Maths Vocabulary Book: Scottish Secondary School Curriculum S1-S6

fàA `tv{tÜ TvtwxÅç Contents Prologue ....................................................................... 0 Arithmetic ........................................................ ......... 1 Maths Algebra ........................................................................ 13 Geometry and Trigonometry................................. 25 Functions and Graphs .............................................. 45 Vocabulary Money and Finance ................................................... 53 Statistics and Probability...................................... 65 Book Calculus ........................................................................ 73 Mensuration and Units............................................ 83 Sets, Logic, Proofs and Genera............................ 94 uç `A ctàxÄ Epilogue........................................................................ 104 Arithmetic Prologue This is a rather comprehensive vocabulary list of words and phrases (‘terms’) encountered in the Scottish secondary school mathematics curriculum from S1 – S6. The first column gives the term to be defined. The second column gives the meaning of each term. Latin terms are italicised. Bolded terms are those which the author feels should be known by all practitioners of numeracy. Many terms are currently not required for assessment purposes; however, there is scope for further investigation of such terms. M. Patel (June 2011) One great use of words is to hide our thoughts Voltaire (18th century) Abacus Absolute value Add Addend Addition Amount Arabic numerals Arithmetic Ascending order Base Base sixty Base ten Basic operations Binary BODMAS Borrow 0 Device used for simple calculations The value of a number, disregarding its sign Combine two numbers by counting to get a total Number to be added To add How much there is The numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 Branch of maths dealing with numbers and how to add, subtract, multiply and divide them In order from smallest to biggest Number that is raised to a certain power; the number b in bⁿ Number system with 60 as base Number system with 10 as base The 4 operations of multiplication, division, addition and subtraction Number system with 2 as base Order in which calculations are to be performed: Brackets, Orders (i.e. exponents and roots), Division, Multiplication, Addition and Subtraction Regroup to help with subtraction 1 Arithmetic Braces Brackets Carry Characteristic Chimney sum Clock arithmetic Common factor Common fraction Complex conjugate Complex number Congruence Congruence class modulo n Conjugate surds Consecutive Correct to the nearest Count Count back The symbols { and } found in sets and piecewise functions The symbols [ and ]; sometimes ( and ) Regroup to help with addition Integer part of a common logarithm Sum (usually adding) set out with numbers underneath each other with correct place value Modulo arithmetic Same factor for two or more (usually natural) numbers Fraction Complex number with the same real part but negative imaginary part of a + bi Number with real and imaginary parts When 2 numbers have the same remainder after dividing by a positive integer n Set of all integers having the same remainder upon dividing by n Surds of the form a + b√c and a – b√c Next to each other in a list Round to the nearest Find out how much there is Subtract by starting from one number 2 Arithmetic Counting rods Count on Cube Cube root Decimal Decimal fraction Decimal place Decimal point Decimal representation Decimal separator Denominator Descending order Dienes’ blocks Difference Digit Directed number Divide Dividend Rods used in China for calculation (including fractions) Add by starting from one number To multiply a number by itself 3 times Number x which satisfies x3 = y, for some number y Number which has an integer and a fractional part Fraction with the denominator equal to a power of ten In rounding, how many numbers are to be written after the decimal point Point used to separate the integer and fractional parts of a number Writing a number as a decimal Decimal point Bottom part of a fraction In order from biggest to smallest Cube blocks used in arithmetic Answer to a take away sum Whole number Positive or negative number Share out equally Number which is to be divided into 3 Arithmetic Divisible Division Divisor Dozen Egyptian fraction Equal Equality Equivalent fractions Even Exact value Exponent Exponentiation Factor Factorisation Factorise Factor tree Arithmetic Number that is divided by another number to give an answer with 0 remainder To divide Number that divides into another number with zero remainder Twelve Fraction written as the sum of different unit fractions Same Being equal Fractions that are the same Fibonacci number Fibonacci sequence Number divisible by 2 Leaving a number simplified without working out roots, dividing etc. Number n in aⁿ Repeated multiplication Number that divides exactly (no remainder) into another number Product of factors of a (usually natural) number Write a (usually natural) number as a product of two or more of its factors Diagram showing factors of a number GCD Genaille-Lucas rulers Greater than HCF 4 Figure Fraction Fractional Fractional part Fundamental theorem of arithmetic Hexadecimal Hindu-Arabic numeral Hundredth Improper fraction Number in the Fibonacci sequence The sequence 1, 1, 2, 3, 5, 8, 13, … starting with 1, 1 and adding 2 successive terms Digit Number written as one integer divided by a non-zero integer To do with fractions Proper fraction part of a decimal number Result that every natural number bigger than 2 can be written in exactly one way (ignoring order) as a product of prime powers Greatest Common Divisor – the HCF Set of rulers with triangles, used for simple multiplication Bigger than Highest Common Factor; biggest positive integer that exactly divides two or more non-zero integers Base 16 Arabic numerals 1 part out of 100 Fraction with the numerator bigger than the denominator 5 Arithmetic Index Integer Integer part Integral Inverse Irrational number Iteration LCM Leading zero Less than Logarithm Magnitude Mantissa Minuend Minus Mixed number Modulo arithmetic Modulus Multiple Power Whole number, the negative of a whole number or 0 Integer part of a decimal number To do with integers The opposite process Number that is not rational; can’t be written as a fraction Repeat a process Lowest Common Multiple; smallest positive integer that 2 or more integers exactly divide into Any zero that occurs before the first non-zero digit in a number Smaller than The number x in bx = a, alternatively written as x = logb a Size Fractional part of a logarithm Number that is taken away from Subtract Improper fraction written as a whole number plus a proper fraction Arithmetic based on congruence classes The number n in a congruence class Number multiplied by an integer 6 Arithmetic Multiplicand Multiplication Multiplier Multiply Napier’s bones Napier’s rods Natural number Negative Negative square root Non-zero th n root of y Number Number base Number bonds Number line Number system Numeral Numerator Numerical Obelus Odd Number that is multiplied To multiply Number that does the multiplying Repeated addition of the same number Abacus used for multiplying and dividing whole numbers Napier’s bones The counting numbers 1, 2, 3, 4, ... Number less than 0 The negative number N in N2 = y Not zero The number x in xn = y Something used in counting and measuring Base Simple two-number addition sum Line with equally spaced numbers Set of numbers with at least one operation Symbol for a number Top part of a fraction To do with numbers The division symbol ÷ Number which gives remainder 1 when divided by 2 7 Arithmetic Operand Number acted on by an operator Operation Order of magnitude Order of operations Palindrome Way of combining numbers Scale of comparing sizes of numbers, usually using base 10 Order in which to do calculations BODMAS Number that reads the same backwards as forwards (e.g. 565) The symbols ( and ) Out of Out of 100 Way of writing a fraction with denominator equal to 100; 1 % is 1 hundredth Out of 1 000 Positional notation Parentheses Per Percent Percentage Permille Place-value notation Positional notation Positive Positive square root Power Prime factor Prime factorisation Way of writing numbers, using the same symbol for different orders of magnitude Number greater than 0 The positive number P in P2 = y Exponent Prime number that is a factor Factorisation of an integer into its prime factors 8 Arithmetic Prime number Product Proper fraction Property of one Property of zero Quotient Radical symbol Radicand Radix Radix point Raised to the power of Ratio Rational number Real number Recurring decimal Recurring digit(s) Remainder Number that has exactly 2 factors, the number itself and the number 1 Result of multiplying two numbers Fraction with the numerator smaller than the denominator 1 times any number equals that number 0 times any number equals 0; 0 add any number equals that number Number of times the divisor goes into the dividend The symbol √ Number under a root Base Symbol used to separate the integer part from the fractional part of a number in any base To the power of One number divided by another Number that can be written as a fraction or as a repeating decimal Number that is either rational or irrational Repeating decimal Repeating block Whole number that is left after dividing 9 Arithmetic Repeating block Repeating decimal Repeating digit(s) Repetend Residue class Rod calculus Roman numeral Root Round to the nearest Scientific notation Score Sequence Sexagesimal Share equally Sieve of Eratosthenes Sign Repeating digit or set of digits (usually found in decimals) Decimal number with a repeating block Number that repeats or a set of numbers in a certain order that repeat Repeating block Congruence class Using counting rods for calculation The numerals, I, V, X, L, C, D and M Number with a radical symbol Approximation of a number by specifying to how many units, tens, hundreds, tenths or hundredths etc. it is to be written Number written as b x 10n, with b a decimal number between 1 and 10 (not including 10) and n an integer Twenty List of numbers Base sixty Divide Method of finding prime numbers Positive or negative 10 Arithmetic Significant figure Simple fraction Slide rule Solidus Square Square number Square root of y Standard form Subitising Subtract Subtraction Subtrahend Successive terms Sum Sum of Surd Take away Tenth Digits of a number that specify the degree of accuracy Fraction Device used for performing many types of calculations, including multiplication, division, taking roots, trigonometry, logarithms and exponentials Division symbol ⁄ (not /) Number times itself Number (usually whole) that is the square of another number; number in the sequence, 1, 4, 9, 16, 25, 36, . . . Number(s) x in x2 = y Scientific notation Instantly knowing how many objects there are without counting Take away To take away Number that is taken away Numbers next to each other Usually means add, but can mean any type of calculation Add Root of a number that is irrational Make less by removing 1 part out of 10 11 Arithmetic Term Thousandth Times Top-heavy fraction Total To the power of Trachtenberg system Trailing zero Triangular number Unit fraction Unity Vinculum Vulgar fraction Whole Whole number Zero Number in a sequence 1 part out of 1 000 Multiply Improper fraction Sum of Exponentiation System of mental calculations involving the four basic operations Any zero that occurs after the last non-zero digit in a number Number in the sequence, 1, 3, 6, 10, 15, 21, 28, 36, . . . Fraction with numerator equal to 1 The number 1 Horizontal bar placed over the repetend in a decimal Fraction Everything; all of Number in the set {0, 1, 2, 3, 4, ...