absolute value The distance of a number from zero on a real number line.

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1 G L O S S A R Y A absolute value The distance of a number from zero on a real number line. acute angle An angle whose measure is less than 90. acute triangle A triangle in which each of the three interior angles is acute. algebraic modelling The process of representing a relationship b an equation or a formula, or representing a pattern of numbers b an algebraic epression. algorithm A set of instructions for carring out a procedure. amortization period The period of time over which a mortgage is paid off with equal paments at regular intervals. amortization table A table that shows the part of each mortgage pament that is interest and principal, and the principal remaining. amortize To repa a mortgage over a given period of time in equal paments at regular intervals amount The sum of the principal and the interest when mone is invested or borrowed. amplitude Half the distance between the maimum and minimum values of a periodic function. The amplitude is angle bisector A line that divides an angle into two equal parts. angle of depression The angle, measured downward, between the horizontal and the line of sight from an observer to an object. Observer 8 a Object a is an angle of depression. angle of elevation The angle, measured upward, between the horizontal and the line of sight from an observer to an object. Observer a a is an angle of elevation. annuit A sum of mone paid as a series of equal paments at regular intervals of time. arc Part of the circumference of a circle. arithmetic sequence A sequence where the difference between consecutive terms is a constant. arithmetic series The sum of the terms of an arithmetic sequence. astronomical unit The distance from Earth to the sun, that is, approimatel km. asmptote A line that a curve approaches more and more closel, but never touches. ais of smmetr B The -ais is an asmptote. The fold line of a smmetrical figure. base (of a power) The number used as a factor for repeated multiplication. In 6 3, the base is 6. BEDMAS An acronm that lists the order of operations. BEDMAS stands for Brackets, Eponents, Division, Multiplication, Addition, Subtraction. binomial An algebraic epression with two terms is a binomial. Object 812 MHR Glossar

2 C centre of an ellipse The point of intersection of the major ais and the minor ais. centre of an hperbola The point of intersection of the transverse ais and the conjugate ais. The centre is located midwa between the vertices and midwa between the co-vertices. chord A line segment joining two points on a curve. circle The locus of all points in the plane that are equidistant from a fied point called the centre. circumference The perimeter of a circle. coefficient The factor b which a variable is multiplied. For eample, in the term 8, the coefficient is 8; in the term a, the coefficient is a. collecting like terms Simplifing an epression containing like terms b adding their coefficients. collinear Three or more points that lie on the same straight line. common difference The constant that is added to a term in an arithmetic sequence to obtain the net term. For the sequence 1, 4, 7, 10, the common difference is 3. common ratio The ratio of consecutive terms in a geometric sequence. For the sequence 1, 2, 4, 8, 16, the common ratio is 2. comple conjugates Comple numbers of the form a + bi and a bi. Their product is real number. comple number A number of the form a + ib, where a and b are real numbers and i is the square root of 1. comple plane The comple numbers considered in two dimensions using the real and the imaginar aes. Imaginar a compression A transformation that is a stretch b a factor less than 1. b a + bi Real compound inequalit A range of values described b combining two inequalities. 0 < n 5 is a compound inequalit that means n > 0 and n 5. compound interest Interest that is calculated at regular compounding periods and is added to the principal to earn interest for the net compounding period. compounding period Each period of time for which compound interest is earned or charged in an investment or loan. conjecture A generalization, or educated guess, made using inductive reasoning. conjugate ais The ais of smmetr of a hperbola that is perpendicular to the transverse ais. conjugate ais conjugate binomials Binomials of the form a b + c d and a b c d where a, b, c, and d are rational numbers. The product of conjugates is a rational number. conjugate hperbolas Hperbolas that share the same asmptotes. The transverse ais of one is the conjugate ais of the other. constant term A term that does not include a variable. continuous graph A graph that consists of an unbroken line or curve. cosine law The relationship between the lengths of the three sides and the cosine of an angle in an triangle. a 2 = b 2 + c 2 2bccos A cosine ratio In a right triangle, the ratio of the length of the adjacent side to the length of the hpotenuse. adjacent cosine = hpotenuse coterminal angles Angles in standard position that have the same terminal arm. Glossar MHR 813

