Pure Mathematics 20 Glossary

Note: not all words in the vocabulary lists will be found in this glossary.

absolute value: the distance a real number, x, lies from the origin on the number line, denoted by | x |

absolute value equation: an equation with a variable within an absolute value symbol

absolute value function: a function with a variable within an absolute value symbol

absolute value inequality: an inequality that has a variable within an absolute value symbol

acute triangle: a triangle with three acute angles

algebraic expression: an expression containing only algebraic symbols and operations—addition, subtraction, multiplication, division, roots, and powers

annuity: a sequence of equal payments made at equal intervals of time

arc: a continuous piece of the circumference of a circle

asymptote: a line a graph approaches more and more closely; a tangent at infinity

axiom: a statement accepted as true without proof

axis of symmetry: a line that divides a curve into halves, reflecting each half into the other

basic deductions: deductions set by the federal government that include Canada Pension Plan (CPP), Employment Insurance (EI), and income tax

biconditional statement: a statement formed by combining a conditional and its converse, using if and only if

biweekly: every two weeks

boundary line: a line on the coordinate plane that separates the plane into two regions compound inequality: a compound statement expressing two inequalities at the same time

central angle: an angle at the centre of a circle subtended by an arc of the circle

centre of a circle: the fixed point from which all points on the circle are equidistant

chequing account: a bank account that allows you to access funds within the account by writing cheques

chord: a line segment joining two points on a circle

circle: a set of points equidistant from a given point

completing the square: the process of transforming a quadratic function from general form to standard form

complex number: a number of the form , where

composition of f with g: the function obtained by replacing x with in , written or

compound statement: two statements linked together with a connective, such as and, or, or not

compounded quarterly: interest calculated every three months and added to the principal for the next interest period

compounding period: length of time over which interest on an investment is calculated

compound interest: interest calculated at regular intervals and added to the principal for the next interest period

concentric: having the same centre

conclusion: the part in the then clause of a conditional statement

conditional statement: an if…then statement

conjecture: a generalization made through inductive reasoning

consumer credit: the ability to purchase an item with an agreement to pay for it at a later date

continuous graph: a graph with no breaks in the curve

contrapositive: a conditional statement formed by negating both the if and then clauses of a converse

converse: a conditional statement formed by interchanging the if and then clauses of another conditional statement

convex polygon: a polygon in which segments joining any two points in the polygon lie entirely within the polygon

corollary: an additional statement that follows directly from a theorem

counterexample: an example that disproves a conjecture

cubic equation: a polynomial equation of degree 3

cubic function: a polynomial function of degree 3

cyclic polygon: a polygon with all of its vertices on the same circle

cylindrical helix: a curve ascending a cylinder at a constant angle

deductive reasoning: a process of demonstrating that, if certain statements are true, then other statements follow logically from them

direct proof: a proof in which you begin with an assumption and work deductively towards a valid conclusion

discontinuous graph: a graph with a break in the curve

discriminant: a part of the quadratic formula, given by b² - 4ac

due date: the date a payment is to be made by

effective rate of interest: the simple interest rate that produces the same amount of interest as the compound interest rate

extraneous root: a number obtained in the process of solving an equation that does not satisfy the equation

Factor Theorem: a theorem stating that is a factor of a polynomial if and only if . Conversely, if , then is a factor of .

foreign exchange: the value of one country's currency in terms of another country's currency

general equation of a circle: the form of an equation of a circle based on the centre and radius of the circle

general form of a quadratic function: a quadratic function written in the form y = ax² + bx + c , where a, b, and c are real numbers and a ≠ 0

gross annual income: total income earned in a year

gross income: the amount of money earned through employment before deductions

half-plane: one of the two regions on the coordinate plane separated by a boundary line

hypothesis: the part in the if clause of a conditional statement

implication: a conditional statement

indirect proof: a process of arguing in which you assume the conclusion you wish to demonstrate is false

inductive reasoning: a type of reasoning by which generalizations are drawn from patterns in observed data

inscribe: to draw inside

inscribed angle: an angle that has its vertex on a circle and is subtended by an arc of the circle

