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- 1. Dictionary of MATH TERMSAAA similarityAccording to the AA similarity if two angles of a triangle are congruent to two angles of anothertriangle, then the triangles are said to be similar to each other.AAS CongruenceAAS congruence is called as angle-angle-side congruence. If there are two pairs ofcorresponding angles and a pair of corresponding opposite sides that are equal in measure, thenthe triangle is said to be congruent.AbscissaThe X-coordinate of a point on the coordinate system is called abscissa. For example, in theordered pair P(2, 3, 5), 2 will be called the abscissa of the point P. In math terminology it will becalled as the length of the point(P) relative to the X-axis.Absolute ValueA general concept of absolute value is that it makes a negative number positive. Absolute valueis also called a mod value. The absolute value of a number (say X) is denoted as |X|. Remember,the absolute value uses bars so dont use parenthesis or any other symbol else the meaningchanges. To put it simply, |-7| = 7 and |7| = 7. Positive numbers and zero are left unchanged inthe absolute value.AccelerationThe rate of change of velocity with time is called acceleration. Mathematically, the secondderivative of the distance traveled by an object is called acceleration.AccuracyThe measure of the closeness of a value to the actual value of a result is called accuracy.Acute AngleAn angle whose measure is less than 900 is called as an acute angle.Acute Angled TriangleA triangle in which all the interior angles are acute is known as an acute angled triangle.Addition Rule Of ProbabilityAddition rule of probability is meant to find out the probability of occurrence of either or boththe events.For Example, If P(A) and P(B) are mutually exclusive events, then the probability P(A or B) =P(A) + P(B) else P(A or B) = P(A) + P(B) – P(A and B). 1
- 2. Dictionary of MATH TERMSAdditive Inverse of a MatrixIf the sign of every matrix element is changed, then the matrix is said to be an inverse of theoriginal matrix. If A is the matrix, then -A will be the inverse of the matrix. If add a matrix andits inverse, then the sum would be zero since the each element in the original matrix is negativeof the other.Additive Property of EqualitySimply stated, additive property states that same number can be added on both side of theequation. For example, x – 3 = 5 is same as x – 3 + 3 = 5 + 3.Adjacent AnglesIf the two angles share a common vertex and common plane and even have a same side but ifthey dont overlap or one of the angles is not contained in the other then the angles are calledadjacent angles.Adjoint MatrixWhen we take the transpose of the co-factor of the original matrix, then it is known as adjointmatrix.AlgebraA branch of pure mathematics that uses alphabets and letters as variables. The variables are theunknown quantities whose values can be determined with the help of other equations. Forexample, 3X – 7 = 78, is an algebraic equation in one unknown variable (here it is X).Algebraic NumbersAll rational numbers are the algebraic numbers. Numbers that are roots of the polynomials withinteger coefficients and are under the surd are also included as algebraic numbers. Any numberthat is not a root of polynomial with integer coefficients is not an algebraic number. Thesenumbers are called transcendental numbers. e and Π are called the transcendental numbers.Alternate AnglesIf two or more parallel lines are cut by a transversal, then the angles formed in the alternatedirection to each other are called as alternate angles.Alternate Exterior AnglesWhen two or more parallel lines are cut by a transversal and the alternate angles that are exteriorto one another is called alternate exterior angle.Alternate Interior AnglesWhen two or more lines are cut by a transversal then the alternate angles that lie interior to eachother are called alternate interior angles. 2
- 3. Dictionary of MATH TERMSAltitudeAltitude is the shortest distance between the base to the apex of a figure like cones, triangle etc.Altitude of a ConeThe distance between the apex of the cone and its base is called the height or the altitude of thecone.Altitude of a CylinderThe distance between the circular bases of the cylinder or the length of the line segment betweentwo of its bases is known as altitude of a cylinder.Altitude of a ParallelogramThe distance between the opposite sides of a parallelogram is called as altitude of aparallelogram.Altitude of a PrismThe distance between the two bases of a prism is called as the altitude of a prism.Altitude of a PyramidThe distance between the apex of the pyramid to the base is called as altitude of the pyramid.Altitude of a TrapezoidThe distance between the two bases of the trapezoid is called as altitude of a trapezoid.Altitude of a TriangleThe shortest distance between the vertex of the triangle and the opposite side is called as altitudeof the triangle.AmplitudeA mathematical definition of amplitude is that it is means the measure of half the distancebetween the maximum and minimum range. For example, if you consider a sine wave, then ½ ofthe distance between the positive and negative curves in called amplitude. It is to be rememberedthat only periodic functions with bounded range have amplitude.Analytic GeometryAnalytical geometry is the branch of mathematics that deals with the study of geometric figureswith the help of co-ordinate axes. The points are plotted and with the help of the points we caneasily find out the required information. 3
- 4. Dictionary of MATH TERMSAnalytic MethodsIf you are asked to analytically solve a problem then it means that you are not suppose to use acalculator. Analytical methods are used to solve the problems by the help of algebraic andnumeric methods.AngleAngle is defined as the figure formed by touching the end of two rays. Angle in other word istwo rays sharing a common point.Angle BisectorThe line that bisects an angle into two equal halves is called as an angle bisector.Angle of Inclination of a LineThe angle subtended by a line with the x-axis is called as angle of inclination of the line. Theangle of inclination is always measured in counter clockwise direction, that means positivedirection of the x-axis. The angle of inclination is always between the range 00 to 1800.AnnulusThe area between two concentric circles of a ring (say) is called annulus.Antiderivative of a FunctionIf F(x) = 2x2 + 3, then, its derivative F(x) = 4x. Here 4x is called as the antiderivative of F(x).Antipodal PointsIn three dimensions the points diametrically opposite on a sphere is called antipodal points.ApothemApothem is the same as the in radius of an inscribed circle in a regular polygon. If we define inother words then it would mean the distance from any of midpoint of the sides of the polygon tothe center of the polygon.Approximation by DifferentialsBy the rule of approximation of differentials the value of a function is approximated and theprinciples of derivation are used in this method. The formula used in the approximation bydifferentials is, f(x + ∆x) = f(x) + ∆y = f(x) + f(x)∆x, where f(x) is the differential of thefunction.Area of a CircleThe area of a circle is given by the formula Πr2. 4
- 5. Dictionary of MATH TERMSArccosThe inverse function of a cosine function is called the arccos function. For example, cos-1(1/2)(read as cos inverse half) or"the angle whose cosine is equal to ½. As we all know it nothing but600.ArccosecThe inverse of a cosec function is called arccosec function. For example, cosec-1(2) means theangle whose cosecant is equal to 2. The answer is 300. It is to be noted that there can be manymore angles with the cosecant equal to 300. What we want is the most basic angle that gives thecosecant equal to 300. For other angles, we need to consider the range of the function.ArccotArc cot is the inverse of the cotangent function. For example, cot-1(1) means the angle whosecotangent is equal to 1. Cot-11 = 450.ArcsecThe inverse of a secant function is called the arcsec function. For example, sec-12 means theangle whose secant is equal to 2. Sec-12 = 600.ArcsinThe inverse of a sine function is called arcsin function. For example, sin-1(1/2) = 300.ArctanThe inverse of a tangent function is called arctan function. For example, tan-1(1) = 450Area of an EllipseThe area of an ellipse is given by the formula ∏ab, where a and b are the lengths of the majorand minor axis of the ellipse. If the ellipse has its center at (h, k) then,Area = [(x-h)2/a2 + (y-k)2/b2]Area of an Equilateral TriangleThe area of an equilateral triangle is given by:a2√3/4, where a = side of the equilateral triangle.Area of a KiteThe area of a kite is given by:½ (product of the diagonals) = ½ x d1d2.Area of a Parabolic SegmentThe area of a parabolic segment is given by 2/3 of the product of width and height. 5
- 6. Dictionary of MATH TERMSArea of a ParallelogramAre of parallelogram = height x base of the parallelogram.Area of a RectangleArea of rectangle = length x breadthArea of a Regular PolygonArea of regular polygon = ½ x apothem x perimeter.Area of a RhombusDiagonals of a rhombus are perpendicular to each other. Area = ½ x product of diagonals orArea= h x s, where h and s are the height and side of the rhombus.Area of a Segment of a CircleWe all know the area of a circle, but what if the area of a segment is to be found out, well theformula for area of a segment of a circle is:Area = 1/2r2(θ – sinθ) (radians)Area of a TrapezoidArea of a trapezium = ½ x (sum of the non- parallel sides) x h = ½ x (b1 + b2) x hArea of a TriangleThere are various formulas to calculate the area of a triangle that are as follows. Area = A = ½ x base x height A = ½ x ab SinC = ½ x bc SinA = I/2 x ca SinB, where A, B and C are the angles of the triangle respectively. Given s= a+b+c/2 (semi perimeter), by Herons Formula, A= [s(s-a)(s-b)(s-c)]1/2. If r and R are the inradius and circumradius of the incircle and outercirlce of a triangle, then the Area (A) = rs and A= abc/4R, a, b and c are the sides of the triangle.Area Using Polar CoordinatesWhen the polar co-ordinates are involved in computation of the area then the area is given by:The area between the graph r = r(θ) and the origin and also between the lines θ = α and θ = β isgiven by the formula:Area = ½ αʃβr2dθ 6
