. By hand: about 2 min.

Question

A store raised the price of a jacket by

p\%

, then lowered the new price by

p\%

. The final price is

96\%

of the original price. What is the value of

p

A. $4$
B. $16$
C. $20$
D. $25$

what we knowwhat we need

Solving it in Desmos

1.Turn each change into a multiplier: up $p\%$ is $1 + \frac{p}{100}$ , down $p\%$ is $1 - \frac{p}{100}$ . Ending at $96\%$ means the product is $0.96$ .

Step 1 of 3

The calculator follows the steps. Feel free to type in it too.

Chained Percents: Type Each One Word for Word

When one quantity is a percent of another, type it straight into Desmos with the %of operator and let a tilde untangle the chain. By hand: about 3 min.

Question

The mass of object A is

462\%

of the mass of object B, and the mass of object A is

0.084\%

of the mass of object C. If the mass of object C is

p\%

of the mass of object B, what is the value of

\frac{p}{1{,}000}

what we knowwhat we need

Solving it in Desmos

1.Only the ratios between the masses matter, so pin one of them to any number: $B_1 = 100$ . Type the percent sign with Shift + 5, then the word of becomes an operator.

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Missing Value in a Mean

Wrap the list in mean(), put the unknown inside, and use a tilde for the target. By hand: about 1 min.

Question

The mean of the seven numbers

4.2, 7.5, 9.1, 3.8, 6.4, 8.0,

and

x

6.8

. What is the value of

x

A. $6.8$
B. $7.9$
C. $8.6$
D. $9.2$

what we knowwhat we need

Solving it in Desmos

1.Call the unknown $a$ . Same idea as $x_1$ in the first trick: Desmos solves a tilde for any letter except $x$ and $y$ .

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Constants That Work for All x

A list of test values plus a tilde makes Desmos find every unknown constant at once. By hand: about 1.5 min.

Question

(ax + 3)(x + b) = 2x^2 + 11x + 12

is true for all real values of

x

, where

a

and

b

are constants, what is the value of

a + b

A. $5$
B. $6$
C. $7$
D. $8$

what we knowwhat we need

Solving it in Desmos

1."True for all $x$ " means any $x$ works. Make a list of test values: $x_1 = [1, 2, 3, 4, 5]$ .

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Solve a System in One Line

Solve a whole system in one line: left sides in one list, right sides in another, a tilde in between. By hand: about 1.5 min.

Question

\begin{cases} x + y = 13 \\ 3x - y = 11 \end{cases}

What is the value of

x^2 + y^2

for the solution

(x, y)

A. $13$
B. $25$
C. $85$
D. $169$

what we knowwhat we need

Solving it in Desmos

1.Put both left sides in one bracket and both right sides in another, joined by a tilde: $[x_1 + y_1,\ 3x_1 - y_1] \sim [13,\ 11]$ .

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

"In Terms Of" Questions: Check with Test Numbers

Give every other letter a random value, let Desmos find the one you're isolating, then see which answer choice gives the same number. By hand: about 3 min.

Question

\frac{1}{R} = \frac{1}{p} + \frac{1}{q} + \frac{1}{s} + \frac{1}{13}

. A parallel electric circuit contains four resistors with resistances of

p

ohms,

q

ohms,

s

ohms, and

13

ohms. The given equation relates the resistance

R

, in ohms, of the circuit, to the resistances of the four individual resistors it contains. Which equation correctly expresses

R

in terms of

p

q

, and

s

A. $R = \frac{13pqs}{p + q + s + 13}$
B. $R = \frac{13pqs}{13qs + 13ps + 13pq + pqs}$
C. $R = \frac{13qs + 13ps + 13pq + pqs}{13pqs}$
D. $R = p + q + s + 13$

what we knowwhat we need

Solving it in Desmos

1.Pick test numbers for every letter except $R$ : $p = 2$ , $q = 3$ , $s = 5$ . Make them all different and never 0 or 1. Those two hide mistakes.

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

Trig in Degrees: Flip One Setting First

Desmos starts in radians. SAT angles are almost always in degrees, so the same input gives a nonsense answer until you switch. By hand: about 1 min.

Question

For two acute angles

X

and

Y

, the measure of angle

Y

28

degrees and

\frac{\sin X}{\cos Y} = 1

. What is the measure, in degrees, of angle

X

A. $28$
B. $45$
C. $62$
D. $73$

what we knowwhat we need

Solving it in Desmos

1.Type the condition as written, with $x_1$ for the angle: $\frac{\sin(x_1)}{\cos(28)} \sim 1$ . Desmos says $x_1 = -1.85$ . A negative angle can't be right. Desmos read $28$ as radians.