} Number indicating nothing; number which, when added to any integer, gives the same integer back Algebra Add Addend Additive identity Additive inverse Algebra Algebraic expression Algebraic fraction Algebraic term Arithmetic sequence Associative law Augmented matrix Back substitution Balance Combine two quantities to get a total Quantity to be added Quantity (usually written as 0) which, when added to any quantity x, gives x Quantity (usually written as – x) which, when added to any quantity x, gives 0 Branch of maths dealing with numbers, variables and the four basic operations together with taking roots Expression involving numbers and letters with some or all of the four basic operations and possibly roots Fraction in which both the numerator and denominator are algebraic expressions Algebraic expression Sequence in which any two successive terms have the same difference Rule that the order in which terms are bracketed for a single operation is irrelevant Matrix formed by attaching at least one column vector to a given matrix; for inverting the given matrix, the identity matrix is attached Substituting variables back into previous equations to solve for other variables Keep the same 12 13 Algebra Binomial Binomial coefficient Binomial theorem Biquadratic Bivariate polynomial Cancel Change the subject Coefficient Cofactor Collect like terms Common difference Common factor Common ratio Polynomial involving exactly two terms Coefficient in the binomial theorem Formula for expanding (x + y)n for any whole number n Quartic Polynomial in 2 variables To simplify an expression or equation by performing the same operation to each part of the expression or to both sides of the equation so that at least one term or part of a term disappears Make a variable the subject of a formula Quantity (usually a number) in front of a term in an expression Signed (plus or minus) minor Add or subtract two or more terms of the same type to simplify an expression Difference between any 2 successive terms (next minus previous) in an arithmetic sequence Factor that is common to 2 or more quantities Ratio of any 2 successive terms (next divided by previous) in a geometric sequence 14 Algebra Commutative law Complex roots Consistent system Cubic equation Cubic formula Degree of a polynomial De Moivre’s theorem Determinant Diophantine equation Direct proportion/variation Discriminant Distributive law Dividend Rule that the order in which 2 quantities are taken for a single operation does not matter Roots that are complex numbers System of (usually linear) equations that have a solution Degree 3 polynomial equated to zero Formula for solving the general cubic equation Highest power in a single variable polynomial Theorem allowing easy evaluation of powers of complex numbers Number associated with a matrix used to decide if the matrix has an inverse Indeterminate polynomial equation in which all variables are integers When 2 variables x and y increase or decrease in the same ratio and are related thus: y = k x Quantity under the square root in the Quadratic formula, used to decide the nature and number of roots Rule that brackets can be expanded Quantity that is divided by another quantity of the same type 15 Algebra Division algorithm (polynomials) Division algorithm (whole numbers) Divisor Elementary row operations Element of a matrix Entry Equal roots EROs Euclidean algorithm Factor Factorial of n Factorise Factorise fully Factor theorem Finite series First-order recurrence relation Method for dividing 2 polynomials by working out the quotient and remainder Method for dividing 2 numbers by working out the quotient and remainder Quantity that divides into another quantity with zero remainder Row operations used to solve a system of equations Entry Content of a matrix in a specific row and column Solutions to an equation that are the same Elementary Row Operations Technique for calculating the HCF of 2 numbers Algebraic expression which divides exactly into another algebraic expression The quantity n x (n – 1) . . . 3 x 2 x 1 Take out common terms in an expression, with the answer having brackets Factorise by taking out the HCF Theorem that a polynomial f has a factor (x – k) if and only if f(k) = 0 Series with a finite number of terms Recurrence relation of the form un+1 = F(un, n) 16 Algebra First-order linear recurrence relation FOIL Formula Fundamental theorem of algebra Gaussian Elimination GCD Geometric sequence HCF i Inconsistent system Indeterminate Indeterminate equation Inequality Recurrence relation of the form un+1 = a un + b First, Outside, Inside, Last – mnemonic for multiplying 2 brackets each with 2 terms Equation for working something out Result that every non-constant polynomial with complex coefficients has at least one complex root Method of solving a system of linear equations Greatest Common Divisor (HCF) Sequence in which any two successive terms have a common ratio Highest Common Factor; biggest algebraic expression that can be taken out of two or more algebraic terms Positive square root of – 1: i2 = – 1 Set of (usually linear) equations that does not have any solutions Variable Equation for which there are infinitely many solutions Expressing something that is not the same 17 Algebra Equation with the equality replaced by an inequality Infinitely many Unlimited number of solutions; with linear solutions systems, the solutions are parametrised Inverse matrix of A Matrix B satisfying AB = I = BA Inverse When a variable x and the reciprocal of proportion/variation the variable y are related directly thus: y = k⁄x Invertible matrix Matrix that has an inverse Irreducible Quadratic expression that has quadratic negative determinant Irreducible Quadratic factor that is irreducible quadratic factor Iterate Value used in an iteration Iteration Using old outputs as new inputs in a recurrence relation Leading coefficient The coefficient an in a single variable polynomial Leading term The term an xn in a single variable polynomial Like terms Terms of the same type or form Limit of a linear Value that is reached when performing recurrence relation iteration on a linear recurrence relation Linear Of the form ax + b Linear Diophantine Equation of the form equation a1 x1 + a2 x2 + . . . + an xn = c Algebra Inequation 18 Linear Diophantine equation (2 variables) Linear equation (1 variable) Linear equation (2 variables) Linear factor Linear recurrence relation Lost solution Matrix Member Minor Minuend Monic polynomial Monomial Multiple for which all variables xi are integers Equation of the form ax + by = c for which x and y are integers Equation of the form ax + b = c Equation of the form ax + by = c Factor of an algebraic expression that is linear Recurrence relation of the form un+1 = an un + an-1 un-1 + . . . + a1 u1, where each ai is a constant number Solution of an equation that is not found due to an unjustified step Bracketed array of numbers arranged in rows and columns Entry of a matrix Determinant of a smaller matrix formed by eliminating a row and column of a larger matrix Quantity that is taken away from Polynomial with leading coefficient equal to 1 Polynomial consisting of only 1 term Product of one quantity (especially an 19 Algebra Multiplicand Multiplicative identity Multiplicative inverse Multiplier Multiply Multivariate Nature of roots Non-invertible matrix No solution(s) Order (matrix) Order (polynomial) Parameter Parametric equation(s) Partial fractions Partial sum Polynomial integer or function) by another Quantity that is multiplied Quantity (usually written as 1) which when multiplied by any quantity x gives x Quantity (usually written as 1⁄x or x-1) which when multiplied by x gives 1 Quantity that multiplies Repeated addition of the same quantity Involving more than 1 variable Real or complex roots Matrix which does not have an inverse Algebra Polynomial (1 variable) Polynomial equation Polynomial long division Proportion Quadratic equation No answer(s) to an equation or inequation Size of a matrix Degree of a polynomial Quantity connecting functions and variables Equation(s) used to write a function using one or more parameters Way of writing a rational function as a sum of proper rational functions with the denominator of each a factor of the original function’s denominator Sum of the first n terms of a sequence Finite algebraic expression written using 20 Quadratic equation (standard form) Quadratic expression Quadratic formula Quadratic trinomial Quartic equation Quartic formula Radicand Ratio variables and constants linked by addition, subtraction, multiplication and non-negative whole number powers Polynomial written with 1 variable: an xn + an-1 xn-1 + . . . + a1 x + a0 Equation that can be rearranged into the form P = 0, for some polynomial P Process of dividing a polynomial to obtain a quotient and remainder How 2 or more variables are related in accordance with some law Equation that can be rearranged into the form ax2 + bx + c = 0 Equation of the form ax2 + bx + c = 0 Expression of the form ax2 + bx + c Formula for solving the general quadratic equation Quadratic with all 3 coefficients non-zero Equation that can be rearranged into the form ax4 + bx3 + cx2 + dx + e = 0 Formula for solving the general quartic equation Quantity under a root How a quantity can be divided into 21 Algebra Rationalise Rationalise a denominator Reciprocal of x Recurrence relation Remainder Remainder theorem Repeated linear factor Repeated roots Root (equation) Root (general) Roots of unity Rules of indices Rules of logarithms parts; size of 2 or more quantities compared to each other; for 2 quantities, how many times the first is contained in the second To make rational Multiply the denominator of an algebraic fraction by the conjugate surd of the denominator to make the denominator rational 1 divided by x Equation of the form un+1 = F(un, un-1, un-2, . . ., u2, u1, n) Something left over after dividing Theorem that when a polynomial f is divided by (x – a), the remainder equals f(a) Factor of an algebraic expression of the form (ax + b)2 Equal roots Solution of an equation Root of an algebraic expression The n solutions of xn = 1 Rules for rewriting and manipulating expressions involving indices Rules for rewriting and manipulating expressions involving logarithms 22 Algebra Rules of surds Sequence Series Simultaneous equations Single variable polynomial Singular matrix Skew-symmetric matrix Solution Subject Substitute Subtrahend Summand Summation Sum to infinity Sum to n terms Symmetric matrix Synthetic division Rules for rewriting and manipulating expressions involving surds List of things (usually numbers) specified by some rule Sequence of numbers added together Set of equations for several variables (usually 2 linear equations in 2 variables) Univariate polynomial Matrix with zero determinant; not invertible Matrix that is the negative of its transpose Value of a variable that satisfies an equation Quantity that has been solved for, written on the LHS of an equation in terms of other quantities Replace, usually a letter by a number Quantity that is taken away Something that is added Add Sum of an infinite series Sum of a series up to n terms Matrix that is the same as its transpose Polynomial long division method in which 23 Algebra System of linear equations Term Transpose (equation) Transpose (matrix) Trinomial Unique solution Univariate Univariate polynomial Unknown Upper triangular form Variable the variables are suppressed Set of linear equations, usually 2 (or 3) equations in 2 (or 3) variables Combination of letters, numbers or functions in an expression Change the subject Matrix obtained by swapping the rows and column of another matrix Polynomial involving 3 terms Only one answer (usually in reference to a system of equations) Involving only 1 variable Polynomial in one variable Missing quantity Matrix in which all entries below the main diagonal are 0 Symbol that stands for a quantity that changes Geometry and Trigonometry 1D 2D 3D Actual distance Acute angle Acute triangle Addition formulae Adjacent Align Alternate angles Altitude Angle Angle bisector Angle fraction Angle of depression Angle of elevation One-dimensional; in one direction Two-dimensional; in two non-collinear directions Three-dimensional; in three