- 7. Dictionary of MATH TERMSArgand PlaneThe complex plane is called as the argand plane. Basically, argand plane is use to denote thecomplex numbers graphically. The x-axis is called as the real axis and the y-axis is called as theimaginary axis.Argument of a FunctionThe term or expression on which the function operates is called as argument of the function. Theargument of the function y= √x is x.Argument of a VectorThe measure of an angle describing a vector or a line in the complex number analysis is calledthe argument of the vector.Arithmetic MeanThe most simple average technique that we use in day to day life.For example, if there are 4 quantities then there arithmetic mean is given by,Arithmetic mean = (a + b + c + c + d)/4Arithmetic ProgressionA mathematical series that has same common difference among its terms.For example, 1, 3, 5, 7, 9.....up to infinity. The nth term of an arithmetic progression is given by,Tn = a + (n-1)d, where a = 1st term, n = number of terms and d= common difference. It is alsocalled as arithmetic sequence. The sum of an arithmetic progression is given by: S = n/2[2a + (n-1)d] or S = n(a1 + an)/2, here n= number of terms.Arm of an AngleOne of the rays/line forming an angle with the other is called the arm of an angle.Arm of a Right TriangleAny of the sides of the right angled triangle is called the arm of a right angled triangle.AssociativeThe operation a + (b+c) = (a + b) + c is called as associative operation. Addition andmultiplication are associative while division and subtraction are not. For example, (4+5)+ 7 = 4 +(5+7)AsymptoteAn asymptote is a curve or line that approaches the curve very closely. There are horizontal andoblique asymptotes but not vertical asymptotes.Augmented MatrixThe matrix representation of a set of linear equations is called the augmented matrix. 7
- 8. Dictionary of MATH TERMSFor example, 3x – 2y = 1 and 4x + 6y = 4, then in a matrix form 3, -2 and 1 (from 1st equation)and 4, 6 and 4 (from 2nd equation) form the elements of 3x3 matrix respectively.AverageAverage is same as the arithmetic mean.Average Rate of ChangeMathematically, the change in the slope of a line is called as the average rate of change of theline. Also, the change in value of a quantity divided by time is average rate of change.Average Value of a FunctionFor a function y =f(x), in the domain [a,b] the average value is given by the formula (1/b-a)aʃbf(x)dxAxesThe x and y, z axes are known as the axes of a co-ordinate system.AxiomA statement that has been assumed to be true without any proof.Axis of a CylinderThe line that passes exactly through the center of the cylinder and also passes through the basesof the cylinder. Simply stated, the line that divides the cylinder into two equal halves vertically.Axis of ReflectionA line across which the reflection takes place.Axis of RotationAn axis along which the rotation of the axis takes place.Axis of SymmetryA line along which the geometrical figure or the shape is symmetrical.Axis of Symmetry of a ParabolaThe axis of symmetry of a parabola is the line that passes through the focus and vertex ofparabola. 8
- 9. Dictionary of MATH TERMSBBase (Geometry)The bottom part of a geometrical figure like a solid object or a triangle is called the base of theobject.Base of an Exponential ExpressionConsider the expression ax. Then a can be called as the base of the expression ax.Base of an Isosceles TriangleThe base of an isosceles triangle is the non-congruent side of the triangle. In other words, it is theside other than the legs of the triangle.Base of a TrapezoidThe trapezoid has four sides with two sides parallel. Either of the two parallel sides can beconsidered as the base of the trapezoid.Base of a TriangleBase of a triangle is the side at which an altitude can be drawn. It is the side which isperpendicular to the altitude.BiconditionalIt is the method of expressing a mathematical statement containing more than one conditions,that means a condition and its converse. These statements are called as biconditionals.Biconditionals are represented by the symbol ⇔. For example the following statements can becalled biconditionals: "A given triangle is equilateral" is same as "All the angles of a trianglemeasure 60º."BinomialA binomial can be simply defined as a polynomial which has two terms, but they are not liketerms. For example, 3x – 5z3, 4x – 6y2.Binomial CoefficientsThe coefficients of the various terms in the binomial expansion of the binomial theorem arecalled as binomial coefficients. Mathematically, a binomial coefficients equals the number of ritems that can be selected from a set of n items. They are simply called as the binomialcoefficients because they are coefficients of the binomial expanded terms. Generally, they arerepresented by nCr.Binomial Coefficients in Pascals TrianglePascals triangle is an arithmetic triangle that is used to calculate the binomial coefficients of thevarious numbers. The binomial coefficients (nCr) in the pascals triangle are called as the 9
- 10. Dictionary of MATH TERMSbinomial coefficients in pascals triangle. Pascals triangle finds major use in algebra andprobability/binomial theorem.Binomial Probability FormulaThe probability of getting m successes in n trials is called binomial probability formula. Theformula is given by:Formula: P(m successes in n trials) = mCnpkqn-k, where,n = number of trialsm = number of successesn – m = number of failuresp = probability of success in one trialq = probability of failure in one trial.Binomial TheoremA theorem used to expand the powers of polynomial terms and equations. It is given by:(a + b)n = nC0an + nC1an-1b +..........+nCn-1abn–1 + nCn.Boolean AlgebraBoolean algebra deals with the logical calculus. Boolean algebra takes only two values in thelogical analysis, either 1 or zero. Read more on Boolean Origination.Boundary Value ProblemAny differential equation that has constrained on the values of the function (not that on thederivatives) is called as the boundary value problem.Bounded FunctionA function that has a bounded range. For example, in the set [2, 9], 9 the upper bounded numberand 2 is the lower bounded number.Bounded SequenceA sequence that is bounded with upper and lower bounds. Like the harmonic series, 1, ½, 1/3,¼,...up to infinity is a bounded function since the function lies between 0 and 1.Bounded Set of Geometric PointsThe bounded set of geometric points is called as the figure or set of points that can be enclosed ina fixed space or co-ordinates.Bounded Set of NumbersA set of numbers with lower and upper bound. For example, [3, 7] is called as the bounded set ofnumbers. 10
- 11. Dictionary of MATH TERMSBoxA rectangular parallelepiped is often referred to as a box. The volume of such a rectangular boxis given by the product of length, breadth and height.BoxplotA data that displays the five number summary in a diagrammatic form represented as:Smallest 1st Quartile Median 3rd Quartile LargestBracesThe symbolic representation {or} that is used to indicate sets etc.BracketsThe symbol [ ] which signifies grouping. They work in a similar way parentheses do.CCalculusThe branch of mathematics that deals with integration, differentiation and various other forms ofderivatives.Cardinal NumbersCardinal numbers are used to indicate the number of elements in an infinite or finite sets.CardinalityIt is same as cardinal numbers. It is to be noted that cardinality of every infinite set is same.Cartesian CoordinatesThe Cartesian coordinates are the axes that are used to represent the coordinates of a point. (x,y)and (x,y,z) are the Cartesian coordinates.Cartesian PlaneThe planes formed by horizontal and vertical axes like the x and y axis is called the Cartesianplane.CatenaryThe curve formed by a hanging a wire or a ring is called as catenary. Generally, a catenary isconfused with a parabola. However, though the looks are similar, it is not same as the parabola.The graph of a hyperbolic cosine function is called the catenary. 11
- 12. Dictionary of MATH TERMSCavalieri’s PrincipleA method to find the volume of solids by using the formula V = bh, where b = area of crosssection of the base (cylinder/prism) and h = height of the solid.Central AngleAn angle in a circle with vertex at the circles center.CentroidThe intersection point of the three medians of a triangle.Centroid FormulaThe centroid of the points (x1, y1, x2, y2,....xn, yn) is given by:(x1 + x2 + x3+......xn)/n , (y1 + y2 + y3+ …..yn)/nCeva’s TheoremCevas theorem is a way that relates the ratio in which three concurrent cevian divides a triangle.If AB, BC and CA are the three sides of a triangle and and AE, BF and CD are the three cevianof the triangle, then according to Cevas theorem,(AD/DB)(BE/EC)(CF/FA) = 1.CevianA line that extends from the vertex of a triangle to the opposite side like altitudes and medians.Chain RuleA method used in differential calculus to find the derivative of a composite function.(d/dx)f(g(x)) = f((g(x))g(x) or (dy/dx) = (dy/du)(du/dx)Check a SolutionChecking a solution means putting the value of corresponding variables in the equation andverify if the equations satisfy the given equation or systems of equation.ChordA chord is a line segment that joins the two points on a curve. In a circle, the largest chord is thediameter that joins the two ends of the circle.CircleThe locus of all points that is always at a fixed distance from a fixed point.Circular ConeA cone with a circular base. 12
- 13. Dictionary of MATH TERMSThe volume of circular cone is given by V = 1/3πr2Circular CylinderA cylinder with circle as bases.CircumcenterThe center of a circumcircle is called as circumcenter.CircumcircleA circle that passes through all the vertices of a regular polygon and triangles is called ascircumcircle.CircumferenceThe perimeter of a circular figure.CircumscribableA plan figure that has a circumcircle.CircumscribedA figure circumscribed by a circle.Circumscribed CircleThe circle that touches the vertices of a triangle or a regular polygon.ClockwiseThe direction of the moving hands of a clock.Closed IntervalA closed interval is the one in which, both the first and last terms are included while consideringthe entire set. For example, [3,4].CoefficientThe constant number that is multiplied with the variables and powers in an algebraic expression.For example, in 234x2yz, 243 is the coefficient.Coefficient MatrixThe matrix formed by the coefficients of a linear system of equations is called the coefficientmatrix 13
- 14. Dictionary of MATH TERMSCofactorWhen a determinant is obtained by deleting the rows and columns of a matrix in order to solvethe equation, it is called as the cofactors.Cofactor MatrixA matrix with the elements of the cofactors, term by term, in a square matrix is called as thecofactor matrix.Cofunction IdentitiesCofunction identities are the identities that show the relation between the trigonometricalfunctions like the sine, cosine, cotangent,CoincidentIf two figures are superimposed on each other, then they are said to be coincident. In otherwords, a figure is coincident when all points are coincident.CollinearTwo points are said to be collinear if they lie on the same line.Common LogarithmThe logarithm to the base 10 is called as common logarithm.CommutativeAn operation is said to be commutative if x ø y = y ø x, for all values of x and y. Addition andmultiplication are commutative operations. For example, 4 + 5 = 5 + 4 or 6 X 5 = 5 X 6. Divisionand subtraction are not commutative.Compatible MatricesTwo matrices are said to be compatible for multiplication if the number of columns of 1st matrixequals to the number of rows of the other.Complement of an AngleThe complement of angle say 75º is 90º – 75º = 15º.Complement of an EventThe set of all outcomes of an event that are not included in the event. The complement of set A iswritten as Ac. The formula is given as: P(Ac) = 1 – P(A) or P (not A) = 1- P(A).Complement of a SetThe elements of a given set that are not contained in the given set. 14
