Glossary

Absolute Value: How far a quantity is away from \(0\). For numbers, this represents the size or magnitued of the number and does not concern the positive or negative sign. Since \(-6\) is six spaces away from \(0\), it has an absolute value of \(6\). This is written as \(|-6|=6\).

Algebra: An area of mathematical study where letters are used to represent variables and constants in expressions and equations.

Algebraic Expression: A combination of variables and/or constants using mathematical operations like addition, multiplication, etc.

Algebraic Equation: A statement uses the equal sign \(=\) to show that two expressions or quantities are equal to each other.

Axis: The horizontal and vertical reference lines on a coordinate plane.

Base: A quantity that has an exponent. See Power for an example.

Binomial: A polynomial containing exactly two terms.

Cartesian Coordinates: A way of communicating the location of a point by referencing its position relative to two perpendicular axis. The coordinates are written as an \(x,y\) ordered pair.

Cartesian Plane: A graphing grid containing two perpendicular axis, typically the \(x\)-axis is horiztontal and the \(y\)-axis is vertical.

Coefficient: A constant that multiplies a varaible. In the expression \(7x^3\), the coefficient is \(7\).

Constant: A quantity whose value does not change.

Denominator: The bottom part of a fraction or rational expression.

Divisor: A number that divides another number.

Equation: See Algebraic Equation.

Exponent: A small number written in the upper right of a quantity to indicate how many times it should be multiplied by iteslf. See also Power.

Expression: See Algebraic Expression.

Factor: When quantites are multiplied together, each one is called a factor.

Factoring: The process of determining the factors which, when multiplied together, give the original quantity. Also called Factorization.

Inequality: A relationship showing that one quantity is greater than or less than another using the symbols \(\gt\) or \(\lt\).

Integers: Positive and negative natural numbers, including \(0\).

Intercept: The point(s) where a graph crosses the axis of a coordinate plane. An \(x\)-intercept is where it crosses the \(x\)-axis. Likewise, a \(y\)-intercept is where it crosses the \(y\)-axis.

Intersection: The point(s) where two graphs cross.

Irrational Numbers: Numbers whose decimal expansion goes on forever with no repeating pattern. These cannot be written as a ratio of integers. Examples include \(\pi\) and \(\sqrt{2}\\).

Like Terms: Terms that have the same variables raised to identical powers. For instance, \(5x^3\) and \(-8x^3\) are like terms because both have the variable \(x\) raised to a power of \(3\).

Linear Equation: Any equation whose graph is a line. The variables in a linear equation do not have any exponents higher than \(1\) and are not in the denominator of a fraction. For instance, \(y=2x-7\) and \(3x+6y=12\) are both linear equations.

Monomial: A polynomial containing just a single term.

Natural Numbers: The numbers we normally count with, ie. \(1, 2, 3, \dots\). Very similar to the whole numbers, except \(0\) is not a natural number.

Number Line: A horizontal line that is a visual representation of all real numbers.

Numerator: The top of a fraction or rational expression.

Operation: A way of combining two numbers to create a new value. Addition, subtraction, multiplication and division are examples of operations, though there are many more.

Order of Operations: The agreed upon order in which operations should be performed. The acronym GEMS can be used to remember that Grouping symbols come first, then Exponents, followed by Multiplication/division and then addition/Subtraction.

Ordered Pair: See Cartesian Coordinates.

Origin: On a Cartesian plane, the origin is the point where the two perpendicular axis meet. It has coordinates of \(0, 0\).

Polynomial: An expression that only involves addition, subtraction, and multiplication of variables and constants. The variables in a polynomial will only have whole number exponents. For example, \(-2x^3 + 4x^2 - x + 5\) is a polynomial.

Power: A quantity being multiplied by itself a specific number of times. The power is written as a small superscript (the Exponent) on the top right corner of the quantity being multiplied (the Base). For instance, \(x^3\), the base \(x\) is has an exponent of \(3\), and this is the third power of \(x\). Frequently called an Exponent and sometimes an Index.

Quadratic Equation: An equation where the highest power is \(2\). The standard way to write a quadratic equation is \(y=ax^2+bx+c\).

Quadratic Formula: A formula that can be used to solve any quadratic equation. If \(ax^2+bx+c=0\), then the two solutions are given by \(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\).

Rational Expression: A fraction involving algebraic expressions.

Rational Numbers: All numbers that can be written as a ratio of two integers. These are fractions.

Real Numbers: All numbers that can be written as a decimal. This includes natural numbers, whole numbers, integers, rational, and irrational numbers. It does not include square roots of negative numbers, which are imaginary numbers.

Root: The operation which is the opposite of taking a power. If \(b=a^n\), then taking the \(n\)-th root of \(b\) would return \(a\).

Slope-Intercept Form: A linear equation written in the format \(y=mx+b\) where \(m\) is the slope and \((0,b)\) is the \(y\)-intercept.

Term: Part of an algebraic expression that might be added or subtracted with other parts. In the expression \(4x+9\), both \(4x\) and \(8\) are terms.

Trinomial: A polynomial containing exactly three terms.

Variable: A quantity whose value can change, usually represented by a letter such as \(x\) or \(y\).

Whole Numbers: The natural numbers along with \(0\).