Reference sheets

Math formulas

Quick, readable SAT and ACT math formula references for practice.

Math

SAT

SAT Math Reference Sheet

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Area and circumference

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

Right triangles

Pythagorean theorem: $c^2 = a^2 + b^2$
30-60-90 triangle side ratio: $x$ , $x\sqrt{3}$ , $2x$
45-45-90 triangle side ratio: $s$ , $s$ , $s\sqrt{2}$

Volume

Rectangular prism: $V = lwh$
Right circular cylinder: $V = \pi r^2h$
Sphere: $V = \frac{4}{3}\pi r^3$
Right circular cone: $V = \frac{1}{3}\pi r^2h$
Pyramid: $V = \frac{1}{3}lwh$

Angle facts

A circle has 360 degrees.
A circle has $2\pi$ radians.
The sum of the angle measures of a triangle is 180 degrees.

Math

ACT

ACT Mathematics I Reference Sheet

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Linear equations

Standard form: $Ax + By = C$
Slope-intercept form: $y = mx + b$
Point-slope form: $y - y_1 = m(x - x_1)$
Slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Quadratics

General form: $y = ax^2 + bx + c$
Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Coordinate geometry

Midpoint: $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
Distance: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Area

Triangle: $A = \frac{1}{2}bh$
Parallelogram: $A = bh$
Trapezoid: $A = \frac{1}{2}(b_1+b_2)h$
Regular polygon: $A = \frac{1}{2}ap$

Surface area and volume

Prism: $V = Bh$
Right prism surface area: $SA = ph + 2B$
Circular cylinder: $V = \pi r^2h$
Right circular cylinder surface area: $SA = 2\pi rh + 2\pi r^2$
Pyramid: $V = \frac{1}{3}Bh$
Right pyramid surface area: $SA = \frac{1}{2}p\ell + B$
Circular cone: $V = \frac{1}{3}\pi r^2h$
Right circular cone surface area: $SA = \pi r\ell + \pi r^2$
Sphere: $V = \frac{4}{3}\pi r^3$
Sphere surface area: $SA = 4\pi r^2$

Circles and polygons

Circle in center-radius form: $(x-h)^2 + (y-k)^2 = r^2$
Circle area: $A = \pi r^2$
Circle circumference: $C = 2\pi r$
Sector area: $A = \frac{n}{360}\pi r^2$
Sum of interior angles of an n-sided polygon: $180(n-2)$

Right triangles and trig

Pythagorean theorem: $a^2 + b^2 = c^2$
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Sequences, interest, and variation

Arithmetic sequence: $a_n = a_1 + (n-1)d$
Arithmetic series: $S_n = \frac{n}{2}(a_1+a_n)$
Simple interest: $I = Prt$
Compound interest: $A = P(1 + \frac{r}{n})^{nt}$
Distance-rate-time: $d = rt$
Direct variation: $y = kx$
Inverse variation: $y = \frac{k}{x}$

SAT & ACT Math Formula Reference Sheets | OpenPrep