Glossary

A

• Absolute value

  An absolute value of a number x, written as |x|, is the distance from x to 0 on a real number line.
  See Absolute Value Equation

• Accuracy

  How close a measurement is to an actual value.

• Algebra

  The branch of mathematics involving the rules of operations and relations when working with variables.

B

• Bar graph

  A graph with rectangular bars (plotted either vertically or horizontally) with lengths proportional to the values they represent.
  See Pie Charts & Bar Graphs

• BEDMAS

  The most common acronym for order of operations, meaning Brackets first, then Exponents, Division, Multiplication, Addition, and Subtraction.
  See Order of Operations

• Binomial

  A polynomial with two terms or a sum of two monomials; e.g. 5x + 1.
  See Expanding

C

• Calculus
  The branch of mathematics involving limits, derivatives and integrals.
  See Calculus: Introducing the Concept
• Chain Rule
  A formula for the derivative of the composite of two functions: [f(g(x))] ′ = f ′(g(x))∗g ′(x)
  See Derivative Rules
• Circle
  A geometrical shape that consists of the set of points in a plane that are equidistant from a given point (the centre).
  See Introduction to Circles
• Circumference
  The distance around a circle.
  See Introduction to Circles
• Commutative Property
  A property for some operations (such as addition or multiplication) which states that changing the order of the operands does not change the end result: a+b = b+a.
• Complex Numbers
  A number that can be represented by an expression of the form a+bi where a and b are real numbers, and i is a symbol with the property i² = −1i² = −1.
  See Complex Numbers
• Composition of Functions
  See Composition of Functions
• Coefficient
  A constant (number) multiplied with a variable; e.g. 5 is a coefficient of x in the term 5x.
• Constant
  A value that does not change.
• Coordinate Plane
  The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin.
• Coplanar
  Points that lie within the same plane.
• Correlation
  See Least Squares Trendline and Correlation
• Cross Product

  Written as a x b that produces a vector c whose length is the product of the lengths of two vectors a and b and the sine of their included angle, and whose direction is perpendicular to the vectors a and b with orientation given by the right-hand rule. To find how to obtain the components of a x b

  See Dot and Cross Product

D

• Decimal
  A base 10 number written with a decimal point; e.g. 13.5
• Denominator
  A bottom number of the fraction, also known as the divisor; e.g. 5 is a denominator in 3/5.
• Dependent Variable
  A variable that depends on one or more other variables; e.g. y is the dependent variable of y = x²
• Derivative
  The slope of the tangent line to a curve at a particular point. The derivative of a function ff can also be thought of as the instantaneous rate of change of the corresponding function at the given point, commonly written as f′(x).
  See Derivative Rules
• Diagonal Matrix
  A square matrix that has entries along the main diagonal and zeros everywhere else.
  See Special Matrices and Definitions
• Domain
  The set of all values that the independent variable can take on.
  See Domain and Range
• Dot Product
  Also called the Euclidean inner product, the dot product of a and b is denoted by a⋅b and is calculated by multiplying corresponding components of a and b and adding the resulting products to obtain a single number.
  See Dot and Cross Product

E

• Equivalent Fractions
  Fractions that have the same value even though they may look different; e.g. 2/5 and 4/10 are equivalent.
  See Intro to Fractions
• Euclidean Inner Product
  See Dot Product
• Euler's Number

  An irrational number e≈2.71828

  See Introduction to Exponential & Logarithmic Functions

• Expand
  To multiply out the parts of an expression.
  See Expanding
• Exponent

  A number n in xⁿ which indicates how many times x is being multiplied by itself, also called power or index; e.g. 3 is the exponent in 4³.

  See Exponent Laws & Logarithm Properties

• Exponential Function
  A function of the form f(x) = a^x where a is a positive constant.
  See Introduction to Exponential & Logarithmic Functions

F

• Factor

  A term that exactly divides a given term; e.g. x³ is a factor of 5x⁷y² since (x³)(5x⁴y²) = 5x⁷y²

  See Factoring

• Factorial

  The factorial of a nonnegative integer n, denoted by n!, represents the product of all the positive integers less than or equal to n; e.g. 5! = 5×4×3×2×1.

  See Factorials

• FOIL
  The acronym which stands for First, Outer, Inner, Last. It is used for finding the product of two binomials, which is given by the sum of the product of the First terms, the Outer terms, the Inner terms, and the Last terms.
  See Expanding
• Fraction
  A rational number expressed as the ratio of two numbers, written as a/b where a and b are integers and b≠0.
  See Intro to Fractions
• Frequency
  The number of complete cycles per unit time. Frequency is the reciprocal of period.
  See Setting up Trigonometric Models
• Function
  A mathematical rule, between two sets, which assigns to each value from the first set exactly one value, called f(x), from the second set.
  See Introduction to Functions

G

• Greatest Common Factor
  The largest number that divides two or more numbers evenly; e.g. The greatest common factor of 8 and 12 is 4.

H

• Histogram
  A graphical summary that shows how many observations fall into a particular class.
  See Histograms

I

• Identity Matrix

  A square matric with 1's on th main diagonal and 0's everywhere else. 