- 15. Dictionary of MATH TERMSComplementary AnglesIf the sum of two angles is 90º, then they are said to be complementary angles. For example, 30ºand 60º are complementary to each other as their sum equals 90º.Composite NumberA positive integer whose factors are the numbers other than 1 and the number itself. Forexample, 4, 6, 9, 12 etc. 1 is not a composite number.Compound FractionA compound fraction is a fraction that has at least one fraction term in the numerator anddenominator.Compound InequalityWhen two or more than two inequalities are solved together it is known as compound inequality.Compound InterestWhile calculating compound interest, the amount that is earned as an interest for a certainprincipal is added to the principal and from that moment the interest is calculated on the newprincipal. Thus, the interest is not only calculated on the original balance but the balance orprincipal obtained after adding the interest.ConcurrentIf two or more than two lines or curves intersect at the same point then they are said to beconcurrent at that point.Conditional EquationA equation that is true for some values of the variables and is false for other values of thevariables. The equation has certain conditions imposed on it that are only satisfied by certainvalues of the variables.Cos-1xThe inverse of cos function is read as cos inverse x. For example, cos-1½ = 60º.Cot-1xBy cot-1x we mean the angle whose cotangent is equal to x. For example, when we are asked tofind the smallest angle whose cotangent is equal to 1? The answer is 45º. Thus, cot-11 = 45º.CubeCube is a three dimensional figure bounded by six equal sides. The volume of cube is given byl3, where l is the side of a cube. 15
- 16. Dictionary of MATH TERMSCube RootA cube root is a number denoted as x⅓ such that b3 = x For example, (64)⅓ = 4.Cubic PolynomialA polynomial of degree 3 is known as the cubic polynomial. For example, x3 + 2x2 + x.CuboidCuboid is a three dimensional box that has length, width and height. Rectangular Parallelepipedis the other name for a cuboid.DDe Moivre’s TheoremDe Moivers Theorem is a formula that is widely used in complex number system in order tocalculate the powers and roots of complex numbers. Mathematically, it is given by:[r(cosθ + isinθ)]n = rn(cosnθ + isinnθ).DecagonA 10 sided polygon is called as decagon.DecilesIn statistics, deciles are any of the nine values that divide the data into 10 equal parts. The firstdecile cuts off at the lowest 10% of the data that is called as the 10th percentile. The 5th decilecuts off the at the lowest 50% of the data that is called as 50th percentile or 2nd quartile ormedian. The 9th decile cuts off lowest 90% of the data that is the 90th percentile.Decreasing FunctionA function whose value decreases continuously as we move from left to right of its graph iscalled decreasing function. A line with negative slope is a perfect example of a decreasingfunction where the value of the function decreases as we proceed on the x-axis. If the decreasingfunction is differentiable then its derivative at all points (where the function is decreasing) willbe negative.Definite IntegralAn integral that is evaluated over an interval. It is given by aʃbf(x)dx. Here the interval is [a, b].Degenerate Conic SectionsIf a double cone is cut with a plane passing through the apex of the plane, it is called as thedegenerate conic sections. It has the general equations of the form:Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 16
- 17. Dictionary of MATH TERMSDegreeDegree is the measure of the slope or the angle that a line or a plane subtends. Degree isrepresented by the symbol °.Degree of a PolynomialThe power of a highest term in an algebraic expression is called as the degree of the polynomial.In the expression 2x5 + 3y4 + 5x3, the degree of the polynomial is 5.Degree of a TermIn 5y7, degree of term is 7, in 5x24y3, the degree of the term is the sum of the exponents of 5xand 4y, that means 5.DenominatorThe lower part of a fraction is called denominator. In fraction (4/5), 5 is the denominator.Dependent VariableConsider an expression y = 2x + 3, here, x is the independent variable and y is the dependentvariable. It is a general notion to plot the graph by taking independent variable on x axis anddependent variable on Y-axis.DerivativeThe slope of a line tangent to a function is called as the derivative of the function. This is thegraphical interpretation of the derivative. As a differentiation operation, consider f(x) = x2 thenits derivative is f(x) = 2x.Descartes Rule of SignsA method for determining the maximum number of positive zeros of a polynomial. According tothis rule, the number of changes in the sign of the algebraic expression gives the number of rootsof the expression.DeterminantDeterminants are the mathematical objects that are very useful in determining the solution of aset of system of linear equations.Diagonal MatrixA square matrix that has zeroes everywhere except the main diagonal.Diagonal of a PolygonA line segment joining non-adjacent vertices of a diagonal. If a polygon is of n-sides then thenumber of diagonals is given by the formula:n(n-3)/2 diagonals. 17
- 18. Dictionary of MATH TERMSDiameterThe longest chord of a circle is called diameter. It can be also defined as the line segment thatpasses through the center of the circle and touches both the ends of the circumference of thecircle.Diametrically OpposedTwo points directly opposite to each other on a circle.DifferenceThe result of subtracting two numbers is called as difference.DifferentiableA curve that is continuous at all points of its domain is called as a differentiable function. Inother words if a derivative exists for a curve at all points of the domains variable, it is said to bedifferentiable.Differential EquationA mathematical equation involving the functions and derivatives. For example, (dy/dx)2 = yDifferentiationPerforming the process of finding a derivative.DigitAny of the numbers among the nine digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.Dihedral AngleThe angle formed by the intersection of two planes.DilationDilation refers to the enlargement of a geometrical figure by transformation method.Dilation of a Geometric FigureA transformation in which all distances are increased by some common factor. The points arestretched from a common fixed point P.Dilation of a GraphIn graphical dilation, the x-coordinates and y-coordinates are enlarged by some common factor.The factor by which the transformation of the graph is done must be greater than 1. If the factoris less than 1, it is called compression. 18
- 19. Dictionary of MATH TERMSDimensionsThe sides of a geometrical figure are often referred to as dimensions.Dimensions of a MatrixThe number of rows and columns of matrix is called as the dimensions of the matrix. Forexample if a matrix has 2 rows and 3 columns, its dimensions will be 2X3 (read as two crossthree).Direct ProportionWhen one of the variables is a constant multiple of the other, it is called as direct variation. Forexample, y = kx (here y and x are the variables and k is a constant factor).Directrices of an EllipseTwo parallel lines on the exterior of an ellipse that are perpendicular to the major axis.Eee is a transcendental number that has a value approximately equal to 2.718. It is frequently usedwhile working with logarithms and exponential functions.EccentricityA number that indicates the shape of a curve. It is represented by the small letter e (This e is inno ways related to the exponential e = 2.718). In conic section, the eccentricity of the curves is aratio between the distance from the center to focus and either the horizontal or vertical distancefrom the center to the vertex.Echelon Form of a MatrixAn echelon matrix is used to solve a system of linear equations.Edge of a PolyhedronOne of the line segments that together make up the faces of the polyhedron.Element of a MatrixThe numbers inside the matrix in the form of rows and columns is called as the element ofmatrix.Element of a SetAny point, line, letter, number etc. contained in a set is called as the element of the set. 19
- 20. Dictionary of MATH TERMSEmpty SetA set that doesnt contains any element. The empty set is represented by {} or Ø.Equality Properties of EquationThe equality properties of algebra that are used to solve the algebraic equations. Themathematical definitions of these equality properties are as followsx = y means, x is equal to y and y ≠ x means y is not equal to x. The operations of addition,subtraction, multiplication and division all hold true for equality properties of equation.Reflexive Property- x = x;Symmetric Property- If x = y then y = x;Transitive Property- If x = y and y = z then x = zEquilateral TriangleAn equilateral triangle has all its three sides equal and the measure of each angle is 60º.Equivalence RelationAny equation that is reflexive, symmetric and transitive.Equivalent Systems of EquationTwo sets of simultaneous equations that have same solution.Even FunctionA function whose graph is symmetric about y-axis. Also, f(-x) = f(x).Even NumberThe set of all integers that are divisible by 2. E= {0, 2, 4, 6, 8......}Explicit DifferentiationThe derivative of an explicit function is called as the explicit differentiation. For example, y = x 3+ 2x2 - 3x. Differentiating it gives,y= 3x2 + 4x – 3.Explicit FunctionIn an explicit function, the dependent variable can be totally expressed in terms of independentvariable. For example, y= 5x2 - 6x.Extreme Value TheoremAccording to this theorem, there is always at least one absolute maximum and one absoluteminimum for any continuous function over a closed interval. 20
- 21. Dictionary of MATH TERMSExtreme Value of a PolynomialThe graph of a polynomial of degree n has at most n-1 extreme values (either maxima orminima)FFace of PolyhedronPolygonal outer boundary of a solid object having no curved surfaces.Factor of an integerIf the given integer is divided evenly by another integer then the resultant is called factor of aninteger. For example: 2, 4, 8, 16 etc, are the factors of 32.Factor of polynomialPolynomial P(x) is completely divided into Polynomial R(x) by Q(x) then Q(x) is called Factorof polynomial. For example: P(x)= x2+6x+8, Q(x)=x+4 then P(x)/Q(x)= x+2. Q(x)=x+4 is thefactor.Factor theoremWhen x-a is factor of P(x), the value x in P(x) is replaced with a, then if the resultant value is 0,such a theorem is called Factor theorem. For example: P(x)= x2+6x+24. Q(x)= x-(-4). If x isreplaced with a, that is -4, then P(x)= 0.FactorialThe product of the an integer with all the consecutive smaller integers is called a factorial. It isrepresented as "n!". For example: 5! = 5*4*3*2*1= 120.Factoring RulesThese are the formulas that govern the factorization of a polynomial. For example x2-(a+b)x +ab= (x-a)(x-b). x2+2(a)x+a2=(x+a)2 x2-2(a)x +a2=(x-a)2FiniteThe term is used to describe a set in which all the elements can be counted using naturalnumbers.First DerivativeA function F(a), which governs the slope of the curve at any given point or the slope of the linedrawn tangent to the curve from that point in the plane is called the first derivative. It is 21
