Common Formulas Cheat Sheet for SAT Math

Quick Answer: The SAT Math section provides a basic reference sheet for geometry, but memorizing essential algebra, advanced math, and trigonometry formulas is critical for pacing. The best strategy is to memorize formulas like the quadratic equation and vertex form, while heavily relying on the built-in Desmos calculator to bypass complex algebraic memorization.

mindmap
  root((SAT Math Formulas))
    Algebra
      Slope Formula
      Slope-Intercept Form
      Point-Slope Form
    Advanced Math
      Vertex Form
      Quadratic Formula
      Exponential Growth
    Geometry & Trig
      Circle Equation
      SOH CAH TOA
      Radians to Degrees
    Problem Solving
      Mean vs Median
      Probability

What Is the Common Formulas Cheat Sheet for SAT Math?

While the College Board provides a built-in reference sheet on the Digital SAT, it is surprisingly limited. The official reference sheet only gives you formulas for the area and volume of basic geometric shapes, Pythagorean theorem, and special right triangles. It completely ignores Algebra, Advanced Math, and Data Analysis—which make up over 80% of the test.

To succeed on the 2026 Digital SAT format, you need your own mental "cheat sheet" of essential formulas. More importantly, because the test features an integrated graphing calculator, your cheat sheet should focus on formulas that help you set up equations quickly, allowing Desmos to do the heavy lifting for the actual calculations.

Building a strong foundation with these formulas, combined with practicing on Khan Academy SAT, will significantly improve your speed and accuracy across both math modules.

The Strategy: Your Essential Formula Cheat Sheet

Instead of trying to memorize every math concept you've learned since middle school, focus on these high-yield formulas broken down by test domain.

1. Linear Equations (Algebra)

Linear equations are the foundation of the SAT. You must know how to translate lines on a graph into equations.

• Slope Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ (Used to find the steepness between two points).
• Slope-Intercept Form: $y = mx + b$ (Where $m$ is slope and $b$ is the y-intercept).
• Point-Slope Form: $y - y_1 = m(x - x_1)$ (Incredibly useful when the SAT gives you a random point and a slope).

2. Quadratics (Advanced Math)

Quadratics appear frequently in Module 2. Knowing these forms allows you to quickly identify key features of a parabola without doing any math.

• Standard Form: $y = ax^2 + bx + c$ (The y-intercept is always $c$).
• Vertex Form: $y = a(x - h)^2 + k$ (The vertex is $(h, k)$. Remember the sign of $h$ flips!).
• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ (Use this when you can't factor easily).
• The Discriminant: $b^2 - 4ac$ (If $>0$, 2 real solutions. If $=0$, 1 real solution. If $<0$, no real solutions).

3. Exponentials (Advanced Math)

Word problems involving population growth, bacteria, or bank accounts will almost always use this formula.

• Exponential Growth/Decay: $y = a(1 \pm r)^t$
  • $a$ = initial amount
  • $r$ = rate of change (as a decimal)
  • $t$ = time
  • Use $+$ for growth and $-$ for decay.

4. Circles (Geometry)

Circle questions on the SAT rarely ask for area; they ask for the graph equation.

• Standard Circle Equation: $(x - h)^2 + (y - k)^2 = r^2$
  • Center is $(h, k)$ and radius is $r$.

5. Trigonometry (Geometry & Trig)

Trig on the SAT is almost entirely based on right triangles.

• SOH CAH TOA:
  • $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$
  • $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
  • $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$
• Complementary Angle Rule: $\sin(x) = \cos(90^\circ - x)$

6. Statistics (Problem Solving & Data Analysis)

• Mean (Average): $\frac{\text{Sum of all values}}{\text{Number of values}}$
• Probability: $\frac{\text{Number of desired outcomes}}{\text{Total number of possible outcomes}}$

To see how to bypass many of these formulas using the built-in calculator, check out our Desmos Tricks Complete Guide.

Key Takeaways

• The SAT reference sheet is not enough: It only covers basic geometry. You must memorize your own algebra and advanced math formulas.
• Signs matter: The most common mistakes across all math domains involve flipping positive and negative signs, especially in vertex form and circle equations.
• Desmos is your backup: If you forget the quadratic formula or how to factor, you can always graph the equation in Desmos to find the roots (x-intercepts).
• Know your basic forms: Being able to instantly recognize $y = mx + b$ and $y = a(x-h)^2 + k$ will save you crucial minutes on the test.

Worked Example

Question: The equation of a circle in the $xy$-plane is $x^2 + y^2 - 6x + 8y = 11$. What is the radius of the circle?

A) $\sqrt{11}$ B) $5$ C) $6$ D) $36$

Solution: To find the radius, we need to convert this equation into the standard circle formula: $(x - h)^2 + (y - k)^2 = r^2$. We do this by completing the square.

1. Group the $x$ terms and $y$ terms: $(x^2 - 6x) + (y^2 + 8y) = 11$

2. Complete the square for $x$ (take half of $-6$, square it, and add to both sides): Half of $-6$ is $-3$. $(-3)^2 = 9$.

3. Complete the square for $y$ (take half of $8$, square it, and add to both sides): Half of $8$ is $4$. $(4)^2 = 16$.

4. Add these values to both sides of the equation: $(x^2 - 6x + 9) + (y^2 + 8y + 16) = 11 + 9 + 16$

5. Factor the perfect square trinomials: $(x - 3)^2 + (y + 4)^2 = 36$

6. The equation is now in standard form. The value on the right is $r^2$. $r^2 = 36$ $r = 6$

The correct answer is C.

(Note: You could also type the original equation directly into Desmos, zoom in, and count the units from the center to the edge to find the radius!)

Common Traps

1. Circle Equation Sign Errors — Based on Lumist student data, 38% of students get the sign of the center $(h,k)$ wrong. In the formula $(x - h)^2 + (y - k)^2 = r^2$, the minus signs mean you must take the opposite of the number you see. If the equation is $(x + 5)^2 + (y - 2)^2 = 16$, the center is $(-5, 2)$, not $(5, -2)$.

2. Confusing Exponential Growth vs. Decay — Our data shows that 60% of students initially confuse the growth factor $(1+r)$ with the decay factor $(1-r)$. Always pay attention to whether the problem says the value is "increasing/appreciating" (use plus) or "decreasing/depreciating" (use minus).

3. Vertex Form Sign Flipping — Similar to the circle equation, 15% of errors in Advanced Math come from confusing the $h$ sign in the vertex form $y = a(x-h)^2+k$. The $h$ (x-coordinate) flips its sign, but the $k$ (y-coordinate) stays exactly as written.

FAQ

Does the Digital SAT give you a formula sheet?

Yes, the Digital SAT provides a built-in reference sheet, but it only covers basic geometry formulas like area, volume, and special right triangles. You must memorize algebra and advanced math formulas on your own.

Do I need to memorize the quadratic formula?

While it is highly recommended to know it, you can often bypass the quadratic formula entirely by graphing the equation in the built-in Desmos calculator to find the x-intercepts (roots).

What is the most important formula to know for SAT Math?

The slope-intercept form ($y = mx + b$) and the slope formula ($m = (y_2 - y_1) / (x_2 - x_1)$) are essential, as linear equations appear constantly throughout the test.

How do I remember the circle equation for the SAT?

The standard circle equation is $(x-h)^2 + (y-k)^2 = r^2$. Remember that the center $(h,k)$ has the opposite signs of what you see inside the parentheses, and the number on the right side is the radius squared, not just the radius!