Mathematics 1 Reference Sheet

A collection of mathematics vocabulary and formulas covering lines, coordinate geometry, quadratics, polygons, solids, circles, and trigonometry based on the reference sheet.

Standard Form (Lines)

$Ax + By = C$, where $A$, $B$, and $C$ are constants, and $A \neq 0$ or $B \neq 0$.

Slope-Intercept Form

$y = mx + b$, where $m = \text{slope}$ and $b = \text{y-intercept}$.

Point-Slope Form

$y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points and $m = \text{slope}$.

General Form (Quadratics)

$ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants and $a \neq 0$.

Area of a Triangle

$A = \frac{1}{2}bh$, where $b = \text{base}$ and $h = \text{height}$.

Area of a Parallelogram

$A = bh$, where $b = \text{base}$ and $h = \text{height}$.

Area of a Trapezoid

$A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are bases and $h = \text{height}$.

Area of a Regular Polygon

$A = \frac{1}{2}ap$, where $a = \text{apothem}$ and $p = \text{perimeter}$.

Volume of a Prism

$V = Bh$, where $B = \text{area of the base}$ and $h = \text{height}$.

Surface Area of a Right Prism

$SA = 2B + Ph$, where $B = \text{area of base}$, $P = \text{perimeter of base}$, and $h = \text{height}$.

Volume of a Circular Cylinder

$V = \pi r^2 h$, where $r = \text{radius}$ and $h = \text{height}$.

Surface Area of a Right Circular Cylinder

$SA = 2\pi r^2 + 2\pi rh$, where $r = \text{radius}$ and $h = \text{height}$.

Volume of a Pyramid

$V = \frac{1}{3}Bh$, where $B = \text{area of the base}$ and $h = \text{height}$.

Surface Area of a Right Pyramid

$SA = B + \frac{1}{2}Ps$, where $B = \text{area of base}$, $P = \text{perimeter of base}$, and $s = \text{slant height}$.

Volume of a Circular Cone

$V = \frac{1}{3}\pi r^2 h$, where $r = \text{radius}$ and $h = \text{height}$.

Surface Area of a Right Circular Cone

$SA = \pi r^2 + \pi rs$, where $r = \text{radius}$ and $s = \text{slant height}$.

Volume of a Sphere

$V = \frac{4}{3}\pi r^3$, where $r = \text{radius}$.

Surface Area of a Sphere

$SA = 4\pi r^2$, where $r = \text{radius}$.

Sum of Degree Measures in a Polygon

$180(n - 2)$, where $n$ is the number of sides.

Degree Measure in a Regular Polygon

$\frac{180(n - 2)}{n}$, where $n$ is the number of sides.

Center-Radius Form of a Circle

$(x - h)^2 + (y - k)^2 = r^2$, where center is $(h, k)$ and $r = \text{radius}$.

Area of a Circle

$$A = \pi r^2$$

Circumference of a Circle

$C = \pi d = 2\pi r$, where $d = \text{diameter}$ and $r = \text{radius}$.

Area of a Sector

$A = \frac{\theta}{360}\pi r^2$, where $\theta$ is the degree measure of the arc.

Pythagorean Theorem

$$a^2 + b^2 = c^2$$

Trigonometric Ratio: Sine

$$\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}}$$

Trigonometric Ratio: Cosine

$$\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}}$$

Trigonometric Ratio: Tangent

$$\tan(A) = \frac{\text{opposite}}{\text{adjacent}}$$

Distance, Rate, Time

$d = rt$, where $d = \text{distance}$, $r = \text{rate}$, and $t = \text{time}$.

Is Perpendicular To (Symbol)

$$\perp$$

Is Parallel To (Symbol)

$$\parallel$$

Is Congruent To (Symbol)

$$\cong$$

Is Similar To (Symbol)

$$\sim$$

Is Approximately Equal To (Symbol)

$$\approx$$