Integral Zero Theorem: a theorem stating that if is an integral zero of a polynomial, , with integral coefficients, then b is a factor of the constant term

inverse of a function: a relation formed by interchanging the coordinates within each ordered pair of the original function

inverse of a relation: a relation formed by interchanging the coordinates within each ordered pair of the original relation

isosceles triangle: a triangle with two congruent sides

linear system: a pair of first-degree equations, each representing a line in the coordinate plane

major arc: the larger arc of a circle defined by two points on the circle

matrix: an arrangement of numbers in rows and columns where the position of each number is of mathematical significance

median: in a triangle, the segment joining a vertex to the midpoint of the opposite side

mill rate: a rate at which property tax is calculated

minor arc: the smaller arc of a circle defined by two points on the circle

mortgage: an agreement between a money lender and a borrower involving the purchase of property

negation: the opposite of a statement, formed using the word not

net income: the amount an employee receives after all deductions are subtracted from the employee's gross income

oblique triangle: a triangle that is not a right triangle

obtuse triangle: a triangle with one obtuse angle

parabola: a U-shaped curve obtained by graphing a quadratic function

paraboloid of revolution: a three-dimensional figure formed by rotating a parabola about its axis of symmetry

point of tangency: the point where a tangent touches a curve

point-slope form: the form of an equation of a line based on the slope and a point on the line

polygon: a closed figure with three or more sides

polynomial equation: the equation formed when a polynomial is set equal to 0

polynomial function: a function of the form

polynomial inequality: an inequality containing a polynomial expression

postulate: an axiom

proof: a convincing argument

proof by contradiction: indirect proof

property tax: money collected by the municipality to pay for services, such as water, road construction and maintenance, and garbage disposal

pure imaginary number: a number of the form bi, where and b is a non-zero real number

quadratic equation: an equation of the form , where a, b, and c are real numbers and

quadratic formula: the formula for determining the roots of a quadratic equation from its coefficients

quadratic function: a function that may be written in the form , where a, b, and c are real numbers and

quartic function: a polynomial function of degree 4

radical equation: an equation with a variable within a radicand

radical function: a function with a variable within a radicand

radical inequality: an inequality with a variable within a radicand

rational equation: an equation formed by setting a rational expression equal to 0

rational function: a function of the form , where and are polynomials and

rational inequality: an inequality containing a rational expression

Rational Zero Theorem: a theorem stating that if is a rational zero of a polynomial with integral coefficients, then the numerator b is a factor of the polynomial's constant term and a is a factor of the coefficient of the highest-degree term

reconcile: to verify the transactions in a personal transaction record book with a bank statement

reflexive property: a property of equality that states, "For any a, a = a."

Remainder Theorem: a theorem stating that when the polynomial is divided by , the remainder equals

root: a solution of an equation

savings account: a bank account that earns interest on the balance of the account . Funds in a savings account can only be withdrawn using your bank card or directly from a teller.

secant: a line that intersects a circle at two points. A secant of a circle contains a chord of the circle.

sector: a region bounded by two radii and an arc of a circle

sector angle: the central angle formed by a sector of a circle

slope and y-intercept form: a linear equation written in the form , where m is the slope and b is the y-intercept

standard form of a quadratic equation: a quadratic equation written in the form ax² + bx + c = 0 , where a, b, and c are real numbers and a ≠ 0

standard form of a quadratic function: y = a (x - p)² + q, where a, p, and q are real numbers and a ≠ 0

statement: a sentence that is either true or false

subtend: to lie opposite to, as an arc subtends the opposite inscribed angle

system of equations: a group of equations that are to be considered at the same time

synthetic division: a simpler, quicker method of dividing a polynomial by a binomial of the form

tangent: a line that touches a curve at a single point

Tangent Chord Theorem: the theorem stating that the angle between a tangent and a chord of a circle equals the inscribed angle on the opposite side of the chord

taxable income: income remaining after all approved deductions are made

theorem: a generalization that must be proven before being accepted as true

unit price: the price of a single item; the price of one unit of an item

Venn diagram: a diagram of overlapping circles drawn within a rectangle used to model relationships among statements

vertex: the point of intersection of a parabola and its axis of symmetry

zero: the value of the independent variable of a function for which the function equals zero

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