non-collinear directions Real-life distance Angle between 0° and 90° (not including these 2 values) Triangle with all angles acute Compound angle formulae Next to Line up When a transversal crosses 2 coplanar (and usually parallel) lines, the angles made on opposite sides of the transversal with the 2 lines Height from bottom to top Figure formed by two rays sharing a corner Line that halves an angle Sector angle divided by 360° Angle between the horizontal and the line of sight of an object from an observer (object below observer) Angle between the horizontal and the line of sight of an object from an observer 24 25 Geometry and Trigonometry Annulus Anti-clockwise Aperiodic tiling Apex Arc Arc length Area Area scale factor Argand diagram Argument Arm ASTC Diagram Asymmetry Axis Axis of symmetry Base Base angle Bilateral symmetry (object above observer) 2D region formed between 2 circles of different radii but the same centre Opposite direction to which clock hands move Tiling that is not periodic Highest corner point in a shape Part of a circumference Length of arc Amount of space in a 2D shape Square of the length scale factor Plot of a complex number in the complex plane Angle made by a complex number to the positive real axis Line together with another one that makes up an angle Diagram used to calculate angles based on where sine, cosine and tangent are positive or negative Not symmetrical Line, usually inside a shape Line of symmetry Bottom side Angle at the base of a 2D or 3D figure Symmetry involving a mirror image 26 Geometry and Trigonometry Bisect Bisector Boundary Breadth Cartesian coordinates Cartesian coordinate system Cartesian form (complex number) Cartesian form (line) Centre Centre of symmetry Centroid Cevian Chord Circle Circular cone Circular prism Circumcentre Cut in half Line that bisects Edge Shorter side of a rectangle Coordinates in a Cartesian coordinate system Coordinate system in which a point is given by 2 or 3 perpendicular distances from an origin Complex number written by specifying its distances from the coordinate axes in a Cartesian coordinate system Line equation written by solving for the parameter (in the parametric form) and equating the resulting 3 expressions Middle Point in a shape that doesn’t move under a rotation Point where the 3 medians of a triangle meet Line segment that joins a vertex of a triangle to some point on the opposite side Line segment joining 2 points on a curve All points in a flat 2D space that are the same distance from a starting point (centre) Cone with a circle as base Cylinder Point where the 3 perpendicular bisectors of a 27 Geometry and Trigonometry Circumference Clockwise Collinear Column vector Complementary angles Complete turn Complex loci Complex plane Compound angle formulae Compound area Compound shape Compound volume Concave Concave polygon Concave polyhedron Concentric Concurrent Cone triangle meet Perimeter of a circle Direction in which clock hands move Points lying on the same straight line Vector written as a column Angles that add up to 90° Full turn Loci described by complex numbers Plane with real axis and imaginary axis used to represent complex numbers Formulae for sin (x ± y) and cos (x ± y) Area of a compound shape Complicated shape made up of simpler shapes Volume of a compound shape Not convex Polygon which is not convex Geometry and Trigonometry Congruent Convex Convex polygon Convex polyhedron Coordinate Coordinate axis Coordinate grid Coordinate system Coplanar Corner Corresponding angles Polyhedron which is not convex Sharing the same centre 3 or more lines that meet at a single point 3D figure with a base, each point on the 28 Cosine ratio Cosine rule edge of which is connected to a common point by straight lines Two shapes that are exactly the same – ‘same shape, same size’ Shape where any straight line drawn between 2 points in the shape stays in the shape Polygon which is convex Polyhedron which is convex Number used to specify part of the location of a point x-axis, y-axis or z-axis Grid in a coordinate system Way of representing points using directed numbers In the same plane Where two edges meet When a transversal crosses 2 coplanar (and usually parallel) lines, the angles made on the same side by the transversal and the 2 lines Adjacent divided by hypotenuse Trigonometric rule involving the cosine function used to find missing angles and sides in any triangle 29 Geometry and Trigonometry Cross product Cross-section Crosssectional area Cube Cuboid Curve Curve segment Curved surface area Cylinder Decagon Diagonal Diameter Dilatation Dilatation matrix Dimension Distance formula Divine ratio Dodecagon Dodecahedron Vector product Region formed when a plane intersects a 3D shape Area of cross-section Cuboid with all 3 sides the same length Right prism with rectangle as a base Line that is not straight Part of a curve Surface area of a curved part of a 3D shape 3D shape consisting of all points that are the same distance from an axis 10-sided polygon Line segment joining 2 non-adjacent vertices Straight line through a circle’s centre with endpoints on the circle Scaling Transformation matrix describing a dilatation Smallest number of coordinates needed to specify a shape or object Formula for calculating the distance between 2 points Golden ratio 12-sided polygon Polyhedron with 12 faces 30 Geometry and Trigonometry Domino Dot product Double angle formulae Draw Edge Endpoint Enlargement scale factor Equation of a circle ((0,0)) Equation of a circle ((a,b)) Equiangular Equidistant Equilateral Equilateral triangle Euler’s formula Exact value table Polyomino with 2 squares Scalar product Formulae for sin 2x and cos 2x written in terms of sin x and cos x Make an accurate picture, especially by using a ruler Line segment joining 2 vertices in a 2D or 3D shape Point at which a line segment or curve segment ends Scale factor with a value bigger than 1 Equation of a circle with centre the origin: x2 + y2 = r2 Equation of a circle with centre (a,b): (x – a)2 + (y – b)2 = r2 All angles the same size Having the same distance All sides the same length Triangle with all sides the same length (equivalently, triangle with all angles the same = 60°) Formula relating the vertices, faces and edges of a convex polyhedron: v+f–e=2 Table of exact values of trigonometric functions 31 Geometry and Trigonometry Exterior angle External angle Face Figure First quadrant Fourth quadrant Fractal Fractal dimension Fractal geometry Full turn General form (circle) General form (line) Geometric transformation Geometry Glide symmetry Golden ratio Angle outside a polygon made by one side of the polygon and an extended line from an adjacent side Exterior angle Flat side 1D, 2D or 3D shape Quadrant described by x > 0 and y > 0 Quadrant described by x > 0 and y < 0 Shape, part of which is (approximately) the same as the whole Dimension of a fractal (not necessarily a whole number) Geometry of fractals Turning through an angle of 360° Equation of a circle in 2D written as x2 + y2 + 2gx + 2fy + c = 0 Equation of a line in 2D written as Ax + By + C = 0 Change of a shape due to rotation, reflection, or scaling Branch of maths dealing with points, lines, planes and shapes Combination of a reflection in a line, then a translation (or vice versa) The ratio (a + b)/a = a/b 32 Geometry and Trigonometry Golden section Great circle Half-turn Half-turn symmetry Hemisphere Hexagon Hexahedron Hypotenuse Image Imaginary axis Incentre Inscribed Interior angle Internal angle Intersect Irregular polygon Irregular polyhedron Isosceles trapezium Golden ratio Circle formed from the intersection of a sphere and a plane through the centre Turning through an angle of 180° Looking the same after a half-turn Half a sphere 6-sided polygon Polyhedron with 6 faces Side of a triangle opposite the right angle Result of a geometric transformation Vertical axis used to show the imaginary part of a complex number Point where the 3 angle bisectors of a triangle meet Shape that fits inside another one with the sides tangent where they meet Angle inside a polygon made by two adjacent sides Interior angle Cross or meet Polygon with not all sides the same length Polyhedron that is not regular Trapezium with equal base angles 33 Geometry and Trigonometry Isosceles triangle Kepler-poinsot polyhedra Kite Length scale factor Line Line of sight Line of symmetry Line segment Locus Magnitude Major arc Map distance Median Meet Midpoint Minor arc Triangle with 2 sides equal and the third side different (equivalently, two angles equal and the third angle different) The 4 regular star polyhedra: small stellated dodecahedron, great stellated dodecahedron, great icosahedron and great dodecahedron Quadrilateral with 2 pairs of congruent adjacent sides and where the diagonals intersect at 90° Length of one side of a shape divided by the corresponding length in a similar one Infinitely extending 1D set of points Line along which something is viewed Line that divides a shape so that one part is the mirror image of the other Part of a line Set of points in 1D, 2D or 3D space which satisfy some defined property Size of a vector; its length Arc that is bigger than a semicircle Distance on a map Line segment joining a corner of a triangle to the midpoint of the opposite side Cross or touch Point at the middle of a line segment Arc that is smaller than a semicircle 34 Geometry and Trigonometry Mirror image Mirror symmetry Modulus n-fold rotational symmetry Net n-gon Non-collinear Normal Oblique cone Obtuse angle Obtuse-angled triangle Octagon Octahedron Opposite Order Origin Image made in a mirror; reversed copy of a shape Bilateral symmetry Distance of a complex number from the origin Property a shape has so that it that looks the same after a rotation of (360 ÷ n) degrees Opened out (2D) outline of a 3D shape with edges indicated Polygon with n sides Not collinear Vector at right angles, usually to a line or plane Cone with its apex not aligned above the centre of the base Angle between 90° and 180° (not including these 2 values) Triangle with an obtuse angle 8-sided polygon Polyhedron with 8 faces On the other side, corner or edge of a shape Number of times a shape must be rotated about its centre to get it back to its original position Point where the x-axis meets the y-axis 35 Orthocentre Parallelogram Parallel (line and plane) Parallel (lines) Parametric form Path Penrose tiling Pentagon Pentagram Pentomino Perimeter Periodic tiling Perpendicular Perpendicular bisector Pi Plan Geometry and Trigonometry Geometry and Trigonometry (or, in 3D, where all 3 axes meet) Point where the 3 altitudes of a triangle meet Quadrilateral with 2 pairs of parallel sides; especially one where the interior angles are not 90° and adjacent sides are of unequal length Line at right angles to the plane’s normal especially a room or building Flat, infinite 2D surface Any of the 5 convex regular polyhedra: tetrahedron, cube, octahedron, dodecahedron and icosahedron Indicate a coordinate by placing a mark Equation of a line in 2D written as y – b = m (x – a) Complex number written by specifying the modulus and argument 2D shape made by joining straight lines and where only 2 lines join at each point 3D shape made by joining polygons and where only 2 polygons join at each edge 2D shape made by joining squares along edges Vector describing the position of a point Argument of a complex number in the interval [0, 2π) or (- π, π] Polyhedron made by joining a polygonal base to the same shape by faces joining corresponding sides of each polygon Polyhedron made by connecting a base polygon to a point (apex) Result that in a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other 2 sides Lines that never meet Equation of a curve or surface, written in terms of x, y and z; for a line, x, y and z are each written in terms of the same parameter Route Aperiodic tiling 5-sided polygon Regular star polygon made from a regular pentagon Polyomino with 5 squares Total distance once around the outside of a 2D shape Tiling that has a repeating unit At right