SAT Math Cheat Sheet: Formulas, Skills, Problem Types

Build a fast SAT Math review system by focusing on the formulas you actually use, the algebra and graph skills behind most questions, and the repeatable problem types that show up every test. Use this sheet to decide what to memorize, what to practice, and how to pick the quickest method under time pressure.

SAT Math is rarely about doing long math. It is about recognizing the situation fast, choosing the right tool, and not falling for a trap answer. If you can spot the form of an equation, read a graph like a sentence, and keep a short list of geometry facts ready, you can grab a lot of points quickly. Here’s the layout of what the test really covers and how to use this sheet like a checklist, not a textbook. Let’s start with the big map:

What SAT Math covers fast

The SAT groups most questions into a few buckets, and each bucket has a small set of repeat skills.

Heart of Algebra is linear equations, inequalities, and systems.
Problem Solving and Data Analysis is ratios, percent, units, tables, and basic stats.
Passport to Advanced Math is quadratics, expressions, and functions.
Geometry and Trig is mostly right triangles, circles, and coordinate geometry.

Calculator rules are simpler than they feel. Use it when arithmetic is the only barrier, not when the structure is the point. If the problem is testing a relationship, the calculator often slows you down.

Fast wins
Most points come from linear equations, functions and graphs, quadratics basics, and right triangles.

Algebra essentials to recognize quickly

A lot of SAT algebra is pattern recognition. When you recognize the form, you know what the question is probably asking.

Slope is the rate of change, computed by $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$ . Slope intercept form is $y=mx+b$ , where $b$ is the $y$ -intercept. Standard form is $Ax+By=C$ , which is great for intercepts and quick rearranging.

Systems usually want the intersection point. If one equation is already solved for a variable, substitution is clean. If both are in standard form, elimination is usually faster.

Inequalities behave like equations, except one move is different. When you multiply or divide by a negative number, the inequality sign flips.

A function is just an input output rule. Function notation means $f(x)$ is the output when the input is $x$ . If they ask for $f(3)$ , you plug in $x=3$ and simplify.

The fastest way to connect these is to see the common forms side by side:

Advanced algebra patterns that repeat

Featured snippet basics that cover most advanced algebra questions.

Quadratic questions usually come in three jobs. Solve for zeros, rewrite to reveal the vertex, or match a graph shift. The most useful forms are:

Factored form $y=a(x-r_1)(x-r_2)$ shows the zeros $r_1,r_2$ .
Vertex form $y=a(x-h)^2+k$ shows the vertex $(h,k)$ .
Standard form $y=ax^2+bx+c$ shows $y$ -intercept $c$ .

Factoring means rewriting a polynomial as a product, so you can use the zero product idea. If $ab=0$ , then $a=0$ or $b=0$ . That is why factoring helps solve equations.

Exponent rules show up constantly. Keep these tight in your head.

$x^a\cdot x^b=x^{a+b}$
$\frac{x^a}{x^b}=x^{a-b}$
$(x^a)^b=x^{ab}$
$x^{-a}=\frac{1}{x^a}$
$\sqrt{x}=x^{1/2}$

Rational expression means a fraction with algebra in it. Your two default moves are to factor and cancel, and to find a common denominator when adding or subtracting. Always note domain restrictions. Anything that makes a denominator $0$ is not allowed.

Parabola shifts are easiest when you can see how $a,h,k$ change the shape:

Word problems as translation templates

Word problems get easier when you turn phrases into operations consistently.

of means multiply
per means divide
total means add
difference means subtract
at least means $\ge$
at most means $\le$

Rates follow one core structure. Rate means per, so it becomes a fraction. Distance problems often use $d=rt$ . Work problems often use $\frac{1}{T}=\frac{1}{a}+\frac{1}{b}$ when two people together finish in time $T$ .

Percent problems are usually one of two types.

Percent of a number. Part $=$ percent $\times$ whole.
Percent change. New $=$ old $\times(1\pm p)$ where $p$ is the decimal.

Mixtures are about totals. If you mix two solutions, total amount and total pure ingredient both add. Units matter more than the numbers. If units do not match, convert before solving.

A few mini templates cover most of what you will see. Let’s reveal them compactly:

Data and graphs quick reference

Graph questions reward slow reading of axes and fast recognition of what is being compared.