3 countereample An eample that demonstrates that a conjecture is false. co-vertices of an ellipse The endpoints of the major ais. co-vertices of a hperbola The endpoints of the conjugate ais. ccle One complete pattern of a periodic function. D dependent variable In a relation, the variable whose value depends on the value of the independent variable. On a coordinate grid, the values of the dependent variable are on the vertical ais. In d = 4.9t 2, d is the dependent variable. depreciation The amount b which an item decreases in value. dilatation A transformation that changes the size of an object. It involves a stretch or a shrink b a scale factor of k. directri The line from which each point of a parabola is the same distance as it is from the focus. directri discontinuit A point at which a function is not defined. The graph has a break at this point. f() = 1 has a discontinuit at = 0. discriminant In the quadratic formula, the quantit under the radical sign, b 2 4ac. distance between two points The length of the line segment joining the points. For points ( 1, 1 ) and ( 2, 2 ), d = ( 2 1 ) 2 + ( 2. 1 ) 2 distributive propert a(b + c) = ab + ac domain The set of the first elements in a relation. double root The solution of a quadratic equation where both roots are the same. E eccentricit A measure of the shape of an ellipse or hperbola, given b e = a c. elements The individual members of a set. ellipse The locus of all points in the plane such that the sum of the distances from two given points in the plane, the foci, is constant. entire radical A number such as 29 or 5 3. equilateral triangle A triangle with all three sides equal. Euclidean distance The square root of the sum of the squares of the differences between the corresponding coordinates of two points. epansion A transformation that is a stretch b a factor greater than 1. eplicit formula A formula for the nth term of a sequence, from which the terms of the sequence ma be obtained b substituting 1, 2, 3, and so on, in turn, for n in the formula. t n = 2n + 1 is an eplicit formula for the arithmetic sequence 3, 5, 7, 9,. eponent The use of a raised number to denote repeated multiplication of a base. In 3 4, the eponent is 4. eponential equation An equation that has a variable in an eponent. 3 = 81 is an eponential equation. eponential function A function in which a variable is an eponent. It can be defined b an equation of the form = ab, where a 0, b > 0, and b 1. etrapolate Estimate values ling outside the range of given data. To etrapolate from a graph means to estimate coordinates of points beond those that are plotted. 814 MHR Glossar

4 F factor Epress a number as the product of two or more numbers, or an algebraic epression as the product of two or more other algebraic epressions. Also, the individual numbers or algebraic epressions in such a product. first-degree inequalit An inequalit in which the variable has the eponent > 2 4 is a first-degree inequalit. focal radii The line segments joining point P on an ellipse or hperbola to the foci. foci of a hperbola The two points P in the plane, F 1 and F 2, such that PF PF 1 2 is constant for all points P on the hperbola. F 1 F 2 foci of an ellipse The two points in the plane, F 1 and F 2, such that PF 1 + PF 2 is constant for all points P on the ellipse. focus of a parabola The point from which each point of a parabola Focus is the same distance as it is from the directri. FOIL An acronm used in multipling binomials where F refers to the product of the first terms, O, to the product of the outside terms, I, to the product of the inside terms, and L, to the product of the last terms. fractal A curve that generates itself b replacing each side of its original shape with a generator and iterating the process. function A set of ordered pairs in which, for ever value of, there is onl one value of. G generalize Determine a general rule or conclusion from eamples. Specificall, determine a general rule to represent a pattern or relationship between variables. F 1 P F 2 geometric mean If a,, and b are consecutive terms of a geometric sequence then is the geometric mean of a and b. geometric sequence A sequence where the ratio of consecutive terms is a constant. Each term after the first is obtained b multipling the preceding term b the same number. geometric series The sum of the terms of a geometric sequence. gradian An angular measure that has 400 equal parts, called grads, in one revolution. graphing calculator A hand-held device capable of a wide range of mathematical operations, including graphing from an equation, constructing a scatter plot, determining the equation of a line of best fit for a scatter plot, making statistical calculations, and performing elementar smbolic manipulation. Man graphing calculators will attach to scientific probes that can be used to gather data involving phsical measurements, such as position, temperature, or force. graphing software Computer software that provides features similar to those of a graphing calculator. greatest common factor (GCF) The monomial with the greatest numerical coefficient and greatest degree, that is a factor of two or more terms. The GCF of 12ab and 8bc is 4b. l greatest integer function f() = [], where [] denotes the greatest integer that is less than or equal to. [2.5] = 2, [ 3.6] = 4, and [0.0] = 0 H half-life The time it takes for half of an sample of a radioactive isotope to deca. hperbola The locus of all points in a plane such that the absolute value of the difference of the distances from an point on the hperbola to two given points in the plane, the foci, is constant. hpotenuse The longest side of a right triangle. Glossar MHR 815