angles Line segment that bisects (and is at right angles to) a line Ratio of the circumference of a circle to its diameter (same answer for all circles) View of something from straight above, 36 Plane Platonic solid Plot Point-slope form Polar form Polygon Polyhedron Polyomino Position vector Principal argument Prism Pyramid Pythagoras’ theorem 37 Geometry and Trigonometry Quadrant Quadrilateral Quarter-turn Quarter-turn symmetry Radius Ratio Ray Real axis Rectangle Rectangular coordinates Reduction scale factor Re-entrant polygon Reflect One of four infinite regions of the plane formed by the coordinate axes in a Cartesian coordinate system 4-sided polygon Turning through an angle of 90° Looking the same after a quarter-turn Straight line from a circle’s centre to the perimeter Size of 2 or more quantities compared to each other; how many times a smaller object is contained in a bigger one Line that extends infinitely in one direction but not the other Horizontal axis used to show the real part of a complex number Quadrilateral with four right angles, two pairs of parallel sides (each pair of equal length) and where the diagonals bisect each other Cartesian coordinates Scale factor with a value smaller than 1 Concave polygon Flip a point, line or shape over a line so 38 Geometry and Trigonometry Reflection Reflection matrix Reflex angle Region Regular polygon Regular polyhedron Regular solid Regular star polygon Regular tiling Representative fraction Resultant vector Revolution Rhombus Right angle Right-angled triangle that it has mirror symmetry Mirror image Transformation matrix describing a reflection Angle between 180° and 360° (not including these 2 values) Part of 1D, 2D or 3D space Polygon that is equilateral and equiangular Any of the 9 polyhedra with all faces congruent regular polygons Regular polyhedron Regular polygon that is not convex and is made by joining a vertex of a regular convex polygon to a non-adjacent vertex and continuing until the starting vertex is reached Tiling made up of a single regular polygon Fraction representing the ratio of map distance to actual distance Vector that results from adding or subtracting 2 or more vectors Turning a full 360° Equilateral quadrilateral with opposite angles equal and diagonals bisecting at 90° Angle equal to 90° Triangle with a right angle 39 Geometry and Trigonometry Right circular cone Right cone Right prism Rotation Rotation angle Rotation matrix Rotational symmetry Row vector Scalar multiple Scalar product Scale drawing Scalene triangle Second quadrant Section formula Sector Sector angle Right cone with a circular base Cone with its apex aligned directly above the centre of the base Prism in which the base is at right angles to the joining faces Turn about a point Angle of rotation Transformation matrix describing a rotation Type of symmetry when an object looks identical after rotating it Vector written as a row Vector that is a constant number times another vector Way of combining vectors to give a scalar Drawing of a real-life object with all sizes in proportion Triangle with all 3 sides of different lengths Quadrant described by x < 0 and y > 0 Formula for calculating the position vector of a point lying between two points Region of a circle between 2 radii and an arc lying between the radii Angle formed by the 2 radii of a sector 40 Geometry and Trigonometry Sector area Segment Self-similar Semicircle Shape Similar Sine ratio Sine rule Sketch Skew lines Slant height Slope-intercept form SOH-CAHTOA Solid Solid angle Solid of revolution Space diagonal Area of a circle’s sector Region of a circle between a chord and an arc lying between the chord’s endpoints Object that is exactly or very closely similar to a part of itself Half a circle Object that takes up space Two shapes one of which is a scaled version of the other – ‘same shape, different size’ Opposite divided by hypotenuse Trigonometric rule involving the sine function used to find missing angles and sides in any triangle Make a rough, free-hand picture 2 straight lines in 3D that neither meet nor are parallel Distance between a cone’s apex and its base, measured along the cone’s surface Equation of a line in 2D written as y = mx + c Mnemonic for remembering trigonometric ratios 3D shape Angle formed in 3D Solid formed by rotating a curve about the x-axis or y-axis Diagonal of a cuboid from 41 Geometry and Trigonometry Square Square-based prism Star polygon Star polyhedron Straight angle Subtend Supplementary angles Surface area Symmetric form Symmetry Tangent line Tangent ratio Tessellation Tetromino Third quadrant Three-quarter turn Tiling one corner to the furthest corner Regular quadrilateral with 2 diagonals and 4 lines of symmetry Cuboid Polygon that is not convex Polyhedron that is not convex (in a repetitive way) and has a star-like appearance Angle of exactly 180° Opposite to and enclosing (normally an angle) Angles that add up to 180° Total area of the outside of a 3D shape Equation of a straight line written by solving for the parameter When an object looks the same after changing it in some way (e.g. reflection) Straight line that touches a line or curve exactly once Opposite divided by adjacent Tiling Polyomino with 4 squares Quadrant described by x < 0 and y < 0 Turning through an angle of 270° Fitting together of shapes in a 2D space with no overlaps or gaps 42 Geometry and Trigonometry Transformation Geometric transformation Transformation Matrix describing a geometric transformation matrix Translation Shift a region Transversal Straight line that crosses 2 coplanar lines Trapezium Quadrilateral with one pair of parallel sides Trapezoid Trapezium Triangle 3-sided polygon Triangular Prism with a triangle as base prism Trigonometric Compound angle formulae expansion Trigonometric Equation linking trigonometric functions identity that is true for all values Trigonometric Ratio involving trigonometric functions, ratio in particular sine, cosine and tangent Trigonometry Study of sides and angles in triangles Tromino Polyomino with 3 squares Unit vector Vector that has magnitude equal to 1 V – kite Kite with one of its interior angles being reflex Vector Directed line segment, described either by magnitude and direction or as a set of n numbers Vector form Writing a line or plane equation using vectors Vector product Way of combining vectors to give another vector Vector sum Result of adding vectors 43 Geometry and Trigonometry Vector component(s) Vertex Vertically opposite angles Volume Volume scale factor Width x-axis x-coordinate y-axis y-coordinate z-axis z-coordinate Zero vector Coordinate number(s) of a vector Corner Non-adjacent angles made when 2 straight lines cross Amount of space in a 3D shape Cube of the length scale factor Distance from side to side; shorter distance The line y = 0, z = 0 First coordinate in the Cartesian coordinate system The line x = 0, z = 0 Second coordinate in the Cartesian coordinate system The line x = 0, y = 0 Third coordinate in the Cartesian coordinate system Vector which has all components equal to 0 Functions and Graphs 1-1 correspondence Abscissa Amplitude Annotate Approach(es) Arccosine Arcsine Arctangent Asymptote Asymptotic Behaviour Bounded above Bounded below Bounded function Closed interval Codomain 44 When each element in one collection is matched to exactly one element in another collection and vice versa x–coordinate in Cartesian coordinates Half of (Maximum value – minimum value) for the graphs of sine or cosine Label a graph, especially turning points and intercepts with axes Heading towards Inverse cosine function Inverse sine function Inverse tangent function (Straight) line that a function approaches as the values of one variable approach a certain value Function that has an asymptote Description of a function Function all of whose y–values are not bigger than some real number Function all of whose y–values are not smaller than some real number Function that is bounded above and bounded below Interval of the form [p, q] which represents all values in between (and including) p and q The set B in f : A → B 45 Functions and Graphs Cofunctions Composition of functions Concave function Constant function Convex function Cosecant Cosine function Cosine graph Cotangent Cubic function Curvature Decreasing function Dependent variable Domain Functions f and g which satisfy f(P) = g(Q) for complementary angles P and Q (e.g. sine and cosine) Work out the value of one function taking as its input the output of another function Function that lies above or on a straight line segment joining any 2 points in a given interval Function with equation f(x) = constant; function with zero gradient or derivative at each point Function that lies below or on a straight line segment joining any 2 points in a given interval Reciprocal of the sine function Function obtained by associating to an angle (between the positive x-axis and the line joining a point to the origin) the value adjacent divided by hypotenuse of the resulting right-angled triangle Graph of the cosine function Reciprocal of the tangent function Function of the form f(x) = a x3 + b x2 + c x + d How much an object is from being flat Function which has a negative derivative over an interval Variable that is the output of a function The set A in f : A → B 46 Functions and Graphs Endpoint Exponential function (to base a) Exponential graph Function (formal) Function (informal) Function machine Gradient Graph Graph paper Horizontal asymptote Horizontal translation Identity function Image Implicit function Point at the end of an interval The function f(x) = ax (a > 0) Graph of an exponential function, which always passes through the point (0,1) Subset f of the Cartesian product of two sets A and B such that each value in A is matched to exactly one value in B; written f : A → B Rule or description f which matches each value in a collection to exactly one value in another collection Diagrammatic way of showing a function with arrows and boxes How steep a function is at a point Plot of the x and y values of a function Paper (normally with evenly sized squares) used to plot graphs Asymptote parallel to the x-axis, having equation y = constant Shifting the graph of a function horizontally The function f(x) = x Element y in f(x) = y Function in which the dependent variable (usually y) is not written explicitly in 47 Functions and Graphs Improper rational function Increasing function Independent variable Input Interval Inverse cosine Inverse function Inverse sine Inverse tangent Inverse trigonometric function Large positive x Large negative terms of the independent variable(s) (usually just x) Rational function with the numerator degree greater than or equal to the denominator degree Function which has a positive derivative over an interval Variable that is an input of a function Values going into a function Fixed set of continuous values (x or y) Inverse of the cosine function, with domain [-1, 1] and range [0, π] Function (usually written f-1 and not to be confused with the reciprocal of f) which, when composed with f (either way), gives the identity function Inverse of the sine function, with domain [-1, 1] and range [-½π, ½π] Inverse of the tangent function, with domain (-∞, ∞) and range (-½π, ½π) Inverse of a trigonometric function, especially the inverse sine, inverse cosine or inverse tangent As x goes to infinity As x goes to minus infinity 48 Functions and Graphs x Linear function Logarithmic function (to base a) Mapping Maximum value Minimum value Modulus function Not defined Oblique asymptote Open interval Operator Ordered pair Ordinate Origin Output Parabola Parametric function Period Function of the form f(x) = a x + b The function f(x) = loga x , the inverse of the exponential function to base a Function Biggest y–value Smallest y–value Function which takes any number and sends its absolute value Cannot work out a y–value Asymptote that is not horizontal or vertical; usually a straight line with positive or negative gradient Interval of the form (p, q), which represents all values in