  See Special Matrices and Definitions

• Improper Fraction
  A fraction in which the numerator is greater than (or equal to) the denominator; e.g. 4/3 or 9/7.
  See Introduction to Fractions
• Independent Variable
  A variable which can be assigned any permissible value without considering values of any other variable; e.g. x is the independent variable of y = x².
• Inequality

  An algebraic relation showing that a quantity is greater than (>), greater than or equal (), less than (<), or less than or equal to () another quantity.

  See Inequalities

• Intersection of Sets
  The intersection of two sets A and B, denoted by A∩B, is the set of all elements which are in both A and B; e.g. {1,2,3,7}∩{1,2,5,7,8} = {1,2,7}.
  See Sets
• Inverse Function
  A function obtained by solving for x as the dependent variable and y as the independent variable, and renaming them according to the usual convention.
  See Inverses
• Irrational Number
  A real number that cannot be written as a fraction; not a rational number; e.g. π,e,√5, etc.
  

L

• Least Square Trendline
  A line that fits a set of paired data as closely as possible by choosing the sum of the squares of the residuals to be as small as possible.
  See Least Squares Trendline and Correlation
• Like Terms
  Terms that have the same variables raised to the same power. The coefficients do not need to match; e.g. 3x² and 5x^2 are like terms.
• Linear Equation
  An equation for a straight line; e.g. y = 3x+2.
  See Introduction to Linear Functions and Solving Linear Equations
• Logarithm
  The logarithm base b of a number x is the power to which b must be raised in order to equal x, written as log_bx; e.g. log₅25 = 2 since 25 = 5².
  See Logarithms
• Log-log graph
  A graph with logarithmic x-axis and logarithmic y-axis.
  See Semi-Log and Log-Log Graphs
• Long Division
  A standard procedure used for dividing numbers.
  See Long Division
• Long Multiplication

  A method used for multiplying larger numbers.

  See Long Multiplication with Large Numbers

• Lowest Common Denominator
  The smallest integer or polynomial that is exactly divisible by each denominator of a set of fractions; e.g. the lowest common denominator of 2/3 and 1/4 is 12.

M

• Matrix

  An array of numbers, usually denoted by a capital letter

  See Introduction to Matrices

• Matrix Size/ Dimension
  The number of rows and columns a matrix contains; e.g. a 3×2 matrix has 3 rows and 2 columns.
• Mean
  The average calculated by finding the sum of all the data points and dividing the sum by the number of data points.
  See Mean, Median, and Mode
• Median

  In statistics, the median is the middle number in a list of numbers arranged in either increasing or decreasing order. If there is an even number of data items, the median is the mean of the two middle numbers.

  See Mean, Median, and Mode

• Mixed Fraction
  A fraction which contains a whole number and a proper fraction together; e.g. 3 _^1/4
  See Introduction to Fractions
• Mode

  The number that occurs most frequently in a set of data.

  See Mean, Median, and Mode

• Monomial
  A polynomial with one term; e.g. 3x² is a monomial.

N

• Normal Distribution
  A pattern for the distribution of a set of data which follows a symmetrical bell-shaped curve.
  See Normal Distribution
• Null Set
  An empty set with no elements, often denoted as Ø.
  See Sets
• Numerator
  The top number of the fraction.
  See Introduction to Fractions

O

• Order of Operations
  The rule used to clarify which calculation comes first in an expression.
  See BEDMAS definition or  Order of Operations
  

P

• Parabola
  A conic section obtained from the intersection of a cone and a plane.  Any point on a parabola is an equal distance from a fixed point (focus) and a fixed straight line (directrix).  A parabola always has a quadratic equation.
  See Parabolas
• Percent

  Percent means per hundred; e.g. 45/100 is equal to 45%.

  See Decimal and Percent

• Perimeter
  The distance around a two-dimensional shape.
• Period
  In math, the period is the smallest interval or horizontal distance required for the graph of a periodic function to complete one cycle; e.g. the period of y = sin(x) is 2π.
  See Introduction to Trigonometric Functions
• Periodic
  Recurrent or self-duplicating at regular intervals.
  See Introduction to Trigonometric Functions
• Phase Shift
  Horizontal shift for a periodic function; e.g. y = cos(x−π) has a phase shift of π.
  See Setting up Trigonometric Models
• Pie Chart
  A circular chart divided into sectors, each sector representing a proportion of the quantities.
  See Pie Charts & Bar Graphs
• Piecewise Function

  A function defined by two or more different functions on a sequence of intervals.

  See Piecewise-defined Functions

• Polynomial
  A mathematical expression involving a sum of terms, each term consisting of a constant multiplied by a variable with non-negative integer exponent; e.g. 4x²+7x−34 is a polynomial.
• Positive Number
  A real number greater than zero.
• Power Rule
  A formula for finding the derivative of a power xⁿ (where n is a real number) :  d xⁿ _{= nx^n-1}
                                                                                                                                  dx
  See Derivative Rules
• Precision
  The level of detail in a number or measurement.  A measurement may be precise without being accurate.
• Product Rule

  In Calculus, a formula for finding the derivative of a product of two functions:  if both f and g are differentiable, (f⋅g)′ = f′⋅g + g′⋅f

  See Derivative Rules

• Proper Fraction