Math Formulas Library

Solves a quadratic equation of the form ax² + bx + c = 0.

Expands the power of a binomial into a sum of terms.

Finds the nth term of an arithmetic sequence with first term a₁ and common difference d.

Finds the nth term of a geometric sequence with first term a₁ and common ratio r.

Calculates the sum of the first n terms of an arithmetic sequence.

Calculates the sum of the first n terms of a geometric sequence where r ≠ 1.

Calculates the sum of an infinite geometric series where |r| < 1.

The area of a rectangle is calculated by multiplying its length (l) by its width (w).

The area of a triangle is calculated as half the product of its base (b) and height (h).

The area of a circle is calculated using pi (π) multiplied by the square of its radius (r).

The circumference of a circle is calculated as 2 times pi (π) multiplied by the radius (r).

In a right triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b).

The volume of a rectangular prism is calculated by multiplying its length (l), width (w), and height (h).

The volume of a cylinder is calculated using pi (π) multiplied by the square of its radius (r) and its height (h).

The volume of a sphere is calculated as (4/3) times pi (π) multiplied by the cube of its radius (r).

The volume of a cone is calculated as (1/3) times pi (π) multiplied by the square of its radius (r) and its height (h).

The surface area of a rectangular prism is calculated as 2 times the sum of the areas of its three distinct faces.

In any triangle, the ratio of the length of a side to the sine of the opposite angle is constant.

Relates the square of one side of a triangle to the squares of the other two sides and the cosine of the included angle.

Defines the tangent of an angle as the ratio of the sine to the cosine of that angle.

A fundamental trigonometric identity that relates the squares of sine and cosine functions.

Expresses the sine of twice an angle in terms of the sine and cosine of the original angle.

The derivative of x raised to the power n is n times x raised to the power n-1.

The derivative of the exponential function e^x is itself.

The derivative of the natural logarithm of x is 1 divided by x.

The derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

The derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

The derivative of the quotient of two functions is the derivative of the numerator times the denominator, minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

The definite integral of a function from a to b is equal to the difference of the antiderivative evaluated at the upper and lower limits.

The mean is the sum of all values divided by the number of values.

The standard deviation measures the amount of variation or dispersion of a set of values.

The probability of an event A is the number of favorable outcomes divided by the total number of possible outcomes.

The number of ways to arrange r objects from a set of n distinct objects, where order matters.

The number of ways to select r objects from a set of n distinct objects, where order doesn't matter.

The force acting on an object is equal to the mass of the object multiplied by its acceleration.

The energy possessed by an object due to its motion.

The energy possessed by an object due to its position in a gravitational field.

The voltage across a conductor is directly proportional to the current flowing through it, with the resistance as the constant of proportionality.

Energy equals mass multiplied by the speed of light squared.