- 22. Dictionary of MATH TERMSrepresented as F. For F(x)= 5x2. F(x)=10x will be the slope of the curve.First Derivative testA Technique which is used to determine the capacity of inflection point.(minimum, maximum orneither)First Order of the differential equation A differential equation P(a) whos order is 1. Forexample: P(a)=3a, here the order of a is 1.FlipIt is also known as axis of reflection. It is a line which divides the plane or a geometric figureinto two halves that are mirror images of each other.Floor Function (Greatest Integer Function)It is a function F(x) which is responsible for finding the greatest integer less that the actual valueof P(x). For example: P(x)= 5.5, here the greatest integer less than 5.5 is 5. The function whichgives F(x)=5 becomes floor function.Foci of the EllipseThey are the fixed two points inside the ellipse such that the vertical curve is governed accordingto the equation L1+L2= 2a and horizontal curve according to equation L1+L2=2b where L is thedistance between the focal point and the curve, a is the horizontal radius and b is the verticalradius.Foci of hyperbolaThey are fixed two points inside of the curve of hyperbola such that the determinant of the L1-L2is always constant. L1 and L2 are the distances between point P (which is the curve) andrespective focus of the curve.FocusThe curves of the conic sections are governed according to distances from a special point calledfocus.FOIL methodFOIL is an acronym for First Outer Inner Last. It is method by which binomials are multiplied.The Multiplication order is First terms of Binomials Outer terms of Binomial Inner terms of binomials 22
- 23. Dictionary of MATH TERMS Outer terms of Binomials.For example: (a+b)(a-b)= a.a+a.(-b)+b.a +b.(-b)FormulaThe relationship between various Variables (sometimes expressed in the form of an equation)depicted using symbols. For example: a+b=7FractalWhen every part of the figure is similar to every other part of other figure, then the figure iscalled fractal.FractionIt is a ratio between two numbers. For example: 9/11.Fraction RulesThe rules of algebra used for uniting various the fractions.Fractional EquationThe expression in the form of A/B on both the sides of equal sign is called fractional equation.For example: x/6= 4/3.Function OperationVarious Operations such as additions, subtractions, multiplications, divisions and compositionswhich have a combining effect on various functions. For example: F(a/b)= F(a)/F(b).Fundamental theorem of AlgebraEvery polynomial characterized by single variable having complex coefficients, will have aminimum of at least one root which is also complex in nature.Fundamental Theorem of ArithmeticThe statement that the factors of a prime number are always distinct and unequal is thefundamental theorem of arithmetic.Fundamental Theorem of CalculusDifferentiation and integration are two most basic operations of the calculus. The theorem thatestablishes a relationship between them is called Fundamental theorem of Calculus.GGauss-Jordan EliminationA method of solving a system of linear equations. In this process the augmented form of the 23
- 24. Dictionary of MATH TERMSmatrix system is reduced into row echelon form by means of row operations.Gaussian EliminationA method of solving a system of linear equations. In Gauss elimination method, the augmentedform of matrix is reduced to row echelon form and then the system is solved by backsubstitution.Gaussian IntegerGaussian integers are the integers in the complex numbers that are represented by a + bi. Forexample, 3 + 2i, 5i and 6i + 5 are called Gaussian integers.GCFThe largest integer that divides a certain set of numbers. Also called as Greatest Common Factor.For example, the GCF of 20, 30 and 60 is 10.General Form for the Equation of a LineThe general form of equation of a line is represented by the equation-Ax + By + C = 0, where, A, B and C are integers.Geometric FigureA geometric figure is a set of points on the plane or space that leads to the formation of figure.Geometric MeanGeometric mean is a method of finding the average of certain set of numbers. For example, ifthere are numbers a1, a2, a3,........anthen multiply the numbers and take the nth root of the product.Geometric Mean = (a1, a2, a3,........an)½Geometric ProgressionA geometric progression is a mathematical sequence whose terms are in a constant ratio with theprevious terms. For example, 2, 4, 8, 16, 32.....128 are the terms of a geometric progression. Herethe common ratio is 2. (as 4/2 = 8/4 = 16/8....)Geometric SeriesGeometric series is a mathematical series whose successive terms are in a constant ratio. Anexample of geometric series is 2, 4, 8, 16, 32........GeometryThe study of geometric figures in two and three dimensions is called as geometry. 24
- 25. Dictionary of MATH TERMSGreatest lower boundThe greatest of all lower bounds of a set of numbers is called as the GLB or greatest lowerbound. For example, in the set [2,7], the GLB is 2.Glide ReflectionA transformation in which a figure has to go through a combination of steps of translation andreflection.Global MaximumThe highest point on the graph of a function or a relation (in the domain of the function). Thefirst and second derivative tests are used to find the maximum values of a function. It is alsocalled as global maximum, absolute maximum and relative maximum.Global MinimumThe lowest point on the graph of a function or a relation. The first and second derivative tests areused to find the minimum values of a function. It is also called as the global minimum, absoluteminimum or global minimum.Golden MeanThe ratio (1 + √5)/2 ≈ 1.61803 is called as the golden mean. The unique property of golden meanis that the reciprocal of golden mean is about 0.61803. Hence, the golden mean is one plus itsreciprocal.Golden RectangleIf the ratio of length and breadth of a rectangle is equal to the golden mean then the rectangle iscalled as the golden rectangle. It is believed that this rectangle is most pleasing to the eyes.Golden SpiralA spiral that can be drawn inside the golden rectangle.GoogolThe number 10100 is called as googol.GoogolplexGoogolplex can be written as 10100100.Graph of an Equation or InequalityThe graph obtained by plotting all the points on the coordinate system. 25
- 26. Dictionary of MATH TERMSGraphic MethodsThe use of graphical methods to solve the mathematical problems.Greatest Integer FunctionThe greatest integer function of any number (say x) is an integer less than or equal to x. Thegreatest integer function is represented as [x]. For example, [3.4] = 3 and [-2.5] = 3HHalf Angle identitiesThe identities of trigonometry that are used to calculate the value of sine, cosine, tangent etc. ofhalf of a given angle.The trigonometric identities are as follows:sin2x = (1 – cos2x)/2cos2x = (1 + cos2x)/2Half Closed Interval/Half Open IntervalIt is a set of all numbers containing only one end point.Harmonic MeanThe inversion of the summation of the reciprocals of a set of numbers. For example: (1, 2, 3) arein a set then their harmonic mean is 1/(1+ ½+ ⅓ )Harmonic ProgressionIt is a sequence in which every term is the reciprocal of the natural number. For example 1, ½, ⅓,¼.Harmonic SeriesThe summation of all the terms in harmonic progression. For example: 1+ ½+ ⅓+ ¼HeightThe least measurable distance between the base and the top of a geometric figure is called as theheight. The top can be the opposite vertex, or an apex or even another base of the figure.Height of the ConeThe distance between the center of the circular base and the vertex of the cone can be called asthe height of the cone.Height of CylinderThe distance between the centers of the circular bases of the cylinder is the height of thecylinder. 26
- 27. Dictionary of MATH TERMSHeight of a ParallelogramThe perpendicular distance between the parallel sides of a parallelogram (i.e. the base to theopposite side).Height of a PrismThe length of the shortest line segment between the bases of the prism.Height of a PyramidThe shortest distance between the vertex and extended base of the pyramid.Height of a TriangleThe length of the shortest line segment between a vertex and the opposite side of the triangle.HelixIt is a spiral shape curve in three dimensional space.HeptagonA heptagon can be called as a polygon which has seven sides. Its other name is septagon, butheptagon is widely used.Heros FormulaSuppose all the three sides of the triangle are known. The formula used to calculate the area ofthe triangle in this scenario is called Heros formula. For example: √[s(s-a)(s-b)(s-c)]HexagonIt is a special geometric figure which has six sides and angles.HexahedronA solid which has no curved surfaces and the number of surfaces are equal to six.HyperbolaA hyperbola is a geometric figure, which is a locus of two points called as foci, where thedifference between the distances to each point is constant.Hyperbolic GeometryGiven two entities, a point and a line, there can be infinitely many lines passing through the pointand are parallel to first point. This is called Hyperbolic geometry.Hyperbolic TrigonometryThe trigonometric functions sine cosine tangent etc. whos values are calculated using e.Mathematical definitions of hyperbolic trigonometry are as follows: 27
- 28. Dictionary of MATH TERMSsinhx = (ex - e-x)/2,coshx = (ex + e-x)/2tanhx = (sinhx/coshx) = (ex - e-x)/(ex + e-x)/2HypotenuseThe hypotenuse is longest side of right angled triangle.Hypotenuse-leg CongruenceTwo different right angle triangles are said to be congruent when their hypotenuse and one of thecorresponding legs are equal in length.Hypotenuse-leg SimilarityIn two right angled triangles when the ratio of the corresponding sides have equal ratios, thensuch triangles are having HL Similarity.IiIn complex number analysis, the letter i denotes iota. Mathematically, iota is given by negativesquare root of 1, that means √-1. = iIcosahedronIcosahedron is a polyhedron with 20 faces. In the case of a regular icosahedron, the faces are allequilateral triangles.Identity (Equation)An equation that is true for any values of the variable. For example, the identity, sin2θ + cos2θ =1 is true for all values of θ.Identity FunctionThe function f(x) = x is called as the identity function.Identity MatrixA square matrix that has 1 as its element in the principal diagonal and rest all elements are zero.Image of a TransformationThe image obtained after performing the operations of dilation or rotation or translation.Imaginary NumbersA complex number like 7i, that is free of the real part is called as the complex number.Imaginary Part 28
