# SAT Math formulas: reference sheet and what to learn Source: https://1600.now/blog/sat-math-formulas --- SAT Math Compare Bluebook reference formulas with algebra, percent, circle, and trig formulas to learn, then practice choosing the right one. Written by [Luke Finigan](https://1600.now/about) 4 min read Updated Oct 2, 2026 Bluebook supplies basic area and volume formulas, the Pythagorean theorem, and special-triangle ratios. Learn the algebra, percent, trig, and coordinate relationships that are not on that sheet. ### Use the reference sheet as a reference College Board's [Bluebook reference-sheet example](https://satsuite.collegeboard.org/media/pdf/ky-sat-junior-state-administration-spring-2026.pdf) includes rectangle, triangle, and circle area; circle circumference; rectangular-solid, cylinder, sphere, cone, and rectangular-pyramid volume; the Pythagorean theorem; and the two special right triangles. It also gives basic circle and triangle angle facts. You can look up a supplied formula, but you still have to identify its variables. In $A=\pi r^2$, r is radius. In $A=\frac12bh$, h is perpendicular height. A formula list can't make that choice for you. Practice with the reference open at first. Once you know where things are, try a few questions without looking. Memorization is helpful when it removes a lookup; using the right dimensions is what makes the result correct. ### Learn linear relationships and their units Slope is $m=\dfrac{y_2-y_1}{x_2-x_1}$ when $x_2\ne x_1$. A line can be written as $y=mx+b$ or $y-y_1=m(x-x_1)$. Parallel nonvertical lines share a slope; perpendicular nonvertical lines have slopes whose product is $-1$. For points $(2,5)$ and $(6,13)$, $m=(13-5)/(6-2)=2$. Substitution gives $5=2(2)+b$, so $b=1$ and the line is $y=2x+1$. Distance is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, and midpoint is $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$. For $(1,2)$ and $(7,10)$, the distance is 10 and midpoint is $(4,6)$. The distance formula is the Pythagorean theorem applied to coordinate differences. ### Recognize each quadratic form Standard form is $y=ax^2+bx+c$. Vertex form is $y=a(x-h)^2+k$, with vertex $(h,k)$. Factored form is $y=a(x-r_1)(x-r_2)$, making the roots visible. The quadratic formula is $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ for $a\ne0$. The discriminant $b^2-4ac$ is positive for two distinct real roots, zero for one repeated real root, and negative for no real roots. For $x^2-6x+9=0$, the discriminant is zero and the root is 3. You could also factor $(x-3)^2=0$. Choose the form that answers the question rather than forcing the quadratic formula onto every quadratic. ### Turn percent and rate statements into models Percent change is $\dfrac{\text{new}-\text{old}}{\text{old}}\cdot100\%$. Growth uses $V=V_0(1+r)^t$ and decay uses $V=V_0(1-r)^t$, when r is a decimal rate per unit of t. A value falling 15% each year has multiplier 0.85. Starting at 200, after two years it is $200(0.85)^2=144.5$. The exponent counts applications of the multiplier. For constant speed, $d=rt$. For a data set, $\text{mean}=\text{sum}/\text{count}$. For equally likely outcomes, $P=\text{favorable}/\text{eligible}$. Label the units and the eligible group; formulas with vague variable definitions invite the wrong denominator. ### Separate a constant change from a repeated percentage An account gaining 20 dollars each month can be modeled by $A=500+20t$. An account gaining 4% each month uses $A=500(1.04)^t$. After two months, the first has 540 dollars and the second has 540.80 dollars. The difference comes from the second percentage applying to the updated amount. A stated percentage rate needs its time unit, and a fixed addition needs its units too. Don't choose an exponential model just because money appears in the question. ### Add the circle and trig relationships A coordinate circle uses $(x-h)^2+(y-k)^2=r^2$. Arc length is $\dfrac{\theta}{360^\circ}\cdot2\pi r$ in degrees, or $r\theta$ in radians. Sector area is $\dfrac{\theta}{360^\circ}\cdot\pi r^2$ in degrees, or $\frac12r^2\theta$ in radians. In a right triangle, sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. The acute angles are complementary, so $\sin\theta=\cos(90^\circ-\theta)$. For radius 6 and central angle $\pi/3$, the arc length is $2\pi$ and sector area is $6\pi$. That example needs both the correct formula and the radian interpretation of the angle. ### Make a formula useful by attaching a question For each formula you review, solve one problem that uses it and one where it would be the wrong choice. Compare a right triangle with a non-right triangle, or percent of with percent greater than. Those pairs test recognition. In the [Math bank](https://1600.now/bank/math/browse), record whether you forgot the formula, mislabeled a quantity, or made an arithmetic error. Use the [Desmos guide](https://1600.now/blog/how-to-use-desmos-on-sat) for graphing checks, but keep exact algebra when a question asks about a parameter or an exact expression. Knowing when a formula applies is part of learning it. - [Use the formula reference beside your practice](https://1600.now/sat-math-formula-chart) Try it yourself: A circle equation is $(x+4)^2+(y-1)^2=36$. What is its radius? · A $4$ B $6$ C $18$ D $36$ ### Sources - [College Board: Bluebook reference-sheet example](https://satsuite.collegeboard.org/media/pdf/ky-sat-junior-state-administration-spring-2026.pdf) Luke Finigan is a student developer and the creator of 1600.now, a free Digital SAT practice platform. [About Luke](https://1600.now/about). ### Keep reading - **[How to use Desmos on the SAT: equations, tables, and checks](https://1600.now/blog/how-to-use-desmos-on-sat)** Use the SAT version of Desmos to solve equations, inspect intersections, evaluate functions, and check models without relying on screenshots. - **[Digital SAT pacing: checkpoints, skipping, and a second pass](https://1600.now/blog/sat-pacing-strategy)** Use flexible SAT module checkpoints, a clear skip rule, and a second pass to reduce rushed guesses without racing every question. [Browse SAT resources →](https://1600.now/sat-resources)