between (but not including) p and q Function Pair of values, in which one is declared to be the first and the other the second y–coordinate in Cartesian coordinates Point with coordinates (0,0) Values coming out of a function Graph of a quadratic function Function written using one or more parameters How often a periodic function repeats 49 Functions and Graphs Periodic function Phase angle Piecewise function Plot Polynomial function Pre-image Proper rational function Quadratic function Range Rational function Reciprocal function Reciprocal of a function Reciprocal trigonometric functions Reflection in Function which, on part of its domain, repeats Angle by which the graph of a trigonometric function (especially sine or cosine) is shifted from its normal zero position Function written as separate functions over separate (and smaller) domains Show coordinates by dots or crosses and then sketch or draw the graph through them Function of the form f(x) = an xn + an-1 xn-1 + . . . + a1 x + a0 Element x in f(x) = y Rational function with the numerator degree less than the denominator degree Function of the form f(x) = a x2 + b x + c Functions and Graphs x–axis Reflection in y–axis Root Secant Sine function Sine graph Singular Singularity Slope Subset f(A) of B in f : A → B Function that is one polynomial divided by another Function given by f(x) = a⁄x Small negative x Small positive x Table of values 1 divided by the function Secant, cosecant and cotangent functions Reflecting a point, line or 50 Tangent function 2D shape in the x–axis Reflecting a point, line or 2D shape in the y–axis Solution of f(x) = 0 Reciprocal of the cosine function Function obtained by associating to an angle (between the positive x-axis and the line joining a point to the origin) the value opposite divided by hypotenuse of the resulting right-angled triangle Graph of the sine function Function that has a singularity Where a function is undefined; cannot work out a y–value as the x–value is not in the domain Gradient As x goes to 0 through negative values As x goes to 0 through positive values Table showing pairs of dependent and independent variables; used to plot the graph of a function Function obtained by associating to an angle (between the positive x-axis and the line joining a point to the origin) the value opposite divided by adjacent of the resulting right-angled triangle 51 Functions and Graphs Unbounded function Vertical asymptote Vertical translation Wave function x–intercept x–scaling x–value y–intercept y–scaling y–value Zero(s) Function that is not bounded Asymptote parallel to the y-axis, having equation x = constant Shifting the graph of a function vertically Function which represents a periodic phenomenon, especially one of the form a sin (bx + c) + d or a cos (bx + c) + d Where the graph crosses the x–axis Stretching or squashing a graph horizontally Input of a function Where the graph crosses the y–axis Stretching or squashing a graph vertically Output of a function Root(s) Money and Finance ABM Account Accounting equation Account number Amortisation Amount Annuity Appreciation APR ARM Asset ATM Balance Bank Bank account Banknote Bankrupt Basic pay Basic rate 52 Automated Bank Machine – an ATM Record of transactions Assets = Liabilities + Equity Number of a bank account Present value of an annuity How much Equal and regular payments Increase in value Annual Percentage Rate – interest rate when borrowing money Adjustable Rate Mortgage – mortgage which has a changing interest rate Something owned that can be exchanged for money Automated Teller Machine – machine used for cash transactions Amount of money in an account Organisation that deals with transactions Account in a bank Paper cash Insolvent entity Normal pay, not including overtime How much basic pay is earned over time, for example, £ 12 per hour 53 Money and Finance Bearer Benefit Bill Bond Bonus Borrow Borrower Bounce Building society Bureau de change Buy Capital Cash dispenser Cash flow Cashier Cash machine Cent Entity who holds something, for example, the bearer of a cheque Something gained Something that is paid by a person using services, for example, a gas bill Contract in which borrowed money is repayed with interest Extra pay given by an employer Take but then give back, usually with interest Entity who borrows; a debtor Cheque that cannot be paid due to insufficient funds Place where financial services are given, especially mortgages Business where money is changed from one currency to another Get something for money Factors of production that are not significantly diminished after producing goods or services ATM Movement of cash Person who handles transactions for a company ATM Currency that is a hundredth 54 Money and Finance Charge Cheque Cheque book Coin Collateral Commission Commodities Compound interest Contract Counterfeit Coupon Credit Credit card Credit crunch Creditor Currency Currency exchange Current account Debenture Debit of some basic amount Sell Paper that orders a payment of money Book with cheques in it Metal currency, usually a flat cylindrical shape Assets pledged as security for a loan Payment as a percentage of goods sold Goods that can be processed and resold Interest paid on the capital as well as the interest left on the deposit Legal agreement Produced illegally Interest in a bond Balance in an account Card used to borrow money or buy goods Situation in which it is very difficult to get capital Entity that has provided credit and owed money Money Bureau de change Account Document that pays for a loan Expense or money paid out of an account 55 Money and Finance Debit card Debt Debtor Decimal currency Deductions Denomination Deposit Depositor Depreciation Direct debit Discount Dole Dole queue Donee Donor Double time Down payment Draw Earnings Economics Card used to withdraw money or put money into an account Something that is owed, usually assets Entity that is in debt Currency in which the main unit is divided into 100 equal parts Money taken off Description of a currency, for example, pounds, pence, euros, cents Put money into an account Entity that makes a deposit Decrease in value Instruction by an account holder to their bank to collect money from another account Reduction in price Jobseekers’ allowance Queue in which one stands to get dole Receiver of a gift Issuer of a gift Getting paid at twice the basic rate Partial payment made when buying an item Take money out; use a cheque for paying Money gained by wages, interest etc. Study of how goods and services are produced, managed etc. 56 Money and Finance Economic system Economy Embezzlement Entity Equity Euro Exchange rate Expenditure Expense Export Extortion Factors of production Finance Financial institution Financial plan Financial service Fixed interest rate Foreign exchange rate Resources, people, organisations etc. that take part in the production, sale etc. of goods Economic system Unlawfully transferring money, for example, by stealing Person, organisation, institution, etc. Assets minus liabilities Unit of currency used in many European countries: 100 cents = 1 euro Value of one currency compared to another Amount spent Something paid for Trading something out of a country Illegally getting money by force Resources used to produce goods and services; capital Study of managing funds Place, such as a bank, which deals with financial services Plan for spending and saving Services provided by banks, building societies etc. Interest rate that does not change Exchange rate 57 Money and Finance Fraud Freightage Fund FX rate Gain Gambling GDP Gift Gift card Goods Gross pay Holder HP IBAN Identity theft Import Income Income tax Inflation Personal gain by deceiving someone Amount charged when transporting a large amount of goods; sometimes just the goods transported Money used for something or someone Exchange rate Get more Risking goods with the aim of making more goods (usually money) Gross Domestic Product, the amount of goods etc. produced in a country in one year Something that is given or received without buying or selling Card given as a gift and used to buy things Items bought or sold Income before deductions Someone who owns money, land etc. Method of paying for goods with a deposit + regular instalments International Bank Account Number Pretending to be someone else to steal their money or other property Trading something into a country Earnings Tax charged on income/wealth Price increase of goods in an economy 58 Money and Finance Insolvent Instalment Instruction Insurance Insurance company Insurance policy Insurance premium Insurance rate Insurer Interest In the black In the red Invest Investment Investor Invoice Islamic banking Item Jobseekers’ allowance Not able to pay debts Regular payment Statement telling someone what to do, e.g. pay money to this person Contract agreeing to compensate someone for loss or damage to property or other things Company that gives insurance Contract in an insurance Payment made by an insured person Amount used to decide how much to charge Insurance company Charge on borrowing money Making a profit In debt Make an investment Property gained to make income Entity that makes an investment Bill describing goods bought Banking in accordance with Islamic law; specifically, banking without interest Thing Money paid by the government to unemployed people looking for work 59 Money and Finance Legal tender Legatee Legator Lend Lender Liability Lien Liquidation Litigant Litigate Litigator Loan Loss Mail order Maker Market Maturity Microfinance Minimum wage Mint Currency that is legally usable Person who gets money etc. from someone who has died Person who leaves money etc. to someone Give (loan) but expect to be returned, usually with interest Someone who lends Amount owed Right to claim assets if a debt is not paid Get rid of all assets and go out of business Person taking out a complaint or claim Take a complaint or claim against someone to court Person employed to litigate Money given by a lender to a borrower Lose money by selling an item for less than its bought price Way of buying and selling from home Person who writes a cheque Actual or theoretical place where buyers and sellers trade Final date at which borrowed money with interest is to be repayed Finance catering for those in poor households Lowest legal wage Place where coins are made 60 Money and Finance Money Money exchange Money laundering Moneylender Monthly payment Mortgage Mortgagee Mortgagor Net pay Non-decimal currency Normal working hours Overdraft Overdrawn Overtime Owe Pay Pay as you go Payee Valuable items (e.g. gold, silver) allowed by law to be exchanged for other items Bureau de change Making legal money that is obtained through illegal means Entity offering personal loans at high interest rates Payment made every month Loan to Lender in a mortgage Borrower in a mortgage Gross pay minus deductions Currency not based on the decimal system, e.g., in Mauritania, 1 ouguiya = 5 khoums Hours worked by agreement or contract When amount withdrawn exceeds balance Being in an overdraft Time that is worked beyond normal working hours Obliged to give something back Give money to receive goods Payments for goods or services as they are used, especially for mobile phones Person(s) receiving a payment 61 Money and Finance Payer pcm Pence Pension Piece rate Piece work Pocket-money Polymer banknote Pound Profit Property Quarter Receipt Recession Regular payments Rent Revenue Salary Savings Service Person(s) making a payment Per calendar month UK unit of money Money an employee gets after retiring Piece work rate Getting paid for each bit of work done or item produced Allowance given, usually to children Banknote made of plastic, used to help stop counterfeiting Currency used in many countries; in the UK, 1 pound = 100 pence Make money by selling an item for more than its bought price Something owned by someone 3 months Paper showing that money has been exchanged for goods Slowdown in the economy, especially the declining of GDP for at least 2 quarters Payments made at an equal interval of time