- 29. Dictionary of MATH TERMSConsider a complex number -7 + 8i, the coefficient of i called as the imaginary part of thecomplex number.Implicit Function or RelationA function in which the dependent variable cant be exactly expressed as a function of theindependent variable.Implicit DifferentiationDifferentiating an implicit function. For example, consider 4x2 + 5y5 - 6x = 1. Here, y cant bewritten explicitly as a function of x.Impossible EventAn event that is impossible to happen or an event whose probability is zero.Improper FractionA fraction that has denominator greater than its numerator.Improper IntegralA integration in which the bounds of integration has discontinuities in the graph. They can alsohave limits between ∞ and -∞. The discontinuities between the bounds of integration makes theuse of limits necessary in evaluating improper integrals.Improper Rational ExpressionIf the degree of a numerator polynomial is more than or equal to the degree of a denominatorpolynomial than the rational expression is called as the improper rational expression.IncenterThe center of a circle inscribed in a triangle or a polygon. Geometrically, incenter is the point ofintersection of the angle bisectors of a triangle.IncircleThe largest possible circle that can be drawn inside a plane figure. All triangles and regularpolygons have incircle.Inconsistent System of EquationsA system of equations that has no solutions.Increasing FunctionA function whose value increases continuously as we move from left to right of its graph iscalled increasing function. A line with positive slope is a perfect example of increasing functionwhere the value of the function increases as we proceed on the x-axis. If the increasing function 29
- 30. Dictionary of MATH TERMSis differentiable then its derivative at all points (where the function is increasing) will benegative.Indefinite IntegralI = a∫bf(x) dx, is known as the improper integralIndefinite Integral RulesIndependent EventsIf the occurrence or non-occurrence of two events is independent of each other it is called as theindependent event.Independent VariableThe quantity in an equation whose values can be freely chosen in an equation without taking intoconsideration the values of the other variables.Indeterminate ExpressionsAn undefined expression that cannot be assigned any value. There are various forms ofindeterminate expressions: 0/0 ±∞/±∞ 00 1∞ ∞0 ∞-∞InductionA method of proving a mathematical problem by the help of a series of steps. Mathematicalinduction is used to prove complex mathematical problems.Independent EventsTwo or more events are said to be independent events if the occurrence or non-occurrence of anyof these events doesnt affect the occurrence or non-occurrence of others. By the principle ofprobability, if A and B are two independent events, then P(A|B) = P(A).Independent VariableIndependent variables are those whose value can be chosen without any restriction. For example,in the equation Y = 2x2 + 3x, y is the dependent variable and x is the independent variable. 30
- 31. Dictionary of MATH TERMSIndirect ProofProving a statement or a fact by the method of contradiction is known as indirect proof. Thismeans that the conjecture is taken to be false and then it is proved that the statement contradictsthe assumption made at the beginning of solving the problem.JJoint variationWhen a quantity varies directly with the other quantity then it is called as the joint variation. Forexample when we say x is directly proportional to the square of y, it means that x = ky2, where k= proportionality constant.KKiteA kite is nothing but a quadrilateral, with each pair of its adjacent sides congruent to each otherand diagonals perpendicular to each other.LLHospitals RuleThis is a technique that is used to find out the limit of the functions that evaluate to indeterminateforms, like 0/0 or infinity/infinity. The solution is found out by individually calculating the limitsof the numerator and the denominator.Lateral Surface AreaLateral Surface Area is nothing but the surface area of the lateral surfaces of a solid. It does notinclude the area of the base(s) of the solid.Latus RectumIt is the line segment that passes through the focus of a conic section and is perpendicular to themajor axis, with both its end points on the curve.Law of CosinesAn equation that relates the cosine of an interior angle of a triangle to the length of its sides iscalled the law of cosines.If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle betweena and c and C the angle between a and b, then the law of cosines states that c2 = a2 + b2 -2abcosC, b2 = a2 + b2 - 2accosB and a2 = b2 + c2 - 2bccosALaw of Sine 31
- 32. Dictionary of MATH TERMSAn equation that relates the sine of an interior angle of a triangle to the length of its sides iscalled the law of sines.If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle betweena and c and C the angle between a and b, then the law of cosines states thatsin A/a = sin B/b = sin C/cLeast Common Multiple (LCM)The smallest common multiple to which two or more numbers can be divided evenly. Forexample, the LCM of 2, 3 and 6 is 12.Leading CoefficientThe coefficient of a polynomials leading term or the term with the variable having the highestdegree.For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7.Leading TermThe term of a polynomial which contains the highest value of the variable is called the leadingterm.For example, the leading coefficient of 7x4 + 5x3 + 92 + 2x +21 is 7x4.Least Common DenominatorThe least common denominator is the smallest whole number that can be used as a denominatorfor two or more fractions. The Least Common Denominator is nothing but the Least CommonMultiple of the denominators of the fractions.For example, the least common denominator of 3/4 and 4/3 is 12. Since 3/4=6/8=9/12 and4/3=8/6=12/9=16/12. Hence we see that the least common denominator is 12.Least Integer FunctionThe least integer function of x is a step function of x, which is the least integer greater than orequal to x. This function is sometimes written with reversed boldface brackets ]x[ or reversedplain brackets ]x[.Least Squares Regression LineThe Linear Squares Regression Line is the linear fit that matches the pattern of a set of paireddata, as closely as possible. Out of all possible linear fits, the least-squares regression line is theone that has the smallest possible value for the sum of the squares of the residuals.It is also known as Least Squares Fit and Least Squares Line. 32
- 33. Dictionary of MATH TERMSLeast-Squares Regression EquationAn equation of any form (linear, quadratic, exponential, etc) that helps in fitting a set of paireddata as closely as possible is called the least squares regression equation.Least Upper Bound of a SetThe smallest of all upper bounds of a set of number is called the Least Upper Bound.Leg of an Isosceles TriangleAny of the two equal sides of an isosceles triangle can be referred to as the leg of the isoscelestriangle.Leg of a Right Angle TriangleEither of the sides of a right angle triangle, between which the right angle is formed can bereferred to as the leg of the right angle triangle.Leg of a TrapezoidEither of the two non parallel sides of a trapezoid that join its bases can be referred to as the legof the trapezoid.LemmaMore accurately referred to as a helping theorem, a lemma helps in proving a theorem. But it isnot important enought to be a theorem.LemniscateA curve that takes form on the numerical number 8, in any orientation can be referred to as thelemniscate. Its equations are generally given in the polar coordinates. r2 = a2cos2θ.Like TermsTerms that have the same variables and with the same power are called like terms. Thecoefficients of the like terms can be directly added and subtracted. For example 5x3y2 and135x3y2 are like terms and hence can be added directly to give the number 140x3y2.LimaconA limacon is a family of related curves usually expressed in polar coordinates.LimitThe limit of a function is the value of the function as its variable tends to reach a particular value.For example for f(x)=limx-><5>1/x2= 1/25. As x->5, the function f(x) tends to reach to 1/25.Limit Comparison TestThe limit comparison test is performed to determine if a series is as good as a good series or as 33
- 34. Dictionary of MATH TERMSbad as a bad series. The test is used specially in cases when the terms of a series are rationalfunctions.Limit from AboveThe limit from the above is usually taken in cases when the values of the variable is taken greaterthan that to which the limit approaches. For example limx->0+1/x=infinity, is taken such that thevalue of x>0. Limit from above is often referred to as limit from the right. This is a one sidedlimit.Limit from BelowThe limit from the below is usually taken in cases when the values of the variable is taken lessthan that to which the limit approaches. For example limx->0-1/x=-infinity, is taken such that thevalue of x>0. Limit from below is often referred to as limit from the left. This is a one sidedlimit.Limit Involving InfinityA limit involving infinity or an infinite limit is one whose result approaches infinity or the valueof the variable approaches infinity.Limit Test for DivergenceA limit test for divergence is a convergence test which is based upon the fact that the terms of aconvergent series must have a limit of zero.LineA line is a geometric figure that connects two points and extends beyond both of them in bothdirections.Line SegmentA line segment is nothing but the set of points between any two points including those twopoints.LinearThe world linear means like a line. It is nothing but a graph or data that can be molded by alinear polynomial.Linear CombinationA linear combination is the sum of multiples of the variables in a set. For example, for the set {x,y, z}, one possible linear combination is 7x + 3y - 4z.Linear Equation 34
