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Formulas

Math

Showing formulas of Math

Showing 24 of 36 formulas Page 1 of 2

Pythagorean Theorem

Math → Geometry → Triangles → Right Triangles
$$a^2 + b^2 = c^2$$
Relates the three sides of a right triangle.
📖 Math 📚 Triangles

Quadratic Formula

Math → Algebra → Polynomials → Quadratic Equations
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Finds the roots of a quadratic equation $ax^2 + bx + c = 0$.
📖 Math 📚 Polynomials

Standard Deviation

Math → Statistics → Descriptive Statistics → Measures of Dispersion
$$\sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{N}}$$
Quantifies the amount of variation or dispersion of a set of data values.
📖 Math 📚 Descriptive Statistics

Euler's Identity

Math → Complex Analysis → Complex Numbers → Euler's Formula
$$e^{i\pi} + 1 = 0$$
A mathematical constant linking five fundamental mathematical constants.
📖 Math 📚 Complex Numbers

Law of Sines

Math → Trigonometry → Triangles → Non-Right Triangles
$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
Relates the lengths of the sides of any triangle to the sines of its angles.
📖 Math 📚 Triangles

Area of a Circle

Math → Geometry → 2D Shapes → Circles
$$A = \pi r^2$$
Total space enclosed within a circle.
📖 Math 📚 2D Shapes

Law of Cosines

Math → Trigonometry → Triangles → General Triangles
$$c^2 = a^2 + b^2 - 2ab \cos C$$
Generalizes the Pythagorean theorem to any triangle by relating the lengths of sides to the cosine of one of its angles.
📖 Math 📚 Triangles

Integration by Parts

Math → Calculus → Integrals → Integration Techniques
$$\int u \, dv = uv - \int v \, du$$
A rule that transforms the integral of a product of functions into other forms.
📖 Math 📚 Integrals

Volume of a Sphere

Math → Geometry → 3d Shapes → Volume
$$V = \frac{4}{3}\pi r^3$$
The amount of space occupied by a sphere.
📖 Math 📚 3d Shapes

Surface Area of a Cylinder

Math → Geometry → 3d Shapes → Surface Area
$$A = 2\pi rh + 2\pi r^2$$
Total area including the lateral surface and the two circular bases.
📖 Math 📚 3d Shapes

Derivative of a Power Function

Math → Calculus → Differentiation → Power Rule
$$\frac{d}{dx} x^n = nx^{n-1}$$
Calculates the rate of change of a variable raised to a constant power.
📖 Math 📚 Differentiation

Sum of an Arithmetic Series

Math → Algebra → Sequences And Series → Arithmetic Progressions
$$S_n = \frac{n}{2}(a_1 + a_n)$$
Calculates the sum of the first $n$ terms of an arithmetic progression.
📖 Math 📚 Sequences And Series

Distance Formula (3D)

Math → Geometry → Coordinate Geometry → 3D Space
$$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$$
Calculates the straight-line distance between two points in three-dimensional space.
📖 Math 📚 Coordinate Geometry

Binomial Probability Formula

Math → Statistics → Probability Distributions → Binomial Distribution
$$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$
The probability of exactly $k$ successes in $n$ independent Bernoulli trials.
📖 Math 📚 Probability Distributions

Area of a Trapezoid

Math → Geometry → 2D Shapes → Quadrilaterals
$$A = \frac{1}{2}(a+b)h$$
Calculates the area of a quadrilateral with at least one pair of parallel sides.
📖 Math 📚 2D Shapes

Integration of Exponential Function

Math → Calculus → Integrals → Basic Integration
$$\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C$$
The integral of the natural exponential function with a linear exponent constant.
📖 Math 📚 Integrals

Mean of a Discrete Random Variable

Math → Probability → Random Variables → Expectation
$$E(X) = \sum x_i P(x_i)$$
Calculates the expected value (average) of a discrete probability distribution.
📖 Math 📚 Random Variables

Surface Area of a Sphere

Math → Geometry → 3d Shapes → Surface Area
$$A = 4\pi r^2$$
The total area of the exterior of a sphere.
📖 Math 📚 3d Shapes

Volume of a Cone

Math → Geometry → 3d Shapes → Volume
$$V = \frac{1}{3} \pi r^2 h$$
Amount of space occupied by a right circular cone.
📖 Math 📚 3d Shapes

Derivative of Sine

Math → Calculus → Differentiation → Trig Derivatives
$$\frac{d}{dx} \sin x = \cos x$$
The instantaneous rate of change of the sine function.
📖 Math 📚 Differentiation

Area of a Sector

Math → Geometry → Circles → Sectors
$$A = \frac{1}{2} r^2 \theta$$
Calculates the area of a 'pizza slice' part of a circle.
📖 Math 📚 Circles

Integration of a Constant

Math → Calculus → Integrals → Basic Integration
$$\int k \, dx = kx + C$$
The antiderivative of a constant value.
📖 Math 📚 Integrals

Volume of a Rectangular Prism

Math → Geometry → 3d Shapes → Volume
$$V = lwh$$
The amount of space inside a rectangular box.
📖 Math 📚 3d Shapes

Integration of 1/x

Math → Calculus → Integrals → Basic Integrals
$$\int \frac{1}{x} \, dx = \ln|x| + C$$
Special case for integrating power functions where $n = -1$.
📖 Math 📚 Integrals
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