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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


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


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


M


N


O


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 = nxn-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
    A fraction in which the numerator is less than the denominator.
  • Proportion
    An equation stating that two ratios are equal; e.g. four quantities a,b,c,d are said to be in proportion if ab = cd.
    See Ratio & Proportion
  • Pythagorean Theorem
    A theorem which states that in any right triangle, if c represents the length of the hypotenuse, and a and b are the lengths of the other two sides, then a2 + b2 = c2.
    See Pythagorean Theorem

Q


R

  • Radian

    A unit used for measuring angles. One can think of a radian as the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle. One radian equals 180/π.

    See Converting Between Radians and Degrees

  • Range

    The set of values that the dependent variable takes on as the independent variable varies throughout the domain.

    See Domain and Range

  • Ratio

    A comparison of numbers or quantities, usually expressed as a quotient; e.g. if the ratio of boys to girls is 14 to 15, it can be written as 14:15
     14/15.

    See Ratio and Proportion

  • Rational Expression
    A ratio of two polynomials.
  • Rational Number
    A number that can be expressed as a fraction (or ratio of integers) with a nonzero denominator. Rational numbers are denoted by Q.

  • Real Number

    Any number on a number line including rational and irrational numbers. The set of all real numbers is denoted by R.

  • Remainder

    The amount left over after division if one quantity does not divide evenly; e.g. when dividing 7 by 3, the answer is 2 with the remainder of 1.

    See Long Division

  • Right-Hand Rule
    A rule that uses the right hand to establish the orientation of vector resulting from a cross product. For the cross product c = a x b, the direction of c is obtained by pointing the right hand with fingers straight in the direction of a and then bending the fingers in the direction of b; the extended thumb now points in the direction of c.
  • Residual
    A difference between an observed value and a predicted value (the vertical distance between a data point and the graph of a regression equation).
  • Rounding

    Approximating a number by eliminating the least significant digits.

    See Significant Figures and Rounding


S

  • Sample Standard Deviation

    A measure of spread for a distribution of a sample that determines the degree to which the values differ from the sample mean. The sample standard deviation, s, is the square root of the sample variance.

    See Standard Deviation

  • Sample Variance

    A measure of the spread for a distribution of a sample that determines the degree to which the values differ from the sample mean. The sample variance, commonly written as s2, is the sum of the squared deviations from the sample mean divided by one less than the number of observations in the sample. The sample variance is the square of the sample standard deviation.

    See Standard Deviation

  • Scalar
    A number or a quantity with only magnitude and no direction.
  • Scientific Notation

    A way of displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10; e.g. the scientific notation of 12,345 is 1.2345×104.

    See Scientific Notation

  • Semi-Log Graph

    A graph with logarithmic y-axis.

    See Semi-Log and Log-Log Graphs

  • Set

    A collection of distinct objects.

    See Set 

  • Significant Figures

    Each of the digits in a number that are used to show the degree of precision in a measurement.

    See Significant Figures and Rounding

  • Simplify

    To reduce (an expression, equation, fraction, etc) to a simpler form by cancellation of common factors, or regrouping of terms in the same variable, etc.

    See Simplifying Expressions

  • Slope

    The steepness or slant of a line, calculated by finding the vertical change over the horizontal change as one travels along the line.

    See introduction to Linear Functions  and Equations of Lines

  • SOHCAHTOA

    Commonly used acronym in trigonometry for remembering the relationship of trigonometric functions and the right triangle. SOH stands for Sine equals Opposite over Hypotenuse; CAH stands for Cosine equals Adjacent over Hypotenuse; and TOA stands for Tangent equals Opposite over Adjacent.

    See Trigonometry on the Unit Circle

  • Solution
    Any value(s) of the variable(s) that satisfies an equation, inequality, system of equations or system of inequalities.
  • Solve
    To find the solution set to an equation, inequality or a system of equations or inequalities involving variables.
  • Special Angles

    The angles for which the exact values of trigonometric functions are known. These special angles in radians are: 0,π/6 ,π/4 ,π/3 ,π/2

    See Trigonometry on a Unit Circle

  • Square Matrix

    A matrix that has the same number of rows and columns.

    See Special Matrices and Definitions

  • Square Root
    A square root of a number is a positive value that can be multiplied by itself to give the original number. It uses √

    symbol; e.g. the square root of 25 is 5 or √25 = 5

    See Square Root

  • Standard Deviation
    The measure of spread of a distribution of data points from their average value (the mean). The standard deviation is the square root of variance.
  • Standard Normal Distribution

    A normal distribution with mean 0 and standard deviation 1.

    See Normal Distribution

  • Subset

    A is a subset of B if every element in set A is also a member of set B; e.g. {1, 3, 5} is a subset of {1, 2, 3, 4, 5, 6}.

    See Sets

  • Symmetric Matrix

    A square matrix that is equal to its transpose.

    See Special Matrices and Definitions


T


U

  • Union of Sets

    The union of two sets A and B, denoted by A∪B, is the collection of elements that are in either A or B; e.g. {2,3}∪{1,2,green}={1,2,3,green}.

    See Sets

  • Unit Circle
    A circle with a radius of one; in Trigonometry, the unit circle is centred at the origin.

V

  • Variable
    A quantity that can change or that may take on different values, usually represented by a letter or a symbol.
  • Variance

    The measure of spread of a distribution of data points from their average value (mean). Variance is the average squared deviations from the mean. It is also the square of the standard deviation.

  • Vector

    A quantity that has both magnitude and direction, usually denoted by a bold-faced lowercase letter or an arrow above the letter.

    See Introduction to Vectors

  • Vector Components

    Parts that define a vector. If a vector is positioned with its initial point at the origin of a coordinate system, the vector components are the coordinates of the vector’s terminal point (the point where the arrow ends); e.g. for the vector w =(2,−5) the components are 2 and −5.

    See Vector Components

  • Vector Direction

    The direction of a vector v ⃗ =(a,b) is the angle θ it forms with the x-axis when its initial position is at the origin. This angle can be calculated using the formula tanθ = ba.

    See Vector Magnitude, Direction and Components

  • Vector Magnitude

    The length of a vector, denoted by |v|or ∥v∥, is found using the formula ∥v∥ = √v12 +v22 +v32  if v = (v1 ,v2 ,v3 )

    See Vector Magnitude, Direction and Components

  • Venn Diagram
    A diagram that shows the relations between a finite collection of sets.

Z