Mathematics Formula Booklet Review

Vocabulary flashcards based on key mathematical concepts, definitions, and formulas.

Straight Line

A straight line is defined by the equation Ax + By + C = 0, where A, B, and C are constants.

Distance Formula

The distance d between two points (x1, y1) and (x2, y2) is given by: d = $rac{ ext{√}((x_2 - x_1)^2 + (y_2 - y_1)^2)}$.

Circle Equation

The standard equation of a circle in the Cartesian plane is given by: $x^2 + y^2 + 2gx + 2fy + c = 0$.

Ellipse

An ellipse is represented by the equation rac{x^2}{a^2} + rac{y^2}{b^2} = 1, where a and b are the semi-major and semi-minor axes.

Parabola

The equation of a standard parabola is given as $y^2 = 4ax$, where (0,0) is the vertex.

Hyperbola

The standard equation of a hyperbola is rac{x^2}{a^2} - rac{y^2}{b^2} = 1.

Limit of Function

A limit exists as x approaches a if $ext{lim}_{x o a} f(x) = L$, meaning f(x) approaches a finite value L.

Differentiation

The process of finding the derivative of a function, which represents the rate of change of the function.

Indefinite Integration

The integral of a function f(x) is denoted as extstyle rac{d}{dx} igg[ ext{∫} f(x)dxigg] = f(x) + C, where C is the constant of integration.

Definite Integration

Defined as the integral over a specific interval $ext{∫}_{a}^{b} f(x)dx$, resulting in the net area under the curve from x=a to x=b.

Quadratic Equation

An equation in the form $ax^2 + bx + c = 0$ where a, b, and c are constants and a ≠ 0. The roots can be found using the quadratic formula.

Binomial Theorem

The expansion of $(a + b)^n$ can be expressed as $extstyle ext{nCr} a^{n-r}b^r$, where r = 0, 1, …, n.

Permutation

The arrangement of n elements taken r at a time is calculated as ext{nPr} = rac{n!}{(n - r)!}.

Combination

The selection of n elements taken r at a time is given by ext{nCr} = rac{n!}{r!(n - r)!}.

Probability

The likelihood of an event occurring can be expressed as the ratio of favorable outcomes to total outcomes, represented as P(A) = rac{m}{n}.

Complex Number

A complex number is expressed in the form $z = a + ib$, where a is the real part and b is the imaginary part.

Vectors

A vector represents both magnitude and direction, and is denoted in a Cartesian plane as $extbf{r} = xi + yj + zk$.