Payment for use of property Money received Weekly or monthly wage Income not spent Non-monetary skills and resources 62 Money and Finance Simple interest Solvent Sort code Speculation Speculator Spend Standing order Statement Stock Sue Superannuation Take-home pay Talking ATM Tariff Tax Tax avoidance Tax evasion Taxpayer Time and a half Time and a quarter Trade Interest calculated only on the capital Not insolvent Bank code used to transfer money Risky investment, to make quick gains Someone involved in speculation Buy goods Order for a bank to pay a fixed, regular amount from one account to another List showing amount of money paid, received, etc. and their total Original capital of a business Take legal action against Pension given after retiring from employment Net pay ATM that provides audible instructions Tax on imports and exports Financial charge forced on a population by a government Legally reducing the amount of tax to pay Not paying tax by using illegal means Payer of tax Getting paid at one and a half times the basic rate Getting paid at one and a quarter times the basic rate Voluntary exchange of goods or services 63 Money and Finance Trade union Transaction Union Union dues Union member Unit Usury Vacillate VAT VAT man Voluntary bankruptcy Wage Withdraw Withdrawal Organisation that promotes the rights of workers Exchange of money or goods Trade union Payment for being a union member Person in a union Amount of electricity Charging interest on loans, especially extremely high charges Prices or rates that constantly change by small amounts Value Added Tax – tax charged on items Government department that collects VAT When someone asks to be made bankrupt Money paid by calculating on an hourly, daily, weekly or piece work basis Take money out Withdraw Statistics and Probability 5-bar gate 5-figure summary Arithmetic mean Average Back-to-back stem-and-leaf diagram Bar chart Bar graph Biased sample Bin Box-andwhisker plot Box plot Central tendency Certainty Chance Class Class interval Conditional 64 Symbol used to denote 5 tally marks List consisting of the lowest number, first quartile, second quartile, third quartile and highest number in a data set Adding up all numbers and dividing by how many there are ‘Middle’ value of a data set 2 stem-and-leaf diagrams sharing a common stem with one set of leaves to the right of the stem, the other set to the left Statistical diagram of bars (with spaces between them) showing frequency against data Bar chart Sample not representative of the population Class interval in a histogram Box plot Statistical diagram showing a 5-figure summary Way in which quantitative data tend to cluster about some value Event with probability equal to 1 Something that cannot usually or practically be predicted – ‘luck’ Adjacent data ordered into a small collection Range of a class Probability of one event, given the probability 65 Statistics and Probability probability Continuous data Continuous random variable Correlation Cumulative frequency Cumulative frequency graph Cumulative frequency table Data Data point Data set Datum Decimal probability Deviation (from the mean) Dice Die of another Data that are viewed as smoothly varying; for example, temperature or height Variable representing continuous data Link between (usually) 2 variables Running total of frequencies Plot of cumulative frequency against the variable in question Statistics and Probability Discrete data Discrete random variable Dispersion Dot chart Dotplot Event Expectation Frequency table with a column for calculating cumulative frequencies Things, usually numbers Datum List of things, usually numbers Member of a data set Probability written as a decimal Difference between the value of a data point and the mean, usually ignoring the sign More than one die Polyhedral object used in statistical trials 66 Expected value Experiment Extrapolate First quartile Fractional probability Frequency Frequency density Frequency Data that are viewed as not smoothly varying; for example, shoe size or ice-cream flavours Variable representing discrete data Way in which data are spread out Dotplot Statistical diagram with vertical dots Collection of outcomes from an experiment; subset of the sample space The long-term average, E(X) = ∑ X P(X) Expectation Process of collecting data, for example, flipping a coin to give a head Predicting new data points outside the range of known data points Lower quartile (Q1) Probability written as a fraction How often an event occurs during an experiment Height of a bar in a histogram Polygon formed by joining the midpoints of the 67 Statistics and Probability polygon Frequency table Grouped data Highest value Histogram Impossibility Independent events Interpolate Interquartile range Joint probability Key Label Leaf Likelihood Likely Line Graph tops of the bars in a histogram Table listing frequencies of members in a data set Data arranged into groups Biggest number in a data set Statistical diagram of vertical bars (without spaces between them) showing frequency against class interval Event with probability equal to 0 Events that do not depend on each other Predicting new data points within the range of known data points Third quartile minus first quartile Probability of (usually 2) events happening together Guide in a statistical diagram Naming a part of a statistical diagram Row in a stem-and-leaf diagram How likely something is; the ‘chances’ How much or often we expect something to happen Statistical diagram obtained by joining points with a straight line from the first point 68 Statistics and Probability Line of best fit Straight line drawn through a set of points so that roughly an equal number of points are on either side of the line Loaded die Die that has been deliberately changed so that one face appears more often than others Lower quartile Median of the first half of a data set Lowest value Smallest number in a data set Mean Arithmetic mean Measures of Quantifying central tendency, especially central using the median, mode or mean tendency Measures of Quantifying spread, especially using the spread range or standard deviation Median Middle value in a list of numbers, after being arranged in ascending order Mode Most common thing in a data set Mutually Independent events exclusive events Negative When one variable is generally decreasing correlation as another increases No Neither a positive nor negative correlation correlation Ogive Cumulative frequency graph Outcome Result of an experiment Outlier Datum that is numerically very far 69 Statistics and Probability Percentage probability Pictograph Pie chart Pie graph Point Population Positive correlation Probability Probability scale Probable Qualitative Quantitative Quantity Quartile Random variable Range Sample Sample space from all other data points Probability written as a percentage Statistical diagram showing data using pictures and their parts Statistical diagram showing data in a circle using percentages and or degrees Pie chart Data point Entire collection of things from which data is collected When one variable is generally increasing as another increases Measure of likelihood Line with a (usually decimal) scale from 0 to 1 used to indicate probability Likely To not do with numbers To do with numbers Amount Any of the 3 values Q1, Q2 or Q3 that divides an ordered data set into 4 equal parts Variable in statistics Biggest number minus smallest number Subset of a population All possible outcomes from an experiment 70 Statistics and Probability Scatter chart Scatter diagram Scattergraph Scatterplot Second quartile Semiinterquartile range Skewed data Spread Standard deviation Statistic Statistical diagram Statistical dispersion Statistical inference Statistics Scattergraph Scattergraph Statistical diagram of coordinates with one variable along the x-axis and the other along the y-axis Scattergraph Median (Q2) Half the interquartile range Data that is more bunched up at one place than any other Statistical dispersion Square root of the variance Something calculated from a data sample Diagram showing data collection Spread of data, especially standard deviation, range or interquartile range Making conclusions about the population based on information about a sample from this population Study and interpretation of how data is distributed, especially in real-life situations 71 Statistics and Probability Stem Stem-and-leaf diagram Stem-and-leaf plot Stemplot Survey Tally Tally mark Tally table Third quartile Title Tree diagram Trend Trial Unbiased sample Uncertainty Upper quartile Variance Vertical list of numbers in a stemplot Statistical diagram consisting of two columns, one containing the stems, the other the leaves Stem-and-leaf diagram Stem-and-leaf diagram Collection of data, usually obtained from the general public Count Small vertical line used to keep count Table with tally marks Upper quartile (Q3) Heading used in statistical diagrams Diagram with branched lines showing possibilities for different events Pattern or important information obtained by analysing data Experiment Sample representative of the population Not certain Median of the second half of a data set Mean of the squares of the deviations 72 Calculus 1st order ODE 2nd derivative 2nd derivative test nd 2 order ODE 1st order DE that involves a function of only 1 variable Derivative of the 1st derivative Criterion for deciding whether a function has a maximum or minimum using the 2nd derivative 2nd order DE that involves a function of only 1 variable Convergence of the series consisting of the modulus of each term of a given series Function F in F ’ = f Integration Absolute convergence Anti-derivative Antidifferentiation Antilogarithm Number x in log x = y Arbitrary Constant of integration constant Arithmetic Series formed from an series arithmetic sequence Auxiliary Quadratic equation obtained by replacing y ’’ by equation m2, y ’ by m and y by 1 in A y ’’ + B y ’ + C y = 0 Binary Base 2 logarithm logarithm Binomial series Maclaurin series for (1 + x)a Calculus Differentiation and integration 73 Calculus Chain rule Common logarithm Complementary function Conditional convergence Constant of integration Converge Convergent sequence Convergent series Critical point Critical value d’Alembert’s Ratio Test Definite integral Derivative Derived function Rule for differentiating a composition of functions Base 10 logarithm General solution of a homogeneous linear differential equation Convergence of a given series, but nonconvergence of the series obtained by taking the modulus of each term of the original series Quantity added on when a function is integrated Approach a limiting value Sequence that converges (has a limit) Series that converges (has a limit) Point where either a stationary point is found or the derivative does not exist y-value at a critical point Test for deciding whether or not a series converges Integral with limits Derived function Function that gives the gradient of the tangent line to a function’s graph 74 Calculus Differentiable Differential Differential Calculus Differential Equation (DE) Differential equation with constant coefficients Differentiate Differentiate from first principles Differentiation Diverge Divergence Divergent sequence Divergent series e Endpoint extrema Endpoint maximum Function that can be differentiated Infinitesimal quantity dx Study of rates of change Equation involving derivatives (and possibly powers thereof) of an unknown function of one or several variables Linear differential equation in which all coefficients of the unknown function and its derivatives are constant functions Find the derivative Differentiate a function using the limit formula Process of working out the derived function Opposite of converge; having no limiting value Diverge Sequence that diverges (has no limit) Series that diverges (has no limit) Base of the natural logarithm Maxima and minima at endpoints Endpoint at which a function has a maximum value 75 Calculus Endpoint minimum Euler notation Euler’s formula Extrema Extreme value Falling point of inflexion