Step 1 of 3

The calculator follows the steps. Feel free to type in it too.

Linear Function from Two Points

Enter the points in a table, type one line with a tilde, and Desmos writes the equation for you. (Desmos calls this a regression.) By hand: about 1.5 min.

Question

A linear function

f

gives the profit, in dollars, from selling

x

items. The profit is

\$190

when

4

items are sold, and

\$670

when

10

items are sold. Find the equation that defines

f

A. $f(x)=180x-670$
B. $f(x)=67x$
C. $f(x)=80x+190$
D. $f(x)=80x-130$

what we knowwhat we need

Solving it in Desmos

1.Click $+$ and pick table. Put the items in $x_1$ ( $4$ , $10$ ) and the profit in $y_1$ ( $190$ , $670$ ).

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Exponential Function from Two Points

Put the points in a table, fit a·b^x, and Desmos hands you both constants. By hand: about 2 min.

Question

The function

f

is defined by

f(x) = a \cdot b^x

, where

a

and

b

are positive constants. If

f(0) = 5

and

f(2) = 45

, what is

f(3)

A. $90$
B. $125$
C. $135$
D. $405$

what we knowwhat we need

Solving it in Desmos

1.Click $+$ and pick table. Enter the two facts as points: $x_1$ gets $0, 2$ and $y_1$ gets $5, 45$ .

Step 1 of 4

The calculator follows the steps. Feel free to type in it too.

Table of g, but They Ask About f

When the table gives a transformed function, define the unknown one, build the given one from it, and regress on the table values. By hand: about 3 min.

Question

The table shows three values of

x

and their corresponding values of

g(x)

, where

g(x) = \frac{f(x)}{x+3}

and

f

is a linear function. What is the

y

-intercept of the graph of

y = f(x)

\begin{array}{|c|c|} \hline x & g(x) \\ \hline -21 & 2 \\ \hline -9 & 0 \\ \hline 15 & 4 \\ \hline \end{array}

A. $(0, -9)$
B. $(0, 3)$
C. $(0, 9)$
D. $(0, 27)$

what we knowwhat we need

Solving it in Desmos

1.The table is about $g$ , but the question asks about $f$ . Define the unknown $f$ first as a line: $f(x) = mx + b$ . Then build $g$ from it exactly as the problem says: $g(x) = \frac{f(x)}{x + 3}$ .

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

When the Curve Misses the Points: Add 0.0001

Sometimes a tilde fit comes back with ugly numbers and a curve that misses your points. A tiny nudge fixes it. By hand: about 3 min.

Question

The function

h

is defined by

h(x) = -\sqrt{x^2 + bx + c}

, where

b

and

c

are constants. In the

xy

-plane, the graph of

y = h(x)

contains the points

(2, 0)

and

(0, -\sqrt{238})

. If

h(m) = 0

, what is the greatest possible value of

m

what we knowwhat we need

Solving it in Desmos

1.Click $+$ and pick table. Enter the points: $x_1$ gets $2, 0$ and $y_1$ gets $0, -\sqrt{238}$ .

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

Scary Questions: Meet Every Condition, Then Read the Answer

For a question you don't recognize: list every condition, make Desmos satisfy all of them with any numbers that fit, and type what's asked. By hand: about 4 min.

Question

The function

q

is defined by

q(x) = a|x - 9|^2 - 87|x - 9| + b

, where

a

and

b

are constants, and

a > b > 87

. If

q(639) = h

and

q(-621) = k

, where

h

and

k

are constants, what is the value of

9(-639)^{h-k} + 621(9)^{k-h}

what we knowwhat we need

Solving it in Desmos

1.List the conditions: $q(x)$ is that formula, $a > b > 87$ , $h = q(639)$ , $k = q(-621)$ . That's all Desmos has to obey. Start by typing $q(x)$ .

Step 1 of 5

The calculator follows the steps. Feel free to type in it too.

What Desmos can't do

Desmos handles about 80% of SAT Math. For the other 20% you still need the fundamentals:

Geometry. SOH-CAH-TOA, angle theorems (vertical, corresponding, supplementary), triangle congruence, circle angle and arc theorems (circle equations do work in Desmos), 3D geometry.
Word-heavy math. Questions built on words like "twice", "reciprocal" or "consecutive integers". Turning English into math is on you.
Symbolic manipulation. Rewriting a formula is still algebra. Desmos only checks your pick with test numbers (trick 14).
Trig concepts. Unit circle and radian reasoning, like why sin x = cos(90° - x). Desmos computes sin and cos (switch to degrees, trick 15), but the idea is on you.