- 35. Dictionary of MATH TERMSAn equation that can be written in the form "linear polynomial" = "linear polynomial" or "linearpolynomial"=constant is known as a linear equation.For example 3x + 26y = 34 is a linear polynomial.Linear FactorizationIf a polynomial can be factorized such that the factors formed after the factorization are linearpolynomials, then this factorization is known as a linear factorization. For example x 2-9 can befactorized as (x+3) and (x-3).Linear Fit Regression LineAny line that can be used as a fit in the process to model the pattern in a set of paired data.Linear InequalityAn inequality that can be written such that the value of a polynomial is greater than, less than,greater than equal to or less than equal to a particular number is called linear inequality. Forexample 3x + 7y >9.Linear Pair of AnglesWhen two lines intersect each other, then the adjacent angles formed due to intersection of thetwo lines are called linear pair angles. The linear pair angles formed are supplementary.Linear PolynomialA linear polynomial is a polynomial with degree 1. The highest power of the variables involvedin the polynomial should be one. For example 9x + 7 is a linear polynomial.Linear ProgrammingThe linear programming is an algorithm that is used for solving problems. The method of usinglinear programming is by asking the largest or smallest possible value of a linear polynomial. Ifthere are any restrictions, then the system of inequalities is used to present any restriction to theequations.Linear RegressionThe process of finding a linear fit is referred to as the linear regression.Linear System of EquationsIf there are more than one equations such that each equation is a linear equation, then the systemof equations will be known as linear system of equations.For example, 2x + 3y - 5z9x + 7y + 12x = 1915x - 6y + 11z = 9 is a linear system of equations, that can be used to determine the values of x, 35
- 36. Dictionary of MATH TERMSy and z.Local BehaviorThe behavior of a function in the immediate neighborhood of any point is called the localbehavior. The local behavior of geometric figures can also be studied with respect to a particularpoint.For example, for the graph of the equation y=2x + 3, if studied closely can be said to have thelocal behavior of a straight line parallel to the x-axis and at a distance of 3 units from the origin.Local MaximumThe local maximum is the highest point in a particular section of the graph. It is also oftenreferred as the local max or relative maximum or relative max.Local MaximumThe local minimum is the lowest point in a particular section of the graph. It is also oftenreferred as the local min or relative minimum or relative min.LocusA locus is nothing but the set of points that form a particular geometric figure. For example, acircle with radius 2 cm is the locus of all points which are at a distance of 2 cms from a particularpoint.LogarithmThe logarithm of x with respect to the base c is the power to which the base c must be raised inorder to be equal to x. For example, logcx=z then cz=x.Logarthmic RulesThe logarithmic rules are the algebra rules that need to be used when working with logarithms.Some of them can be listed as under:If log x = y then 10y=x. It means that if the base of the logarithm is not mentioned then considerthe base as 10.If ln x = y then ey=x. It means that when log is replaced by ln then take the logartihm as naturallogartihm and has the base e.log 1 = 0, since whatever be the base, if raised to the power 0 then the result is always 1.log ab = log a + log blob (a/b) = log a - log blog b3 = 3log blogax = logbx/logbaLogarithmic DifferentiationIt is the type of differentiation that is used in special circumstances. For example the equation y = 36
- 37. Dictionary of MATH TERMSxtan x can be differentiated, more easily if the logarithm of both the sides are taken.On taking the logarithm of both the sides the equation can be reduced to log y = tan x. log x(using logarithmic formula). Hence the process of differentiation becomes simple.Logistic GrowthA logistic growth is shown by using an equation. It is used to determine the demand of productsin situations where the demand increases initially, then the demand goes down and finallyreaches a particular upper limit.Long Division of PolynomialsThe process of dividing polynomials is known as polynomial long division. The polynomial longdivision is used to divide improper rational numbers into proper rational numbers or sum ofpolynomials. The process of polynomial long division is same as that of long division ofnumbers.Lower BoundThe lower bound of a set is any number that is less than or equal to all the numbers in a set. Forexample 1, 2 and 3 are all lower bounds of the interval [4, 5].Low QuartileThe low quartile is the number for which 25% of the number is less than the number.Least Upper Bound of a SetThe smallest of all the upper bounds of a set of numbers is called the least upper bound of theset. For example the least upper bound of the interval [9, 10] is 10.MMaclaurin SeriesThe power series in x for a function f(x) is known as Maclaurin series.MagnitudeThe magnitude is the absolute value of a quantity. Magnitude is a value and it can never be anegative number.Magnitude of a vectorThe magnitude of a vector is the length of the vector.Main Diagonal of a Matrix: It is the numbers of a matrix taken diagonally starting from thenumber at the upper left corner and ending at the lower right corner. 37
- 38. Dictionary of MATH TERMSMajor ArcThe longer of the two arcs between the two arcs of a circle is called the major arc of the circle.Major Axis of an EllipseThe line passing through the two foci, the two vertex and the center of the eclipse is called themajor axis of the ellipse.Major Axis of a HyperbolaThe line passing through the two foci, the two vertex and the center of the hyperbola is called themajor axis of the hyperbola.Major Diameter of an EllipseThe line segment joining the two vertex of ellipse and passing through its center and two foci isknown as the major diameter of the ellipse.Mathematical ModelMathematical Model or model is nothing but a system of equations that is used for representing agraphs, some data or even some real world phenomenon.MatrixA matrix is a rectangular or square array of numbers. All the rows of the matrix is equal lengthsand all the columns are also of equal lengths.Matrix AdditionTwo matrices with the same dimensions can be added using the process of matrix addition. Theprocess of matrix addition is such that the element in the position Row 1, Column 1 must beadded to the element at the location Row 1, Column 1 of the other matrix.Matrix ElementAny number in a matrix is known as the matrix element. The position of the number in thematrix is defined by the row number and column number.Matrix InverseThe matrix inverse of a matrix is the one, which on being multiplied with the matrix gives theidentity matrix. If the matrix is denoted by A, then its inverse is denoted by A-1.Matrix MultiplicationTwo matrices can be multiplied only if the number of columns in the first matrix is equal to thenumber of rows in the second matrix.Maximum of a Function 38
- 39. Dictionary of MATH TERMSThe highest point in the graph of the function is often referred to as the maximum of thefunction.MeanIt is nothing but another word for average. When the word mean is used, it is generally referredto the arithmetic mean of a function.For example, the arithmetic mean of the numbers 1, 4, 6, 7, 8 is (1+4+6+7+8)/5.Mean of a Random VariableThis is often referred to in the case of probability where a number of trials are performed to seethe most expected result. The average of all the outcomes of all these trials is considered themean of a random variable.Mean Value TheoremThis is a theorem used in Calculus. It states that for every secant for the graph of a nicefunction, there is a tangent parallel to the secant.Mean Value Theorem for IntegralsThe mean value theorem for integrals states that for every function there is at least one pointwhere the value of the function equals the average value of the function.Measure of an AngleThe value of an angle in radians or degrees is referred to as the measure of an angle.MeasurementThe process of assigning a value for any physical quantity (eg. Length, breadth, height, area,volume, etc.) is called measurement.Median of a Set of NumbersThe median of a set of numbers is the number which is greater than half the numbers in the setand smaller than the remaining half. In case of two medians, simply find out the arithmetic meanof the two numbers.Median of a TrapezoidThe line joining the two non parallel lines of the trapezoid and parallel to the base of thetrapezoids is called the median of the trapezoid.Median of a TriangleThe line segment joining the vertex of a triangle to the mid point of the opposite side is called themedian of the triangle. It is very clear from the definition that every triangle has three medians. 39
- 40. Dictionary of MATH TERMSMembers of an Equation For any equation, the polynomials on the two sides of the equationare referred to as the members of the equation. For example; for the equation, 3x2+5=26x, themembers of the equation are 3x2+5 and 26x.Menelaus TheoremThe Menelaus theorem is an equation that shows how the two cevians of a triangle divide thetwo sides of the triangle and each other.For example, if A, B and C are the three vertex of the triangles and BF is the line segment fromB to the side AC intersecting AC at F, CD is the line segment from C intersecting at B and BFand CD intersect at the point P then, (AD/DB)(BP/PF)(FC/CA)=1.MensurationThe process of finding out the measurement of the physical quantities in geometry is refered asmensuration.Mesh of a PartitionIn any partition, the width of the largest sub interval is called the mesh of the partition.MidpointThe point at exactly half of the distance from the two points on the line segment joining the twopoints.Midpoint FormulaThe midpoint formula states the for any two points (x1, y1) and (x2, y2) the mid point is given by((x1+x2)/2 ,(y1+y2)/2).Max/Min TheoremThe max/min theorem states that for any continuous function f(x) in the interval [a,b] there existtwo numbers in the interval (say c and d) such that, for f(c) and f(d) the function has its absolutemaximum and minimum.MinimumThe process of finding out the smallest possible value of the variable in a function is referred toas the minimum of the function.Minimum of a functionThe minimum value of the function within a limited region or entire region of the function isreferred to as the minimum of the function. 40
- 41. Dictionary of MATH TERMSMinor arcIf the circumference of the circle is divided into two arcs, then the smaller arc is referred to as theminor arc of the circle.Minor Axis of an EllipseThe minor axis of an ellipse is the line passing through the center of the ellipse and perpendicularto the major axis.Minor Axis of a HyperbolaThe minor axis of a hyperbola is the line passing through the center of the hyperbola andperpendicular to the major axis.Minor Diameter of an EllipseThe minor diameter of an ellipse is the line passing through the center of the ellipse andperpendicular to the major diameterMinuteA minute is a measurement equal to 1/60th of a degree. It is represented by the symbol . Thus12°36 is called 12 degree and 36 minutes.Mixed NumberMixed number is also called mixed fraction. This is a way of representing improper fraction asthe sum of a number and a proper fraction. For example 31/4 can be written as the mixed number7 ¾, since 7+3/4 is 31/4.Mobius stripA mobius strip is a figure that can be represented as a strip of paper fixed at both the ends andwith a half turn in the middle.Mode The number that occurs the maximum times in a list is referred as the mode of thenumber. For example, in the series 1, 3, 3, 3, 5, 6. 6 the mode is 3 since, it occurs the maximumnumber of times.Modular ArithmeticWhen normal arithmetic operations are performed and the result is given in modular form thenthe process is known as modular arithmetic.For example 15 – 3 = 12, but in mod(7) form the result is 15 – 3 = 5(mod 7).Modular equivalence Two or more integers are considered to be in modular equivalence if theyleave the same integer on being divided by the same number. For example 10 and 16 are both 41