First derivative test First-order linear ODE Fundamental theorem of calculus General antiderivative General solution Geometric series Global extrema Global maximum Global minimum Higher order Endpoint at which a function has a minimum value The ‘big D’ notation for derivatives : Df = f ’ eix = cos x + i sin x Maxima and minima Maximum or minimum value Point (of inflexion) where the derivative is negative either side of the point Test using the first derivative for deciding the nature of a stationary point Differential equation of the form a y ’ + b y = f where a, b and f are functions of x only Result that if F is an antiderivative of f (F ’ = f), then ∫ab f = F(b) – F(a) Function F + C where F ’ = f and C is an arbitrary constant Solution of a differential equation with the arbitrary constant(s) unevaluated Series formed from a geometric sequence Extrema over the whole of a function’s domain Maximum on the domain of a function Minimum on the domain of a function Derivative bigger than 1st order 76 Calculus derivative Homogeneous differential equation Homogeneous linear differential equation Implicit differentiation Indefinite integral Infinite series Inhomogeneous differential equation Inhomogeneous linear differential equation Initial conditions Integrable Integral Differential equation that is identically satisfied by the zero function Linear differential equation of the form an y(n) + an-1 y(n-1) + … + a1 y(1) + a0 y = 0 where the ai are functions of the independent variable Differentiating an implicit function Integral without limits Series with infinitely many terms Differential equation that is not homogeneous Linear differential equation of the form an y(n) + an-1 y(n-1) + … + a1 y(1) + a0 y = f where the ai and f are functions of the independent variable(s) and f is not the zero function Given values of the dependent and independent variables used to evaluate the arbitrary constant in the solution of a differential equation Has a primitive Antiderivative 77 Calculus Integral Calculus Integrand Integrate Integrating factor Integrating factor DE Integration Integration by parts Integration by substitution Lagrange notation Left-hand derivative Leibniz notation Limit Limit formula Limits of integration Linear differential equation Study of antiderivatives, in particular their interpretation as areas and volumes Function to be integrated Find an integral Function that is the multiplicand of each term in a DE DE that uses an integrating factor to solve it Process of working out an integral Technique for integrating a product of functions Integration technique involving replacing part of the integrand by a new variable The ‘f dash’ notation for derivatives Derivative just to the left of a given point The ‘dy by dx’ notation for derivatives Value a function approaches Definition of the derivative: f ’ (x) = lim [f(x + h) – f(x)]/h The quantities a and b in the notation ∫ab Differential equation of the form an y(n) + an-1 y(n-1) + … + a1 y(1) + a0 y = f where the ai and f are functions 78 Calculus Local extrema Local maximum point Local minimum point Logarithmic differentiation Lower limit Maclaurin expansion Maclaurin series Maxima Maximum value Minima Minimum value Natural logarithm Nature of stationary point Nature table Newton quotient of the independent variable(s) Local maxima and local minima Stationary point through which the derivative changes from positive to negative Stationary point through which the derivative changes from negative to positive Differentiation technique where natural logarithms are taken before differentiating Bottom limit in a definite integral symbol (a in ∫ab) Maclaurin series Power series for any differentiable function Maximum points y-coordinate of a maximum point Minimum points y-coordinate of a minimum point Base e logarithm Maximum, minimum or point of inflexion Table used to find the nature of stationary points The expression [f(x + h) – f(x)]/h in the definition of the derivative 79 Calculus Nonhomogeneous DE Nonlinear differential equation Non-stationary point of inflexion Not differentiable Not integrable nth derivative Optimization Order (DE) Ordinary Differential Equation (ODE) Parametric differentiation Partial Differential Equation (PDE) Particular Inhomogeneous differential equation Differential equation that is not linear Point of inflexion for which the first derivative is non-zero Calculus integral Particular solution Point of inflexion Power series Primitive Product rule Does not have a derived function Quotient rule Does not have a primitive Result of differentiating a function n times Using differentiation to find the maximum or minimum values of a function Highest derivative in a differential equation Differential equation in which the unknown function (the dependent variable) is a function of only one independent variable Differentiation involving (usually) 2 functions of the same variable Differential equation in which the unknown function (the dependent variable) is a function of at least 2 independent variables Solution of a non-homogeneous DE that takes a 80 Rate of change Ratio Test Right-hand derivative Rising point of inflexion Saddle point Second derivative test Second-order linear ODE with constant coefficients similar form to the RHS of the DE Solution of a differential equation in which the arbitrary constant is evaluated using initial conditions Point on a curve at which the second derivative changes sign Infinite series with polynomial terms Indefinite integral Rule for differentiating functions that are multiplied Rule for differentiating functions that are divided How one variable changes compared to another; the derivative D’Alembert’s Ratio Test Derivative just to the right of a given point Point (of inflexion) where the derivative is positive either side of the point Stationary point that is not an extremum Test using the second derivative for deciding the nature of a stationary point DE of the form A y ’’ + B y ’ + C y = f where A, B and C are constant real numbers and f is a function of x only 81 Calculus Separable DE Stationary Stationary point Stationary point of inflexion Stationary value Turning point Upper limit Nonlinear DE that can be written as M y ’ = N where M is a function of y only and N is a function of x only When a function has zero derivative Point where the derivative of a function is 0 Point of inflexion for which the first derivative equals zero Mensuration and Units 12-hour time 24-hour time Absolute zero Acre am Analogue y-coordinate of a stationary point Stationary point Top limit in a definite integral symbol (b in ∫ab) 82 Angle Annual Apparent solar day Apparent solar time April Arc length Arcminute Arcsecond Area Atomic clock August Back bearing Balancing scales Base unit Time written using am or pm with the hours between 1 and 12 Time written without am or pm with the hours between 0 and 23 Lowest possible temperature: 0 K = -273.15 C (approx.) Area unit: 1 acre = 4 840 square yards Any time between 12 midnight and 11.59 (1 minute before noon) – ante meridiem Clock readout using hands and written numbers Arc length divided by radius Every year Time between 2 successive returns of the Sun to the same meridian True solar time 4th month of the year having 30 days Length of an arc Angle unit: 60’ = 1° Angle unit: 60’’ = 1’ Amount of space in a 2D shape Precision clock for measuring time th 8 month of the year having 31 days Bearing from B to A Device for comparing weights Unit from which other units are found 83 Mensuration and Units Bearing BST Cable Capacity Cardinal directions/points Carroll diagram Celestial sphere Celsius Centennial Centilitre Centimetre Chain Clepsydra Clock Compass Conversion Conversion graph Coordinated Universal Time (UTC) Angle measured clockwise from a North line at a point A to another point B, written using 3 digits British Summer Time Length unit: 10 cables = 1 Nm Ability to hold a fluid The directions north, south, east and west Diagram showing groupings of things into ‘ yes/no ’ Imaginary sphere with random radius, but concentric with the Earth and rotating on the same axis Temperature unit Every 100 years Volume unit: 100 cl = 1 l Length unit: 100 cm = 1 m Length unit: 1 chain = 22 yards Water clock Device for measuring time Device for indicating direction (bearing) Changing units Graph used to convert units Time standard which the world uses to reckon time and set clocks 84 Mensuration and Units Cosmic year Counting frame Cubic centimetre Cubic metre Daily Day Daylight saving time December Degree (Angle) Degree (Temperature) Depth Derived unit Digital Dozen East Electronic balance Equinox Estimate Fahrenheit Fathom February Galactic year Abacus Volume unit: 1 000 cm3 = 1 L Volume unit: 1 m3 = 1 000 L Happening every day Time unit: 1 day = 24 hours Putting the clocks forward in summer 12th month of the year having 31 days Angle unit: 360° = a full circle angle Unit of temperature Distance below something (usually water level) Unit obtained from a base unit Clock readout using lit up numbers Twelve Direction with bearing 090° Device for measuring weight Moment when the Sun is directly overhead Roughly give an answer to Temperature unit related to Celsius by the formula, F = (9/5) C + 32 Length unit: 1 fathom = 2 yards nd 2 month of the year having 28 or 29 85 Mensuration and Units Fluid ounce Foot Foot-poundsecond units Fortnight Friday Furlong Galactic year Gallon (imperial) Gallon (US liquid) Gill GMT Gram Gregorian calendar Half past Hectare Height Horology Hour Hourly Imperial units days Volume unit: 20 fl. oz = 1 pint Length unit: 1 ft = 12 inches Imperial units Time unit: 1 fortnight = 2 weeks 5th day of the week Length unit: 1 furlong = 220 yards Time taken for the Solar system to go once around the Milky Way galaxy Volume unit: 1 gallon = 4.54609 L Volume unit: 1 US gallon = 3.785 411 784 L Volume unit: 1 gill = 5 fl. oz Greenwich Mean Time Mass unit: 1 000 g = 1 kg Calendar in official use, based on the Julian calendar, but having an average year length of 365.2425 days 30 minutes past the hour Area unit: 1 ha = 10 000 sq. m Length measured vertically upwards Study of timekeeping Time unit: 1 hour = 60 minutes Happening every hour System of units that uses the 3 base units of foot, pound and second 86 Mensuration and Units Inch International Date Line International Prototype Kilogram January Julian calendar July June Kelvin Kilogram Kilometre Kilometres per hour (kph) Latitude League Leap second Leap year Length Length unit: 1 inch = 2.54 cm Imaginary north-south line in the Pacific ocean, travelling across which changes the date Right circular cylinder made of an alloy of 90% platinum and 10 % iridium (by mass) of diameter 39.17 mm st 1 month of the year having 31 days Calendar with 365 days divided into 12 months, with a leap day added to February every 4 years, the average year having 365.25 days th 7 month of the year having 31 days 6th month of the year having 30 days Basic unit of temperature SI base unit of mass – mass of the International Prototype Kilogram Length unit: 1 km = 1 000 m Speed unit found in a speedometer - 1 kph means going 1 kilometre every hour Angle measured north or south from the equator Length unit: 1 league = 3 miles Adjustment to UTC Year with 366 days Distance between 2 points 87 Mensuration and Units Light year Litre Longitude March Mass May Mean solar time Mensuration Meridian Metre Metres per second (m/s) Metre stick Metric system Midday Midnight Mile Miles per hour (mph) Distance that light travels in a year, approximately 10 trillion kilometres Unit of volume: 1 l = 1 000 cm3 Angle measured east or west from the prime meridian rd 3 month of the year having 31 days Amount of substance – how much stuff there is in an object th 5 month of the year having 31 days Time based on Earth’s rotation compared to distant astronomical objects Measurement Imaginary curved line from the North pole to the South pole, at right angles to the horizon SI base unit of length – distance travelled by light in vacuum in 1/299 792 458 s Speed unit – 1 m/s means going 1 