5 I identit An equation that is true for all values of the variable for which the epressions on each side of the equation are defined. imaginar ais The vertical ais in the comple plane. imaginar number A comple number, a + bi, where a 0, b 0, and i 2 = 1. imaginar part The part bi in a comple number a + bi, where a 0, b 0, and i 2 = 1. imaginar unit The number i, where i 2 = 1 and i = 1. independent variable In a relation, the variable whose value determines that of the dependent variable. On a coordinate grid, the values of the independent variable are on the horizontal ais. In d = 4.9t 2, t is the independent variable. inequalit A mathematical statement that contains one of the smbols <,, >,, or. initial arm The ra, of an angle in standard position, that is on the positive -ais. integer Whole numbers and their opposites. intercept The distance from the origin of the -plane to the point at which a line or curve crosses a intercept given ais. 0 intercept interest rate The percent of the principal that is earned, or paid, as interest. interpolate To estimate values ling between elements of given data. To interpolate from a graph means to estimate coordinates of points between those that are plotted. invariant Points that are unaltered b a transformation. inverse function Two functions that undo each other. A function f has inverse f 1 defined b f 1 (b) = a if f(a) = b. irrational number A number that cannot be written as the ratio of two integers. 2, 3, and π are irrational numbers. isosceles trapezoid A trapezoid in which the two non-parallel sides are equal in length. isosceles triangle A triangle with eactl two equal sides. iteration A method that evaluates a function for an initial value, and uses the output of that calculation as the input for the net calculation. L like radicals Numbers that have the same radicand. 2 3 and 8 3 are like radicals. like terms Terms that have eactl the same variable(s) raised to eactl the same eponent(s). 3 2, 2, and are like terms. line of smmetr A line such that a figure coincides with its reflection image over the line. line segment The part of a line that joins two points. linear relation A relation between two variables that appears as a straight line when graphed on a coordinate sstem. Ma also be referred to as a linear function. locus A set of points determined b a rule or condition. lowest common denominator (LCD) The least common multiple of the denominators of two or more rational epressions. M magic square A square arrangement of numbers in which the sum of the numbers in an line (horizontal, vertical, and diagonal) is the same. major ais The longer of the two line segments that form the aes of smmetr for an ellipse. major ais 816 MHR Glossar

6 mathematical model A mathematical description of a real situation. The description ma include a diagram, a graph, a table of values, an equation, a formula, a phsical model, or a computer model. mathematical modelling The process of describing a real situation in a mathematical form. median (geometr) A line segment that joins a verte of a triangle to the midpoint of the opposite side. mean The sum of a set of values divided b the number of values. The mean of 2, 4, 6 and 8 is 5. midpoint The point that divides a line segment into two equal points. For the line segment joining points ( 1, 1 ) and ( 2, 2 ), the midpoint is 1 +, ordered pair A pair of numbers used to locate a point in the coordinate plane. ordinar annuit A series of equal paments in which a pament is made at the end of each regular pament period. origin The point of intersection of the -ais and the -ais on a coordinate grid. P parabola The graph of a quadratic function whose domain is the set of real numbers. The locus of all points P in the plane such that the distance from P to a fied point F, the focus, equals the distance from P to fied line l, the directri. minor ais The shorter of the two line segments that form the aes of smmetr for an ellipse. minor ais F P l mied radical A number such as 3 10 or monomial An algebraic epression with one term. 7 is a monomial. mortgage A special tpe of borrowing arrangement between a borrower and a lender. The borrower uses propert as a guarantee of repament of the debt. N natural number A number in the sequence 1, 2, 3, 4,. non-linear relation A relationship between two variables that does not fit a straight line when graphed. O oblique triangle A triangle that is not right-angled. obtuse angle An angle that measures more than 90 but less than 180. obtuse triangle A triangle containing one obtuse angle. pament interval The time between successive paments of an annuit. pament period Another name for the pament interval. perfect square trinomial The trinomial that results from squaring a binomial. perimeter The distance around a polgon. period The horizontal length of one ccle of a periodic function period (of a pendulum) The time it takes to complete one back-and-forth swing. periodic function A function that has a pattern of -values that repeats at regular intervals. phase shift The horizontal translation of a trigonometric function. Also sometimes called the phase angle. 6 8 The period is Glossar MHR 817

