Mathematical Concepts and Equations Flashcards

These flashcards cover key mathematical concepts, equations, and their definitions pertinent to the material in the solution notes.

Arithmetic Series

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Series

A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ratio.

Sum to Infinity

The total of all terms of an infinite geometric series when the common ratio is less than 1 in absolute value.

Logarithm Properties

Rules that explain how to manipulate logarithmic expressions including product, quotient, and power rules.

Inverse Function

A function that reverses the effect of the original function, such that if f(g(x)) = x, then g is the inverse of f.

Partial Fractions

A technique to express a rational function as a sum of simpler fractions.

Minimum Value of a Function

The lowest point on the graph of a function, representing its smallest output.

Remainder Theorem

A theorem that states that the remainder of a polynomial f(x) divided by (x - c) is equal to f(c).

Roots of an Equation

The values of the variable that satisfy the equation, making it equal to zero.

Inequality

A mathematical statement that one quantity is less than, greater than, less than or equal to, or greater than or equal to another.

Polynomial Division

The process of dividing a polynomial by another polynomial to find a quotient and a remainder.

Consecutive Terms of a Series

Terms that follow one another in a sequence without any gaps.

Coefficients in Polynomial

The numerical factors in front of the variables in a polynomial expression.

Interval Notation

A way of writing subsets of the real numbers to indicate the range of values that a variable can take.

Arithmetic Progression (A.P)

A sequence of numbers in which the difference of any two successive members is a constant.

Geometric Progression (G.P)

A sequence where each term is found by multiplying the previous one by a fixed non-zero number.

Real Roots

The solutions to an equation that are real numbers.

Function Domain

The set of all possible input values (or 'x' values) for which the function is defined.

Function Range

The set of possible output values (or 'y' values) that a function can produce.

Logarithmic Identities

Equations involving logarithms that are true for all values in their domains.

Convergence of a Series

A property of an infinite series where the sum approaches a specific limit as more terms are added.