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SAT Math Formulas Cheat Sheet

Build a fast SAT math formula toolkit by knowing what the test gives you, what it does not, and how to pick the right equation under time pressure. Use the same handful of algebra, geometry, and data formulas across most questions with fewer avoidable mistakes.

Some SAT questions feel hard only because you cannot recall the right SAT math formulas fast enough. You might know the idea, like slope or area, but freeze on the exact setup. This cheat sheet keeps the core algebra, geometry, and data analysis formulas in one place, plus the common traps when the formula is not given.

What SAT gives you vs what you must know

The SAT provides a reference sheet, but it is not a full SAT math formulas cheat sheet. It leans heavily toward geometry and a few key facts, while many everyday algebra moves are assumed knowledge.

What you can typically rely on being provided includes:

Circle area and circumference
Triangle area
Volume formulas for common solids
The Pythagorean Theorem
Special right triangle side ratios

What you should still memorize because you use it constantly:

Line formulas like $y=mx+b$ and point slope
Exponent rules and common factoring patterns
Percent and average formulas
Coordinate geometry distance and midpoint

Trap check
When a problem says circle and gives diameter, do not plug it in as $r$ .

To make the split easy to scan and connect to common question types, use this map:

Algebra essentials you use every set

If you can set up a line, interpret a function, and solve a system, you cover a huge chunk of SAT Math. The formulas are short. The hard part is remembering what each symbol means and what the question is actually asking for.

Lines and slope

Slope is the rate of change, written $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$ . Positive slope rises left to right, negative slope falls.

Common line forms:

Slope intercept form: $y=mx+b$ where $b$ is the $y$ intercept
Point slope form: $y-y_1=m(x-x_1)$ when you have a point and a slope
Standard form: $Ax+By=C$ often used for systems and quick intercepts

A quick connection that saves time is that the $x$ intercept is where $y=0$ and the $y$ intercept is where $x=0$ .

Systems and function notation

A system is two or more equations you solve together. The solution is the point that satisfies all equations at once. You can solve by substitution, elimination, or graphing, and SAT questions often only need one of those.

A function is a rule that assigns each input exactly one output. If $f(x)=2x+3$ , then $f(4)=11$ . The most common move is to substitute the input value everywhere you see $x$ .

The terms get mixed up under pressure, so keep a tight glossary nearby:

Exponents, radicals, and factoring patterns

Exponent rules and factoring patterns are SAT multipliers. They show up in algebra, quadratics, and even word problems that hide the algebra inside.

Core exponent rules:

$a^m\cdot a^n=a^{m+n}$
$\frac{a^m}{a^n}=a^{m-n}$ for $a\neq0$
$(a^m)^n=a^{mn}$
$(ab)^n=a^nb^n$

A radical is a root, like $\sqrt{x}$ . Two must know simplifications:

$\sqrt{ab}=\sqrt{a}\sqrt{b}$ for $a,b\ge0$
$\sqrt{a^2}=|a|$ , which matters when $a$ could be negative

Factoring is reverse distributing. On the SAT, it is often used to find zeros, simplify rational expressions, or rewrite something to cancel. The highest value patterns are the special products, since they also let you expand quickly.

Compare the patterns side by side so your eyes learn them:

Fast check
If you see $x^2$ and a constant with subtraction, try difference of squares first.

Quadratics and polynomial must knows

A quadratic is any function that can be written as $ax^2+bx+c$ with $a\neq0$ . Most SAT quadratic questions are about one of four things: roots, vertex, intercepts, or how shifting changes the graph.

A compact cheat sheet for quadratics:

Standard form: $y=ax^2+bx+c$
Factored form: $y=a(x-r_1)(x-r_2)$ so the zeros are $x=r_1$ and $x=r_2$
Vertex form: $y=a(x-h)^2+k$ so the vertex is $(h,k)$
Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Discriminant is the expression $b^2-4ac$ . It tells you how many real solutions:

$b^2-4ac>0$ gives two real roots
$b^2-4ac=0$ gives one real root
$b^2-4ac<0$ gives no real roots

A visual makes it much easier to connect each form to what you can read off quickly:

Geometry formulas you will actually use

Geometry on the SAT is less about memorizing dozens of shapes and more about not mixing up what each variable represents, especially radius versus diameter and slant height versus vertical height.

Angles and triangles

Triangle angle sum: $A+B+C=180^\circ$ .

Pythagorean Theorem for right triangles: $a^2+b^2=c^2$ .