7 point of intersection The point that is common to two non-parallel lines. point-slope form of a linear equation The equation for the line through ( 1, 1 ) with slope m is given b 1 = m( 1 ). polhedron A three-dimensional object with faces that are polgons. polnomial An algebraic epression formed b adding or subtracting monomials. polnomial epression An algebraic epression of the form a + b + c 2 +, where a, b, and c are numbers. power A product obtained b using a base as a factor one or more times. 5 3, 6, and a m are powers. present value The principal that must be invested toda at a given interest rate, compounding frequenc, and term, in order to result in a given final amount. present value of an annuit The principal that must be invested toda at a given interest rate, compounding frequenc, and number of pament intervals, in order to provide regular paments over a given term. prime number A number with eactl two factors itself and 1. 2, 5, and 13 are prime numbers. principal The original mone invested or borrowed. principal square root The positive square root of a number. prism A three-dimensional figure with two parallel, congruent polgonal bases. A prism is named b the shape of its bases, for eample, rectangular prism, triangular prism. probabilit The ratio of the number of favourable outcomes to the number of possible outcomes. proportion An equation that states that two ratios are equal. Pthagorean identit In trigonometr, sin 2 θ + cos 2 θ = 1 for all values of θ. Pthagorean theorem In a right triangle, the square of the length of a c the longest side is equal to the sum of the squares of the lengths of the b other two sides. a 2 + b 2 = c MHR Glossar pure imaginar number A number that can be written as i, where i 2 = 1 and is a positive real number. 7i, i 2, and 3i 5 are pure imaginar numbers. Q quadrant One of the four regions formed b the intersection of the -ais and the -ais. Second Quadrant 0 Third Quadrant First Quadrant Fourth Quadrant quadratic equation An equation in the form a 2 + b + c = 0, where a, b, and c are real numbers and a 0. quadratic formula The roots of a quadratic function of the form = a 2 + b + c, where b ± b c 2 4a a 0, are given b. 2a quadratic function A function defined b a quadratic equation of the form = a 2 + b + c, where a, b, and c are real numbers and a 0. quartic equation A fourth degree polnomial equation. quotient identit In trigonometr, sin θ = tan θ for all values of θ. cos θ R radian The measure of the angle subtended at the centre of a circle b an arc equal in length to the radius of the circle. radical epression An epression involving the square root of an unknown. radical sign The smbol. radicand An epression under a radical sign. In ab the radicand is ab.

8 radius The distance from the centre to an point on a circle. range of a relation The set of the second elements in a relation. ratio A comparison of two quantities with the same units. rational epression The quotient of two polnomials. 3 a 2 + b 2, and are rational epressions. k 1 a + b rational number A number that can be epressed as the ratio of two integers, where the divisor is not zero. 0.75, 3 8, and 2 are rational numbers. rationalize the denominator The process of multipling the numerator and the denominator of a rational epression b the same quantit, to make the denominator a rational number. 4 3 = = 4( 3 ) 3 ( 3 ) real ais The horizontal ais in the comple plane. real number A member of the set of all rational and irrational numbers. real part The part a in a comple number a + bi, where a 0, b 0, and i 2 = 1. reciprocals Two numbers that have a product of 1. and 1 are reciprocals. rectangular form A comple number in the form a + bi where (a, b) are its rectangular coordinates in the comple plane. rectangular prism A three-dimensional figure with two parallel, congruent rectangular bases. recursion formula A formula consisting of at least two parts. The parts give the value(s) of the first term(s) in the sequence, and an equation that can be used to calculate each of the other terms from the term(s) before it. t 1 = 1, t n = t n is a recursion formula for the arithmetic sequence 1, 4, 7, 10,. reduction A dilatation in which the image after the dilatation is smaller than the original image, that is, 0 < k < 1 reflection A transformation in which a figure is reflected over a reflection line. reflection image The image of a figure in a plane after a reflection. refle angle An angle that measures more than 180 but less than 360. relation An identified relationship between two variables that ma be epressed as ordered pairs, a table of values, a graph, or an equation. restriction An value that must be ecluded for a variable. 8 has restriction rhombus A parallelogram in which the lengths of all four sides are equal. right angle An angle that measures 90. right bisector of a line segment A line that is perpendicular to a line segment and divides the line segment into two equal parts. right prism A three-dimensional figure with two parallel, congruent polgonal bases and lateral faces that are perpendicular to the bases. right triangle A triangle containing a 90 angle. roots The solutions of an equation. S scalene triangle A triangle with no sides equal. scientific notation A method of writing large or small numbers that contain man zeros. The number is epressed in the form a 10 n, where a is greater than or equal to 1 but less than 10, and n is an integer. second-degree polnomial A polnomial in at least one term of which the variable has the eponent 2, and no term has the eponent of the variable greater than is a second-degree polnomial. sequence A set of numbers, usuall separated b commas, arranged in an order. Glossar MHR 819

