# SAT math formulas: what the sheet gives you and what to know cold

> Use this full Digital SAT Math formula inventory to separate the geometry reference sheet from the algebra, rate, percent, and probability tools to know.

Published 2026-07-17 | Math | StudyHall

Canonical: https://trystudyhall.com/blog/sat-math-formulas

The SAT Math reference sheet is useful, but it has a narrow job. It supplies a compact set of geometry facts. Most of the formulas that run the rest of the section, including linear forms, quadratic tools, exponent rules, percent change, rates, and basic probability, still have to be available without a scavenger hunt.

The built-in SAT reference sheet gives you common geometry formulas and special right-triangle relationships. You should know the main algebra, exponent, rate, percent, and probability formulas cold because they are not the sheet's focus.

**Key takeaways:**
- Use the sheet for **geometry lookup**, especially area, circumference, volume, the Pythagorean theorem, and special right triangles.
- Know the linear forms $y=mx+b$ and $y-y_1=m(x-x_1)$, plus slope as change in $y$ over change in $x$.
- Know how quadratic form changes the visible feature: standard form supports the quadratic formula, factored form shows roots, and vertex form shows the turning point.
- Treat exponent, percent, rate, average speed, and probability rules as translation tools, not decorative facts.
- Recognition matters more than recitation. Name what the variables mean before substituting.

## Which SAT math formulas are on the reference sheet?

| Given on the sheet | What you still must recognize | Typical use |
| --- | --- | --- |
| Circle area and circumference | Whether the given length is a radius or diameter | Find a missing length, area, or circumference |
| Rectangle and triangle area | The base and perpendicular height | Translate a diagram or word problem into area |
| Pythagorean theorem | Which side is the hypotenuse | Connect side lengths in a right triangle |
| Special right-triangle relationships | When the angle pattern makes them relevant | Find a side without rebuilding the ratio |
| Common solid volumes | Units and which measurement each variable represents | Find volume or solve backward for a dimension |
*The sheet supplies formulas. It does not label the diagram, choose the formula, or notice that a diameter has been handed the radius's job.*

The [SAT geometry formula guide](https://trystudyhall.com/blog/sat-geometry-formulas) covers this sheet in depth, including angles, circles, triangles, and solids. This article has a wider scope: it inventories the formula tools used across the full Math section, including the algebra and data rules that are not supplied as a geometry lookup table.

## Which algebra formulas should you know cold?

| Tool | Formula or form | What it reveals |
| --- | --- | --- |
| Slope | $m=\frac{y_2-y_1}{x_2-x_1}$ | Rate of change between two points |
| Slope-intercept form | $y=mx+b$ | Slope and vertical intercept |
| Point-slope form | $y-y_1=m(x-x_1)$ | A line from one point and its slope |
| Quadratic formula | $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ | Roots of $ax^2+bx+c=0$ |
| Discriminant | $b^2-4ac$ | Whether a quadratic has two, one, or no real roots |
| Vertex form | $y=a(x-h)^2+k$ | Vertex $(h,k)$ and opening direction |
*Forms are views of the same relationship. Choose the view that exposes the feature the question asks for.*

Also know the exponent rules: multiplying like bases adds exponents, dividing subtracts them, raising a power to a power multiplies them, and a negative exponent takes the reciprocal. These rules are especially useful when answer choices look different but represent the same quantity. The broader [SAT Math strategy guide](https://trystudyhall.com/blog/sat-math-strategies) explains when algebra, a graph, backsolving, or the built-in calculator is the cleaner representation.

## Which rate, percent, and probability formulas matter?

| Question type | Core relationship | Common mistake |
| --- | --- | --- |
| Percent change | $\frac{N-O}{O}\times100$ | Dividing by the new value instead of the original value |
| Growth or decay | $N=O(1+r)$ or $N=O(1-r)$ | Using the percent rate without converting it to a decimal rate |
| Distance, rate, time | $D=RT$ | Mixing units or solving for the wrong variable |
| Average speed | $D_{\mathrm{total}}/T_{\mathrm{total}}$ | Averaging two speeds when the travel times differ |
| Basic probability | $P=F/T$ | Using the wrong total or double-counting outcomes |
*Here $N$ is new, $O$ is original, $D$ is distance, $R$ is rate, $T$ is time, and $F/T$ means favorable outcomes over total possible outcomes.*

> **Watch out: Average speed has one denominator** Add the entire distance and divide by the entire time. The ordinary mean of two speeds works only under special conditions, so it is a poor default and an excellent trap answer.

## How should you memorize SAT math formulas?

1. **Sort by job.** Group formulas by what they reveal: line, root, vertex, repeated growth, rate, or chance. A job is easier to retrieve than an isolated symbol string.
2. **Recall before looking.** Cover the formula, write it from memory, and state what every variable means. Recognition after opening a note is not retrieval.
3. **Attach one cue.** Pair each formula with a phrase from a question, such as rate of change, exactly one solution, percent increase, or average speed.
4. **Use mixed questions.** Mix formula families so you must select the relationship before using it. The test does not provide a chapter heading above each item.
5. **Check the result.** Substitute, inspect units, or graph the relationship. A memorized formula can still be used with impressive precision on the wrong quantity.

## Can you identify the useful quadratic form?

**Example: Nonlinear functions.**

The graph of $y=x^2-6x+5$ has a minimum value. Which equivalent form makes that minimum easiest to identify?

- A) $y=(x-1)(x-5)$
- B) $y=(x-3)^2-4$
- C) $y=x(x-6)+5$
- D) $y=(x+3)^2+4$

**Answer:** B. Vertex form $y=a(x-h)^2+k$ displays the vertex directly. In $y=(x-3)^2-4$, the squared term cannot be negative, so its smallest value is zero and the minimum value of the function is negative 4. The factored form in choice A makes the roots easy to see, but the question asks for the minimum. Choice C is equivalent but does not expose the vertex, and choice D is not equivalent to the original expression.

**[Practice choosing the formula](https://trystudyhall.com/bank)**: Run a mixed Math set, name the requested feature first, and use Click to inspect the first formula choice that goes off course.

## FAQ

### What math formulas are given on the SAT?

The Digital SAT reference sheet supplies common geometry formulas, including circle, area, right-triangle, special-triangle, and solid-volume relationships. It does not serve as a complete algebra and data formula list.

### Do you need to memorize the quadratic formula for the SAT?

Yes, it is useful to know the quadratic formula and discriminant cold. You should also recognize when factoring, vertex form, or a graph exposes the requested feature with less work.

### Do you need to memorize SAT geometry formulas?

Many common geometry formulas are printed on the reference sheet. You still need to recognize the relevant shape, label its measurements correctly, and know relationships such as angle rules and basic trigonometry.

### What is the best way to learn SAT math formulas?

Group formulas by purpose, recall them without looking, connect each one to a question cue, and choose among them in mixed practice. Always state what the variables represent before substituting.

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