- 42. Dictionary of MATH TERMSmod 3 equivalent numbers, because they leave the remainder 1 on being divided by 3.Modular Equivalence RulesThe modular equivalence rules can be listed as under:Suppose a and b are two mod n equivalent numbers. a+c and b+c are modular equivalent. Similarly a-c and b-c are modular equivalent. a.c and b.c are modular equivalent. If ac and bc are modular equivalent numbers then a and b are modular equivalent.Modulo nModulo n or mod n of a number is the remainder of the number when divided by n. For examplethe number 7 when written in mod 3 form can be written as 7 ≡ 1 (mod 3).Modulus of a Complex NumberThe modulus of a complex number is the distance of the number from the origin on the complexplane. For example, for the number a+bi, the modulus of the number is given by (a2 + b2)½. If thenumber is given in polar coordinates and the number is rcos θ + irsin θ, then the modulus isgiven by r.Modus PonensModus Ponens is a form of logical argument. For example if the pen is working the pencil isworking. Now, if the argument is that the pen is working then we can conclude that the pencil isworking.Modus TolensModus Tolens is a form of logical argument that employs the proof of contradiction. Forexample, if the pen is working then the pencil is working. The pen is not working, hence thepencil is not working.MonomialA polynomial with one term is called monomial.Multiplication RuleThe multiplication rule is used in probability to find out if two events have occured. Forexample, if there are two events A and B then, P(A and B) = P(A)P(B) or P(A andB)=P(A).P(B|A). 42
- 43. Dictionary of MATH TERMSMultiplicative Inverse of a NumberThe multiplicative inverse of a number is nothing but the reciprocal of the number. In otherwords, it is 1 divided by the number. For example, the multiplicative inverse of the number 3/5 is1/(3/5)=5/3.Multiplicative Property of EqualityThe multiplicative property of equality states that if a and b are two numbers such that a = b, thena.c = b.c.MultiplesMultiples are the numbers that can be evenly divided by the number whose multiple we areconsidering. For example, 16 is a multiple of 4 because 16 can be evenly divided by 4.MultiplicityThe multiplicity of a polynomial is the number of times the number is zero for the givenpolynomial. For example in the function f(x) = (x + 3)2(x-2)4(x – 7)3, the number -3 hasmultiplicity 2, 2 has multiplicity 4 and 7 has multiplicity 3.MultivariableAny problem that involves more than one variable is called a multivariable problem.Multivariable calculusIf the problems in calculus involve two or more independent or dependent variables then thecalculus is called multivariable calculus.Mutually ExclusiveIf the outcome of two events in probability have no common outcomes then the events are calledmutually exclusive.NNatural NumbersAll integers greater than 0 are called natural numbers.Negative DirectionThe negatively associated data is often described in the form of a scatterplot. This way ofdescribing natural numbers is known as negative direction.Negative ExponentA negative exponent is used to describe the reciprocal of the number. For example, 5-2=1/52 43
- 44. Dictionary of MATH TERMSNegative NumberAny real number less than 0 is called a negative number.Negative ReciprocalThe process of taking the reciprocal of a number and then its negative is called the negativereciprocal. For example the negative reciprocal of ¼ is -4.Negatively Associated DataIf in a set of paired data, the value of one side increases with the decrease in the other, then thedata is referred to as the negatively associated data.NeighborhoodThe neighborhood of any number a is the open interval containing the number. For example, theneighborhood of a can be written as (a + d, a - d).n – gonA polygon with n number of sides is called n – gon. For example, a hexagon can also be called 6-gon.Not AdjacentTwo angles or lines are said to be not adjacent to each other, if they are not near to each other.NonagonA polygon having nine sides is called a nonagon.Non collinearThe points that do not lie in a single line are said to be noncollinear points.Non-Euclidean GeometryTo understand Non-Euclidean geometry we need to understant the parallel postulate. Theparaller postulate states that for an given point say P and a line l, not passing through P, there isexactly one line that passes through P, which is parallel to l. The Non-Euclidean Geometry, thusrefers to that branch of geometry that does not obey the parallel postulate principle. Thehyperobolic geometry and elliptic geometry fall in the class of Non-Euclidean Geometry.NonnegativeAny quantity that is not less than zero is refered as nonnegative. 44
- 45. Dictionary of MATH TERMSNonnegative NumbersThe set of integers starting from 0 to infinity in the positive direction of the X-axis is referred toas whole numbers.Non-overlapping setsTwo sets of numbers which do not have a single element in common are called non-overlappingsets.Non real numberAny complex number of the form a + bi, where b is not equal to 0 is called a non real number. Inother words, any number with an imaginary part is called non real number.Nonsingular MatrixNonsingular matrix is also called Invertible Matrix. Any square matrix whose determinant is not0 is called a nonsingular matrix.NontrivialThe solution of an equation is said to be nontrivial, if the solution does not include zeroes.NonzeroAny positive or negative number is a nonzero number.Normalizing a vectorThe process of finding out a unit vector parallel to the given vector and of unit magnitude iscalled normalization of the vector. The process is carried out by dividing the vector with itsmagnitude.n th derivativeThe process of taking the derivative of a function n times is called nth derivative. If thederivative of f(x) is taken n times, then its nth derivative will be represented as fn(x).n th Partial SumThe sum of the first n terms in an infinite series is called the nth partial sum.n th RootThe n th root of a number is the number which when multiplied with itself n times gives thenumber in question. The n th root of 5 can be represented as 51/n.Null Set Any set with no elements in it is called a null set. 45
- 46. Dictionary of MATH TERMSNumber LineA line representing all real numbers is called the number line.NumeratorThe top part of any fraction is called the numerator. In case of integers, the number itself is thenumerator, as it is divided by 1.OObliqueA line or a plane that is neither horizontal nor vertical but is tilted at some specific angle is calledoblique.Oblique ConeAn oblique cone is a cone in which the center of the base of the oblique cone is not aligned (notin line) with the center of the apex of the cone.Oblique CylinderIf the bases of the cylinder are not aligned just one above the other, it is called the obliquecylinder.Oblique PrismA prism whose bases are not aligned directly one above the other is called as oblique prism.Obtuse AngleAn angle whose measure is more than 90º but less than 180º.Obtuse TriangleIf one of the angles of a triangle is an obtuse angle then it is called as the obtuse triangle.OctagonA polygon with 8 sides is called octagon. It may have equal or unequal sides.OctahedronOctahedron is a polyhedron with 8 faces. An octahedron appears like two square based pyramidsplaced on one another. All the faces of an octahedron are equilateral triangles.OctantsThe eight parts into which the three dimensional space is divided by the co-ordinate axis. 46
- 47. Dictionary of MATH TERMSOdd/Even IdentitiesTrigonometric identities show whether each trigonometric function is an odd or even function.For example:sin(-x) = sinxcos(-x) = cosxtan(-x) = tanxcsc(-x) = -cscxsec(-x) = secxtan(-x) = tanxcot(-x) = -cotxOdd FunctionIf the graph of a function is symmetric about x axis then the function is said to be an oddfunction. Alternately, an odd function satisfies the condition, f(-x) = -f(x).Odd NumberThe set of integers that are not a multiple of 2. For example, {1, 3, 5, 7, 9, ...)One DimensionA dimension of the space where motion can take place in only two directions, either backward orforward.One-to-One FunctionA one-one function is type of function in which every element of the range corresponds to atleast one element of the domain. A one-to-one function passes both the tests, the horizontal andvertical test.Open IntervalA set interval excluding the initial and final numbers of the domain. For example in the intervalof (2, 5) , 2 and 5 are the excluded from the set of numbers while performing any mathematicaloperation.Operations on FunctionsThe operations on functions are as follows:Addition: (f +g)(x) = f(x) + g(x)Subtraction: (f - g) = f(x) – g(x)Multiplication: (fg)(x) = f(x). g(x)Division: (f/g)(x) = f(x)/g(x) 47
- 48. Dictionary of MATH TERMSOrder of a Differential EquationThe power on the highest derivative of a differential equation is called as the order of differentialequation.Ordered PairTwo numbers written in the form (x,y) are called as the ordered pairs.Ordinal NumbersThe numerical words that indicate order. The ordinal numbers are first, second, third etc,Ordinary Differential EquationA differential equation free of partial derivative terms.OrdinateThe y coordinate of a point is usually called as the ordinate. For example, if P is a point (5,8)then the ordinate is the 8.OriginThe reference point of any graph indicated by (0,0) in 2-D and (0,0,0) in 3-D.OrthocenterThe point of intersection of three altitudes of a triangle is called orthocenter.OrthogonalOrthogonal means making an angle of 90ºOutcomeThe result of an experiment, like throwing a dice or taking out a pack of cards from a set ofcards.Overdetermined System of EquationsAn equation in which there are more equations than the number of variables involved.PPiPie is defined as the ratio of circumference of a circle to its diameter. It is represented by theGreek letter Π. Many great mathematicians have done pioneering work in researching on thenumber pi like, Archimedes, Euler, William Jones etc, to name a few. 48