Special right triangles you should memorize:

$45^\circ\text{–}45^\circ\text{–}90^\circ$ has sides $x,x,x\sqrt2$
$30^\circ\text{–}60^\circ\text{–}90^\circ$ has sides $x,x\sqrt3,2x$

Triangle area: $A=\frac12 bh$ where $h$ is perpendicular to the base.

Circles, area, and volume

Circle circumference: $C=2\pi r$ .

Circle area: $A=\pi r^2$ .

A common SAT move is to convert diameter $d$ to radius with $r=\frac d2$ before using circle formulas.

Coordinate geometry

Distance between $(x_1,y_1)$ and $(x_2,y_2)$ :

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Midpoint:

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

Use this table to match each shape to the formula and the classic unit mistakes:

Units win points
Area uses square units, volume uses cubic units, and perimeter uses plain units.

Data, statistics, and probability basics

SAT data questions reward careful reading and one clean formula at a time.

Core averages:

Mean: $\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$
Median is the middle value when ordered, or the average of the two middle values
Weighted average: $\frac{\sum(w\cdot x)}{\sum w}$

Percent change is one of the most common traps. The formula is:

\text{percent change}=\frac{\text{new}-\text{original}}{\text{original}}\times100\%

An increase of $p\%$ and then a decrease of $p\%$ does not return you to the start, because the second change uses a different original.

Basic probability:

P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}

If events are independent, multiply probabilities.

Seeing how one value shift changes mean versus median and how percent changes compound builds the right instinct:

Test day formula use that saves time

Most time loss is not from missing a formula. It is from choosing the wrong one, plugging in the wrong number, or carrying units incorrectly. A reliable method is to label what each number represents before doing any arithmetic. If the question gives diameter, write d=... and convert to r=... before you touch $\pi r^2$ .

A simple accuracy workflow:

Identify what the question asks for in one noun phrase, like y intercept or surface area
Write the formula with symbols first, then substitute numbers
Check units before final arithmetic, especially for area and volume
Use estimation to sanity check, like whether an average should be between the extremes

The most common SAT formula mistakes are predictable, so it helps to keep a short fix list ready:

Next step practice plan that makes formulas stick

Build your own one page sheet from this cheat sheet, but only after you solve problems. Every time you miss a question, add the exact formula or pattern that would have made it easy, plus one five word reminder like diameter to radius first.

A lightweight weekly loop:

Do a small mixed set and mark every question where setup felt unclear
Add one line to your personal sheet, then redo that problem from scratch
Drill two patterns at a time, like percent change and slope, until setup is automatic

You will remember formulas best when they are tied to a mistake you do not want again.

Common SAT math formula questions learners ask

Was this lesson helpful?

Dive Deeper

Generate a follow-up sub-lesson on any aspect of this topic

Guide complete

SAT Math Formulas Cheat Sheet

Build a fast SAT math formula toolkit by knowing what the test gives you, what it does not, and how to pick the right equation under time pressure. Use the same handful of algebra, geometry, and data formulas across most questions with fewer avoidable mistakes.

What SAT gives you vs what you must know

The SAT provides a reference sheet, but it is not a full SAT math formulas cheat sheet. It leans heavily toward geometry and a few key facts, while many everyday algebra moves are assumed knowledge.

What you can typically rely on being provided includes:

Circle area and circumference
Triangle area
Volume formulas for common solids
The Pythagorean Theorem
Special right triangle side ratios

What you should still memorize because you use it constantly:

Line formulas like $y=mx+b$ and point slope
Exponent rules and common factoring patterns
Percent and average formulas
Coordinate geometry distance and midpoint

Trap check
When a problem says circle and gives diameter, do not plug it in as $r$ .

To make the split easy to scan and connect to common question types, use this map:

Algebra essentials you use every set

Lines and slope

Slope is the rate of change, written $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$ . Positive slope rises left to right, negative slope falls.

Common line forms:

Slope intercept form: $y=mx+b$ where $b$ is the $y$ intercept
Point slope form: $y-y_1=m(x-x_1)$ when you have a point and a slope
Standard form: $Ax+By=C$ often used for systems and quick intercepts

A quick connection that saves time is that the $x$ intercept is where $y=0$ and the $y$ intercept is where $x=0$ .

Systems and function notation

A function is a rule that assigns each input exactly one output. If $f(x)=2x+3$ , then $f(4)=11$ . The most common move is to substitute the input value everywhere you see $x$ .

The terms get mixed up under pressure, so keep a tight glossary nearby:

Exponents, radicals, and factoring patterns

Exponent rules and factoring patterns are SAT multipliers. They show up in algebra, quadratics, and even word problems that hide the algebra inside.

