Formulas

Difference of Two Squares (a² - b)

(a - b)(a + b)

Pythagorean Theorem

a² + b² = c²

Isosceles Triangle

45°, 45°, 90° $x,\ x,\ x\sqrt{2}$

Scalene Triangle

30°, 60°, 90 $x,\ x\sqrt{3},\ 2x$

Area of a Parallelogram

$$A = bh$$

Area of a Rectangle

$$A = lw$$

Area of a Square

$$A = s^2$$

Area of a Triangle

$$A = \frac{1}{2}bh$$

Area of a Circle

$$A = \pi r^2$$

Volume of a Rectangular Prism

$$V = lwh$$

Volume of a Cube

$$V = s^3$$

Volume of a Cylinder

$$V = \pi r^2 h$$

Volume of a Sphere

$$\frac{4}{3}\pi r^3$$

Probability of a Single Event

number of favorable outcomes / total number of possible outcomes

Independent Event Intersection

$$P(A \cap B) = P(A) \cdot P(B)$$

Independent Event Union Not Mutually Exclusive

$$P(A \cup B) = P(A) + P(B) - P(A) \cdot P(B)$$

Independent Event Union Mutually Exclusive

$$P(A \cup B) = P(A) + P(B)$$

Dependent Event Conditional Probability

$$P(B \mid A) = \frac{P(A \cap B)}{P(A)}$$

Arithmetic Sequence Explicit Formula

$$a_n = a_1 + d(n - 1)$$

The Explicit Formula Using Any Two Terms

$$a_n = a_m + d(n - m)$$

The Sum of an Arithmetic Series

$$S_n = \frac{n(a_1 + a_n)}{2}$$

Distance Formula

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

Midpoint Formula

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

Quadratic Equation Standard Form

$$y = ax^2 + bx + c$$

Quadratic Equation Vertex Form

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

Axis of Symmetry

$$x = -\frac{b}{2a}$$

Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Area of a Sector

$$A = \frac{\theta}{360^\circ}(\pi r^2)$$

Length of an Arc

$$s = \frac{\theta}{360^\circ}(2\pi r)$$

Sum of Interior Angles

$$(n - 2)(180^\circ)$$

Interior Angle

$$\frac{(n - 2)(180^\circ)}{n}$$

Surface Area of a Rectangular Prism

$$SA = 2(lw + lh + wh)$$

Surface Area of a Cube

$$6s^2$$

Surface Area of a Sphere

$$4\pi r^2$$

Surface Area of a Cylinder

$$2\pi r^2 + 2\pi rh$$

Volume of a Cone

$$\frac{1}{3}\pi r^2 h$$

Surface Area of a Cone

$$\pi r^2 + \pi r l$$

Volume of a Pyramid

$$\frac{1}{3}bh$$

Surface Area of a Pyramid

$$B + \frac{1}{2}Pl$$

Combined Work

$$\frac{ab}{a + b}$$

Point Slope

$$y - y_1 = m(x - x_1)$$

Square of a Sum

$$(a + b)^2 = a^2 + 2ab + b^2$$

Square of a Difference

$$(a - b)^2 = a^2 - 2ab + b^2$$