Scatterplots usually ask about direction, strength, and outliers. A line of best fit is about trend, not exact hits. If the question asks for a prediction, use the line, not a random point.

Two way tables ask conditional probability, which means given. Translate given into a smaller denominator. For example, given it is a junior means your denominator is the junior row total, not the whole table.

Stats basics that show up often:

Mean is average, $\frac{\text{sum}}{n}$ .
Median is the middle after sorting.
Range is max minus min.
A boxplot shows min, $Q_1$ , median, $Q_3$ , max.

Probability on the SAT is usually simple counting. Probability is $\frac{\text{desired}}{\text{total}}$ . If choices are independent, multiply probabilities.

Visual examples make these patterns stick faster:

Geometry formulas you actually use

Most geometry points come from a short formula set plus a few triangle facts.

Areas and perimeters:

Rectangle area $A=lw$
Triangle area $A=\frac{1}{2}bh$
Circle area $A=\pi r^2$
Circle circumference $C=2\pi r$

Volumes:

Rectangular prism $V=lwh$
Cylinder $V=\pi r^2h$
Cone $V=\frac{1}{3}\pi r^2h$
Sphere $V=\frac{4}{3}\pi r^3$

Coordinate geometry shows up as geometry in disguise. Midpoint is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ . Distance is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . A circle in the coordinate plane often uses $(x-h)^2+(y-k)^2=r^2$ .

Triangle essentials:

Angles in a triangle sum to $180^\circ$ .
The Pythagorean theorem is $a^2+b^2=c^2$ for right triangles.

Common trap
Mixing radius and diameter. If they give diameter, $r=\frac{d}{2}$ first.

Use the compare sheet to match shapes to formulas and typical givens:

Trigonometry that appears on SAT

SAT trig is mostly right triangle trig, plus knowing what radians are.

SOHCAHTOA is the mapping from an angle $\theta$ to side ratios in a right triangle.

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$
$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$

Special right triangles are shortcut factories.

In a $45-45-90$ , legs are equal and hypotenuse is $\text{leg}\cdot\sqrt{2}$ .
In a $30-60-90$ , short leg, long leg, hypotenuse follow $x,x\sqrt{3},2x$ .

Radians are another unit for angle. The key link is $\pi$ radians equals $180^\circ$ . So $90^\circ$ is $\frac{\pi}{2}$ , $60^\circ$ is $\frac{\pi}{3}$ , $45^\circ$ is $\frac{\pi}{4}$ .

Quick recall beats rereading, so drill them as prompts:

Test day problem types and tactics

The SAT rewards flexible strategy choice. If you feel stuck, switch methods instead of pushing harder.

Plugging in numbers works when there are variables but no specific values. Pick easy numbers that fit constraints like even, positive, or nonzero. Then test answer choices by computing.

Backsolving works when the answers are numbers. Start with a middle option, often C, and see if it is too big or too small. This is especially good for word problems.

Answer choice traps are predictable.

They give $x$ but you solved for $2x$ .
They want the positive solution but you picked the negative.
They use a common arithmetic slip like forgetting to distribute a negative.

Time triage matters. If a question is taking longer than it should, mark it, guess strategically, and move on. You can often return with a clearer head and still finish.

If you want help picking the quickest method for a specific problem type, we can choose it interactively:

Next step 7 day quick review plan

A week is enough to sharpen recognition if you keep the work narrow and repeated.

Day 1. Build your formula page from this sheet. Memorize the geometry and triangle facts, and practice 15 linear equation questions.

Day 2. Functions and graphs. Focus on slope, intercepts, and reading what the axes mean. Do 10 graph questions and explain each answer in one sentence.

Day 3. Quadratics and exponent rules. Practice factoring, vertex form meaning, and zeros.

Day 4. Word problems. Drill percent change, rates, and unit conversions. Write the equation before calculating.

Day 5. Data analysis. Do scatterplots, two way tables, mean and median, and simple probability.

Day 6. Mixed timed set. Two short sets, then review mistakes by category, not by question.

Day 7. Full practice or a long mixed set. Recheck your top three error types and rewrite your personal trap list.

Score lever
Review mistakes by pattern. One fixed pattern can save multiple future questions.

Pick two weak areas and commit to 20 focused questions each. The goal is to reduce surprise, not learn everything.