Frequently asked questions

Will College Board remove Desmos from the SAT?

There is no sign of that. They have been tweaking question types so the calculator matters less, though. Learn Desmos first, then keep the algebra as a backup.

Can I really get 750+ on SAT Math using mostly Desmos?

Yes, many students score 750 to 790 with Desmos as their main tool. The trick is knowing when to use it and when to solve by hand (geometry, trig). The 21 techniques above cover most question types where Desmos helps.

What if Desmos crashes or freezes during the test?

Close the calculator and reopen it from the toolbar. If it stays frozen, fall back on solving by hand, which is why the hand method is shown under every trick.

Should I use Desmos on Module 1 or only Module 2?

Both. Module 1 questions are easy and go faster with Desmos, which saves time for Module 2. On the hard Module 2 questions, sliders, regression and intersections are worth the most.

How long does it take to learn all these tricks?

About 4 to 6 hours of focused practice. Start with graphing (tips 1 to 3), then sliders and solution counts (4 to 7), then the tilde tricks (8 to 16), then tables (17 to 20). Save trick 21 for last. Practice each one on 5 to 10 similar questions until it's automatic.

Now practice

Every question on PlaynTest has the same built-in Desmos calculator, so you can use these tricks on real SAT-style questions. Pick a topic in the question bank or take a practice set.

Thanks for reading this far. Use code DESMOS30 for 30% off PlaynTest Plus. You can start free and upgrade only if you want more.

See plans

The Desmos SAT Guide: 21 tricks for a higher Math score

21 tricks · about 3 min each · Updated October 2026

Why bother: about 80% of SAT Math can be solved with Desmos, it saves 2 to 3 minutes per question on average, and 750+ is a realistic score once you know it well.

Before you start: typing in Desmos

Tilde ~ is Shift plus the key left of 1. On a Russian or Kazakh layout that key is Ё, so switch to English first.

Subscript x₁: type x_1, then press the right arrow to leave the subscript.

Slider: type a line with a new letter, like y = 2x + k, and click the “k” button Desmos shows under it.

Tilde lines also print statistics and residuals. Ignore them and read only the values of your letters.

Exponent with a sum: after ^ type ( first. Otherwise the + or - jumps out of the exponent.

Fraction with several terms on top: select the whole top part, then press /.

Skip the keypad: typing sqrt, cbrt, nthroot or pi turns into the symbol.

No copy and paste in Bluebook. Type a long expression once as f(x) = ... and reuse f(2), f(x+3) and so on.

Ugly decimal = check again. SAT answers are almost always whole numbers or clean fractions. A result like 3.71829 usually means a typo or a missed condition.

Test numbers: when you pick values for letters, never use 0 or 1. They hide mistakes, because 1² = 1 and 0 · anything = 0.

What Desmos can't do

Desmos handles about 80% of SAT Math. For the other 20% you still need the fundamentals:

Geometry. SOH-CAH-TOA, angle theorems (vertical, corresponding, supplementary), triangle congruence, circle angle and arc theorems (circle equations do work in Desmos), 3D geometry.

Word-heavy math. Questions built on words like "twice", "reciprocal" or "consecutive integers". Turning English into math is on you.

Symbolic manipulation. Rewriting a formula is still algebra. Desmos only checks your pick with test numbers (trick 14).

Trig concepts. Unit circle and radian reasoning, like why sin x = cos(90° - x). Desmos computes sin and cos (switch to degrees, trick 15), but the idea is on you.

Frequently asked questions

Will College Board remove Desmos from the SAT?

There is no sign of that. They have been tweaking question types so the calculator matters less, though. Learn Desmos first, then keep the algebra as a backup.

Can I really get 750+ on SAT Math using mostly Desmos?

What if Desmos crashes or freezes during the test?

Close the calculator and reopen it from the toolbar. If it stays frozen, fall back on solving by hand, which is why the hand method is shown under every trick.

Should I use Desmos on Module 1 or only Module 2?

Both. Module 1 questions are easy and go faster with Desmos, which saves time for Module 2. On the hard Module 2 questions, sliders, regression and intersections are worth the most.

How long does it take to learn all these tricks?

Now practice

Every question on PlaynTest has the same built-in Desmos calculator, so you can use these tricks on real SAT-style questions. Pick a topic in the question bank or take a practice set.

Thanks for reading this far. Use code DESMOS30 for 30% off PlaynTest Plus. You can start free and upgrade only if you want more.

See plans