Core exponent rules:

$a^m\cdot a^n=a^{m+n}$
$\frac{a^m}{a^n}=a^{m-n}$ for $a\neq0$
$(a^m)^n=a^{mn}$
$(ab)^n=a^nb^n$

A radical is a root, like $\sqrt{x}$ . Two must know simplifications:

$\sqrt{ab}=\sqrt{a}\sqrt{b}$ for $a,b\ge0$
$\sqrt{a^2}=|a|$ , which matters when $a$ could be negative

Compare the patterns side by side so your eyes learn them:

Fast check
If you see $x^2$ and a constant with subtraction, try difference of squares first.

Quadratics and polynomial must knows

A quadratic is any function that can be written as $ax^2+bx+c$ with $a\neq0$ . Most SAT quadratic questions are about one of four things: roots, vertex, intercepts, or how shifting changes the graph.

A compact cheat sheet for quadratics:

Standard form: $y=ax^2+bx+c$
Factored form: $y=a(x-r_1)(x-r_2)$ so the zeros are $x=r_1$ and $x=r_2$
Vertex form: $y=a(x-h)^2+k$ so the vertex is $(h,k)$
Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Discriminant is the expression $b^2-4ac$ . It tells you how many real solutions:

$b^2-4ac>0$ gives two real roots
$b^2-4ac=0$ gives one real root
$b^2-4ac<0$ gives no real roots

A visual makes it much easier to connect each form to what you can read off quickly:

Geometry formulas you will actually use

Geometry on the SAT is less about memorizing dozens of shapes and more about not mixing up what each variable represents, especially radius versus diameter and slant height versus vertical height.

Angles and triangles

Triangle angle sum: $A+B+C=180^\circ$ .

Pythagorean Theorem for right triangles: $a^2+b^2=c^2$ .

Special right triangles you should memorize:

$45^\circ\text{–}45^\circ\text{–}90^\circ$ has sides $x,x,x\sqrt2$
$30^\circ\text{–}60^\circ\text{–}90^\circ$ has sides $x,x\sqrt3,2x$

Triangle area: $A=\frac12 bh$ where $h$ is perpendicular to the base.

Circles, area, and volume

Circle circumference: $C=2\pi r$ .

Circle area: $A=\pi r^2$ .

A common SAT move is to convert diameter $d$ to radius with $r=\frac d2$ before using circle formulas.

Coordinate geometry

Distance between $(x_1,y_1)$ and $(x_2,y_2)$ :

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Midpoint:

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

Use this table to match each shape to the formula and the classic unit mistakes:

Units win points
Area uses square units, volume uses cubic units, and perimeter uses plain units.

Data, statistics, and probability basics

SAT data questions reward careful reading and one clean formula at a time.

Core averages:

Mean: $\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$
Median is the middle value when ordered, or the average of the two middle values
Weighted average: $\frac{\sum(w\cdot x)}{\sum w}$

Percent change is one of the most common traps. The formula is:

\text{percent change}=\frac{\text{new}-\text{original}}{\text{original}}\times100\%

An increase of $p\%$ and then a decrease of $p\%$ does not return you to the start, because the second change uses a different original.

Basic probability:

P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}

If events are independent, multiply probabilities.

Seeing how one value shift changes mean versus median and how percent changes compound builds the right instinct:

Test day formula use that saves time

A simple accuracy workflow:

Identify what the question asks for in one noun phrase, like y intercept or surface area
Write the formula with symbols first, then substitute numbers
Check units before final arithmetic, especially for area and volume
Use estimation to sanity check, like whether an average should be between the extremes

The most common SAT formula mistakes are predictable, so it helps to keep a short fix list ready:

Guide complete

Related content

SAT Math Formulas Cheat Sheet

What SAT gives you vs what you must know

Algebra essentials you use every set

Lines and slope

Systems and function notation

Exponents, radicals, and factoring patterns

Quadratics and polynomial must knows

Geometry formulas you will actually use

Angles and triangles

Circles, area, and volume

Coordinate geometry

Data, statistics, and probability basics

Test day formula use that saves time

Next step practice plan that makes formulas stick

Common SAT math formula questions learners ask

Guide complete

Related content

SAT Math Formulas Cheat Sheet

What SAT gives you vs what you must know

Algebra essentials you use every set

Lines and slope

Systems and function notation

Exponents, radicals, and factoring patterns

Quadratics and polynomial must knows

Geometry formulas you will actually use

Angles and triangles

Circles, area, and volume

Coordinate geometry

Data, statistics, and probability basics

Test day formula use that saves time

Next step practice plan that makes formulas stick

Common SAT math formula questions learners ask