9 series The sum of the terms of a sequence. simple interest Interest calculated onl on the original principal using the formula I = Prt. simplest form of an algebraic epression An epression with no like terms. For eample, is in simplest form; is not. sine law The relationship between the lengths of the sides and their opposite angles in an triangle. a b c = = sin A sin B sin C sine ratio In a right triangle, the ratio of the length of the opposite side to the length of the hpotenuse. opposite sine = hpotenuse sinusoidal function A function that is used to model periodic data. slide A transformation that is comprised of horizontal and vertical translations of an object on the plane. slope A measure of the steepness of a line. The slope of a line, m, containing the points P( 1, 1 ) and Q( 2, 2 ) is vertical change rise m = or horizontal change run = = 2 1 2, P( 1, 1 ) 0 Q( 2, 2 ) horizontal change (run) 2 1 or vertical change (rise) 2 1 or slope and -intercept form of a linear equation The equation for the line through ( 1, 1 ) with slope m and -intercept b is given b = m + b. solving a triangle Finding the values of all the unknown sides and unknown angles of a triangle. spreadsheet Computer software that allows the entr of formulas for repeated calculations. square root A number that is multiplied b itself to give another number. standard position The position of an angle when its verte is at the origin and its initial ra is on the positive -ais. straight angle An angle that measures 180. subtended angle An angle for which the arms end on arc of a circle. supplementar angles Angles whose sum is 180. surface area The number of square units needed to cover the surface of a three-dimensional object. sstem of equations Two or more equations that are considered together. smmetr A qualit of a plane figure that can be folded along a fold line so that the halves of the figure match eactl. T tangent ratio In a right triangle, the ratio of the length of the opposite side to the length of the adjacent side. opposite tangent = adjacent term A number or a variable, or the product or quotient of numbers and variables. The epression has two terms: 2 and 5. term of a mortgage The length of time that a mortgage agreement is in effect. terminal arm The ra, of an angle in standard position, that is not on the positive -ais. transformation A move of a plane figure from one position to another position in the same plane. translation A slide transformation. translation image The image of a plane figure after a slide transformation. 820 MHR Glossar

10 transversal A line that crosses or intersects two or more lines. transverse ais The line segment between the vertices of an hperbola that is one of its ais of smmetr. transverse ais X -intercept The -coordinate of the point where a line or curve crosses the -ais. -plane A coordinate sstem based on the intersection of two straight lines called aes, which are usuall perpendicular. The horizontal ais is the -ais, and the vertical ais is the -ais. The point of intersection of the aes is called the origin. trapezoid A quadrilateral with one pair of parallel sides. trigonometric equation An equation that contains one or more trigonometric functions. trinomial A polnomial with three terms is a trinomial. V variable A letter or smbol, such as, used to represent an unspecified number. For eample, and are variables in the epression verte A point at which two sides of a polgon meet. verte of a parabola The point of the parabola at which the graph intersects the ais of smmetr. The verte is located midwa between the focus and the directri. vertical line test A method of determining a function. If an vertical line passes through more than one point on the graph of a relation, then the relation is not a function. vertices of an hperbola The endpoints of the transverse ais. vertices of an ellipse The endpoints of the major ais. volume The amount of space that an object occupies, measured in cubic units. Y -intercept The -coordinate of the point where a line or curve crosses the -ais. Z zero of a function An value of for which the value of the function f() is 0. zero product propert The propert that, if the product of two real numbers is zero, then one or both of the numbers must be zero. W whole number A number in the sequence 0, 1, 2, 3, 4, 5,. Glossar MHR 821

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