Essential Math Formulas

101 flashcards by MentisLibrary

Formulas from geometry, algebra, trigonometry, calculus, statistics, probability, sequences and finance, each in LaTeX with its symbols explained, a worked example and the mistake to avoid.

Area of a rectangle

$A = lw$, the length times the width.

Area of a triangle

$A = \tfrac{1}{2}bh$, half the base times the perpendicular height.

Area of a circle

$A = \pi r^2$

Circumference of a circle

$C = 2\pi r$, equivalently $C = \pi d$.

Volume of a cube

$V = s^3$

Volume of a rectangular prism

$V = lwh$

Volume of a cylinder

$V = \pi r^2 h$, the circular base area times the height.

Volume of a sphere

$V = \tfrac{4}{3}\pi r^3$

Pythagorean theorem

$a^2 + b^2 = c^2$ in a right triangle, where $c$ is the hypotenuse.

Quadratic formula

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ solves $ax^2 + bx + c = 0$.

Perimeter of a rectangle

$P = 2(l + w)$

Surface area of a cube

$S = 6s^2$, six identical square faces.

Surface area of a sphere

$S = 4\pi r^2$

Law of sines

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Law of cosines

$c^2 = a^2 + b^2 - 2ab\cos C$

Binomial theorem

$(a + b)^n = \displaystyle\sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k}$

Fundamental theorem of calculus

$\displaystyle\int_a^b f(x)\,dx = F(b) - F(a)$, where $F' = f$.

Area of a square

$A = s^2$, the side length squared.

Area of a parallelogram

$A = bh$, base times perpendicular height.

Area of a trapezoid

$A = \tfrac{1}{2}(b_1 + b_2)h$, the average of the parallel sides times the height.

Volume of a cone

$V = \tfrac{1}{3}\pi r^2 h$

Volume of a pyramid

$V = \tfrac{1}{3}Bh$, one third of the base area times the height.

Surface area of a cylinder

$S = 2\pi r^2 + 2\pi r h$, two circular ends plus the curved side.

Sum of the interior angles of a polygon

$S = (n - 2) \times 180^\circ$

Arc length of a circle

$s = r\theta$ with $\theta$ measured in radians.

Area of a circular sector

$A = \tfrac{1}{2}r^2\theta$ with $\theta$ in radians.

Distance between two points

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Midpoint of a segment

$M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$

Slope of a line

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$, rise over run.

Equation of a circle

$(x - h)^2 + (y - k)^2 = r^2$