- 49. Dictionary of MATH TERMSPoint-Slope Equation of a Liney – y1 = m (x – x1) is known as the point slope equation of a line, where m is the slope of the lineand (x1, y1) represents a point on the line.For example, equation of a line passing through (3,4) and making an angle of 45 degrees with thepositive direction of x-axis is, y – 4 = 1(x – 3), here, (x1, y1) = (3,4) and slope = m = tan 45° = 1.Polar AxisThe x axis is known as the polar axis.Polar Conversion FormulasThe rules that are required to change the rectangular coordinates into polar coordinates areknown as the polar conversion formulas.Conversion FormulasPolar to rectangular- x = rcosθ , y = rsinθRectangular to polar- r2= x2 + y2Tanθ = y/xPolar CurvesSpirals, lemniscates and lima cones are the curves that have equations in polar form. Such typesof curves with equations in the polar form are known as the polar curves.Polar Integral FormulaPolar integral formula gives the area between the graph of curve r = r(θ ) and origin and alsobetween the rays θ= α and θ= β (where α ≤ β).PolygonA closed figure bounded by line segments. The name of the polygon describes the number ofsides of a polygon. Triangle, pentagon,hexagon etc are the examples of polygon.Polygon InteriorAll the points enclosed by a polygon is called as the polygon interior.Polynomial FactsAn expression of the form, p(x) = anxn + an-1xn-1 +.............+ a2 + a1x + a0 is called as the standardpolynomial equation. Examples of polynomial equations are 3x + 2y2 = 5 and 5x2+ 3y = 3.Polynomial Long DivisionPolynomial long division is useful method to express a n improper rational expression as the sumof a polynomial and a proper rational expression. 49
- 50. Dictionary of MATH TERMSPositive NumberA real number greater than zero is known as a positive number.Positive SeriesA series that consists of only positive terms.PostulateA postulate is just like an assumption that is accepted to be true without proof.PowerThe number or variable (called as base) that is raised to the exponent is called as power.Power RulePower rule is a formula that is used to find the derivative of power of a variable.Power SeriesA series that represents a function as a polynomial and whose power goes on increasing withevery term. In other it has no highest power of x.Power series in x is given by: n=∞n=0∑ anxn + a1x+ a2x2 + a3x3 +......Prime NumbersA number that has one and the number itself as the factors. For example, 1, 2, 3, 5, 7, 11....ProbabilityThe likelihood of occurrence of an event is called as probability. It is one of the most researchedareas of mathematics. There are some basic rules of probability: For any event A, 0≤ P(A) ≤ 1 P = 1 for a sure event. P = 0 for an impossible event P (not A) = 1- P(A) or P(Ac) = 1 – P(A)Proper FractionIf the numerator of a fraction is less than the denominator then the fraction is said to be proper.Proper Rational ExpressionA rational expression having degree of the numerator less than the degree of denominator. 50
- 51. Dictionary of MATH TERMSPythagorean TheoremAccording to Pythagoras theorem, the sum of squares of the two arms or legs of a right angledtriangle is equal to the sum of the square of the hypotenuse. If AB, BC and AC are the threes sideof a right angled triangle taken in same order then AC2 = AB2 + BC2 .QQ1Q1 or the first quartile is the median of the data which are less than the overall median. Forexample, consider a set of data, 3, 5, 7, 8, 9, 10. The median of this set of data is 7. 3, 5 are theonly numbers less than the median. The median of the numbers 3 and 5 is 4, so the 1st quartile is4.Q3Q3 or the third quartile is the median of the data which is more than the overall median. Forexample, if we consider a set of data, 2, 3, 5, 6, 8 the median is 5. Now, 6 and 8 are the numbersin this set that are greater than the overall median. These are called as Q3 or third quartile.QEDQED stands for quod erat demonstrandum, which means "That which has to be proven".QuadrangleA polygon with four sides.QuadrantsThe four sections into which the x-y plane is divided by the x and y axis.QuadraticA two degree polynomial equation represented by the equation,ax2 + bx + c = 0, where, a ≠ o.Quadratic PolynomialAny polynomial of degree 2.QuadrilateralA closed figure bounded by four lines.QuadrupleFour times any number or a value is called as quadruple.Quartic Polynomial 51
- 52. Dictionary of MATH TERMSA polynomial of degree four.Example: ax4 + bx3 + cx2 + dx + e = 0Quintic PolynomialA polynomial of degree 5a5 + b3 + cQuintilesFrom a set of data, the 20th and 80th percentiles are called the quintiles.QuintupleMultiplying any number by a factor of 5.RRadianIt is the unit of measuring angles. For example, 180 º = Π radians, 45 º = Π/4 radians etc,RadicalThe designated symbol for the square root of any mathematical entity is called radical.RadicandThe mathematical quantity whose nth root is taken. It is the number under the radical symbol.Radius of a circleThe distance or the measure of the line segment between center of circle and any point on thecircle is called the radius of the circle.RangeThe limit within which set of values reside. For example, the range of the function y = x2 is [0,∞] or {y|y ≥ o}RatioThe resultant quantity derived by dividing one number with the other.Rational ExponentsThe exponents which are composed of rational numbers are called rational exponents.Rational FunctionGiven two polynomials, one divided by another, the resultant is expressed as a function, then it iscalled rational equation. 52
- 53. Dictionary of MATH TERMSRational numbersThe set of all ratios, made up of real numbers, which do not have zero as denominator.Rational root theoremAll possible roots of a polynomial are provided by the rational root theorem.Rationalizing SubstitutionIt is a method of integration capable of transforming a fractional integrand into more than onekind of root.Rationalizing the DenominatorThe process of adjusting a fraction is such a way that denominator becomes a rational number.RayA line having only one end point and extending infinitely in the other direction is called a ray.Real numbersIt is a set of all numbers consisting of positive, negative, rational, square root, cube root etc. Realnumbers form the set of all the numbers on the number line.Reciprocal NumbersOne divided by the given number is the reciprocal of the number.RectangleA rectangle is a quadrilateral having all equal angles. They are equal to 900.Rectangle ParallelepipedRectangle Parallelepiped is a polyhedron where every face is a rectangle.Recursive FormulaIn a series of numbers, the next term in the series is calculated by a formula which uses previousterms in that same series. This term is called recursive term and the process is called recursiveformula.Reducing a fractionWhen numerator and denominator, both have common factors, we cancel out all of them until nocommon factor remains.Regular OctahedronA polyhedron which has eight faces is called regular octahedron. 53
- 54. Dictionary of MATH TERMSRegular PolygonA regular polygon is one in which all angles and sides are are congruent to each other.Regular PrismRegular Prism is a prism in which all the face comprise of regular polygons.Regular PyramidThe pyramid whos base is made up of regular polygon is called regular pyramid.Regular Right PrismA regular right prism is one whose bases are made up of right polygonsRight PyramidRight Pyramid is a pyramid where base is a regular regular polygon and the apex is directly ontop of the center of the base of polygon.Regular TetrahedronRegular Tetrahedron is a pyramid where all the faces of the polygon are triangles.Related RatesThe set of all the problems, where the changes in various rates are calculated by means ofdifferentiation.RelationThe ordered pair of entities which have some distinct abstraction between them is called arelation.Relative MaximumRelative maximum is a point in the graph which is at the highest point for that particular section.Relative MinimumRelative minimum is a point in the graph which is at the lowest point for that particular section.Relative PrimeThose numbers which have the greatest common factors as prime numbers are called relativeprime numbers.RemainderThe number which is left over after the division as an undivided whole number is called 54
- 55. Dictionary of MATH TERMSremainder.ResidualThe measure of a line which is parallel to Y axis and one end of which is touching the data pointis called residual.RhombusThe parallelogram having all equal sides is called rhombus.Reimann GeometryReimann geometry is a type of geometry where all the lines are considered non parallel,intersecting and happening on the surface of the sphere.Right Circular ConeA right circular cone is a cone whose base is a circle and any radius is making right angle to theline segment from apex of the cone to center of the circle.Right Circular CylinderRight circular cylinder cylinder whose bases is are circular.Regular HexagonA hexagon with all sides equal to each other is called regular hexagon.Rose CurveThe leaves of the curve which have complete symmetry over the center of the curve is called arose curve.RotationWhen figure is transformed according to a fixed point is called rotation (generally in sameplane).Rounding a NumberWithout compromising the degree of accuracy to a large extent, the approximation of number tothe nearest value is called rounding of the number.SScalene TriangleScalene Triangle is a triangle, wherein, all the sides of the triangle are unequal or of differentlengths.Scalar 55
- 56. Dictionary of MATH TERMSA scalar is the one with magnitude, but with no definite direction. Examples of scalars arelength, temperature and mass. Mathematically, a scalar is said to be any real number or anyquantity that can be measured by using a single real number.Solid GeometrySolid geometry is a term used for the surfaces and solids in space. It includes the study ofspheres, cones, pyramids, cylinders, prism, polyhedra, etc. It also involves the study of relatedlines, shapes, points and regions.SegmentA segment constitutes all points between two given points, including those two points.Segment of a CircleSegment of a circle is any internal region of a circle, that is bounded by an arc or a chord.SAS SimilaritySAS similarity is side-angle-side similarity. When two triangles have corresponding angles ascongruent and corresponding sides with equal ratios, the triangles are similar to each other.SSS CongruenceWhen two triangles have corresponding sides congruent, the triangles are said to be in SSScongruency.SemicircleSemicircle is a half circle, with a 180 degree arc.Spherical TrigonometrySpherical trigonometry is a term used for the study of triangles on the surface of any sphere. Thesides of these triangles are arcs of great circles. This study is useful for navigation purposes.Solving AnalyticallyA technique of solving a mathematics problem, by using numeric or algebraic methods. Thistechnique does not involve the use of a graphic calculator.Solve GraphicallyA technique of solving a mathematics problem, by using graphs and picture. Graphic calculatorsare used to solve a problem graphically.SpheroidSpheroid actually refers to an oblate spheroid. But, in some cases, it refers to an ellipsoid thatlooks more or less like a sphere. 56

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