metre every second Measuring device of length 1 metre Decimal system of measurement Noon Beginning or end of each day Length unit: 1 mile = 1 760 yards (= 1 609.344 m) Speed unit found in a speedometer – 1 mph means going 1 mile every hour 88 Mensuration and Units Millennial Milligram Millilitre Millimetre Minute (Angle) Minute of arc Minute (Time) Monday Month Monthly Nautical mile Newton Noon North Northeast Northwest November October Ounce Parallel Pint pm Every 1 000 years Mass unit: 1 000 mg = 1 g Volume unit: 1 000 ml = 1 l Length unit: 10 mm = 1 cm Arcminute Arcminute Time unit: 1 min. = 60 s 1st day of the week Time unit related to the Moon Happening every month Length unit: 1 Nm = 1 852 m Basic unit of force – weight is a force 12 o’clock in the daytime Direction with bearing 000° Direction with bearing 045° Direction with bearing 315° th 11 month of the year having 30 days 10th month of the year having 31 days Mass unit: 16 oz = 1 lb (1 oz = 0.028 349 523 125 kg) Imaginary line running from east to west connecting all places with the same latitude Volume unit: 8 pints = 1 gallon Any time between 12 noon and 11.59 (1 minute before midnight) – post meridiem 89 Mensuration and Units Pound ppm Prime meridian Quart Quarter past Quarter to Radian Reading Ready reckoner Ruler Sand timer Saturday Scale Second (Angle) Second of arc Second (Time) September Sidereal Sidereal day Sidereal month Mass unit: 1 lb = 0.453 592 37 kg Parts per million Meridian with longitude 0° Volume unit: 1 quart = ¼ of an imperial gallon 15 minutes past the hour 15 minutes to the hour Angle unit: π rad = 180° Mark or number on a measuring instrument Table, normally with 2 columns, that gives conversions Device used to measure length Device used to measure time using sand 6th day of the week Equally spaced marks on a measuring device Arcsecond Arcsecond SI unit of time, equal to the time needed for a particular type of caesium atom to make 9 192 631 770 oscillations th 9 month of the year having 30 days To do with the stars or constellations Period of time based on sidereal time and equal to approximately 23 hours 56 minutes and 4.091 seconds Time taken by the Moon to return to the 90 Mensuration and Units Sidereal time SI system Solar calendar Solar day Solar noon Solar time Solstice South Southeast Southwest Speed of light Speedometer Square centimetre Square kilometre Square metre Square millimetre same point in the sky, approximately 27 days, 7 hours and 43 minutes Time based on the Earth’s rotation relative to the background of fixed stars The International System of Units Calendar in which dates show the position of the Earth around the Sun Time between 2 successive returns of the Sun to the local meridian Moment when the Sun is at its highest point in the sky Time measured by the Sun’s motion Moment when Sun’s apparent position is at its northernmost and southernmost extremes Direction with bearing 180° Direction with bearing 135° Direction with bearing 225° Basic unit of speed equal to exactly 299 792 458 m/s (in vacuum) Device for measuring speed Area unit: 10 000 cm² = 1 m² Area unit, equal to the amount of space in a square of side length 1 km Area unit: 1 000 000 m² = 1 km² Area unit: 100 mm² = 1 cm² 91 Mensuration and Units Steradian Stone Stopwatch Sunday Sundial Synodic day System of measurement System of units Tachograph Tape measure Temperature Ten past Ten to Thermometer Thursday Time Time zone Tonne True solar time Trundle wheel Unit of solid angle Mass unit: 1 st = 14 lb Device for measuring time accurately 7th day of the week Clock measuring time by the Sun’s position Time it takes for a planet to rotate once about the object it is orbiting; for Earth around Sun, this is 24 hours (solar day) Collection of units to describe things that can be measured System of measurement Device for recording speed over a period of time Device that can measure lengths, including those that are not straight Measure of hotness or coldness 10 minutes past the hour 10 minutes to the hour Device for measuring temperature 4th day of the week Measure of duration – how long something lasts Region on Earth bounded by 2 lines of longitude separated by 15° Mass unit: 1 t = 1 000 kg Time based on the solar day Wheel attached to a stick, 92 Mensuration and Units Tuesday Unit Universal Time Volume Watch Water clock Wednesday Week Weekend Weekly Weight West Workweek Yard Year Yearly Zulu time used for measuring length 2nd day of the week Size of a physical quantity GMT How much space there is in a 3D shape Device for measuring time Clock using water to measure time 3rd day of the week Time unit: 1 week = 7 days Saturday and Sunday Happening every week How heavy something is Direction with bearing 270° The 5 days from Monday to Friday Length unit: 1 yard = 0.9144 m Time unit: 1 year = 12 months Happening every year GMT 93 Sets, Logic, Proofs and Genera Aleph-null Aleph-one Algebraically Algorithm Analytically Answer Antecedent Approximate Argument Arithmetically As a result of Axiom Bad form Barber’s paradox Base case Belongs to Biconditional Calculate Cardinality of the set of all natural numbers Infinite cardinal after aleph-null Using algebra Ordered collection of instructions to do something Using calculus End result of a calculation Statement P in ‘If P, then Q’ Get an answer or reading close to the actual one Attempt to convince someone of the truth of something Using arithmetic Consequence of Statements assumed to be true, used at the start of a logical argument Working or notation that is not acceptable Version of Russell’s paradox involving a barber who only shaves those people who don’t shave themselves; does the barber shave himself ? First part of proof technique in mathematical induction Contained in (a set) Two-way conditional: A implies B and B implies A Work out, not necessarily 94 Sets, Logic, Proofs and Genera Calculation Cardinal Cardinality Cardinality of the continuum Case Complement Conclusion Conditional Conjecture Consequence Consequent Consequently Consistency Continuum Continuum hypothesis Contradiction with a calculator Any type of mathematical procedure, especially adding, subtracting, multiplying or dividing Quantity used to measure cardinality Size of a set Cardinality of the set of all real numbers Part of something For a set A, and universal set U, the set consisting of everything in U that’s not in A Statement reached at the end of a logical argument; the ‘then…’ part of a conditional Statement of the form, ‘If…, then…’ (A implies B) Suggest a statement believed to be true, but is not proven to be true or false Follows from Statement Q in ‘If P, then Q’ Result of Does not have contradictions Set of all real numbers Hypothesis that the power set of aleph-null equals aleph-one When a statement does not fit logically with another one 95 Sets, Logic, Proofs and Genera Contrapositive Converse Countable Countably infinite Counterexample Decrement Deduce Deduction Deductive reasoning Define Definition Demonstrate Determine Direct proof Statement obtained by switching the hypothesis and conclusion of a conditional negating both: not B implies not A Switching the hypothesis and conclusion of a conditional: B implies A Set which is either finite or has the same number of elements as the set of all natural numbers Having the same number of elements as the set of all natural numbers Specific example which makes a statement false Decrease; to go down Figure out logically Deduce Making conclusions from definitions and axioms Give a definition Something that is given a meaning to, either in words or by an equation Show Work out Proof technique used to prove a statement by starting with axioms and employing modus ponens Disjoint sets Sets which have no common elements 96 Sets, Logic, Proofs and Genera Disprove Empty set Equal to Error Estimate Evaluate Expression Extrapolate Fact False Fields Medal Figure out Final answer For all Form General case Geometrically Graphically Guess Prove a statement false by giving a counterexample Set with no elements Same Mistake Educated guess; reasoned judgement Work out Combination of numbers and variables combined using brackets, adding, subtracting, multiplying, dividing, taking powers, taking roots, logarithms, etc., but not containing equality or inequality symbols Extending a method to new situations Something that is thought to be true Not true Prize given to mathematicians every 4 years Work out Answer For every value How something looks Case not involving a specific instance of something Using geometry Using graphs Give an answer without working or much thinking 97 Sets, Logic, Proofs and Genera Hence Hilbert’s Hotel Hypothesis If If and only if (iff) Illogical Illogical argument Implicand Implicant Implication Implies Imply Increment Indirect proof Inductive reasoning Inductive step Insoluble Intersection Inverse For this reason Theoretical hotel with infinitely many rooms Statement at the beginning of a logical argument; the ‘If…’ part of a conditional When A implies B, B is true if A is true Biconditional Not logical Argument that is not logical Statement B in ‘A implies B’ Statement A in ‘A implies B’ Conditional Imply Usually means, ‘to follow from’ Increase; to go up Proof by contradiction Making generalisations from specific examples Second part of proof technique in mathematical induction Cannot be solved Set composed of the collection of all common elements in a number of sets Statement obtained by negating the hypothesis and conclusion of a conditional (not A implies not B) 98 Sets, Logic, Proofs and Genera It follows Law of the excluded middle Lemma LHS Liar paradox Logic Logical argument Logically Mathematical induction Mathematically Mathematician Mathematics Meaningless Member Mental Makes logical sense from a previous idea Idea that either a statement or its negation is true, with no other possibility Proven statement that is used as a stepping-stone to a larger result Left Hand Side ‘This sentence is false’ Study of reasoning; how to think using rules Chain of reasoning using logic Using logic Proof technique for statements involving natural numbers involving verification of the first case and then verifying the truth of the next case assuming the previous case Using mathematics Professional who studies mathematics Study of logical relations between things, often involving numbers, functions, patterns, hypotheses, conjectures, generalisations and proofs Does not make logical sense Something that belongs to a set Calculation done purely within the brain; no 99 Sets, Logic, Proofs and Genera calculation Method Millenium Prize Problems Modus ponens Modus tollens Necessary Necessary and sufficient Not equal to Null set Numeracy Only if Otherwise Paradox Pattern Power set Problem Proof Proof by cases working out by pencil, calculator etc. Technique One of 7 unsolved problems in mathematics, whose proof or disproof wins 1 million US dollars The rule: If P implies Q, and P is true, then Q is true The rule: If P implies Q, and Q is not true, then P is not true Statement B in ‘A implies B’ If and only if Not the same Empty set Simple number work; arithmetic In ‘A implies B’, A is true only if B is true Using another method or technique Something leading to a contradiction Something that repeats, is ordered or follows some specific rule Set of all subsets of a given set Question or something that is to be proven or disproven Convincing chain of reasoning to show that a mathematical statement is true Proof by exhaustion 100 Sets, Logic, Proofs and Genera Proof by contradiction Proof by exhaustion Proof by induction Property Proposition Prove Q.E.D. Question Proof technique used to prove a statement by showing that if the statement is assumed false, this contradicts one of the assumptions Proof by considering a finite number of cases Proof technique used to prove a statement involving the natural number variable n Feature of something Statement Give a proof Quod Erat Demonstrandum – that which was to be demonstrated (shown); used at the end of a proof Statement that demands an answer Reductio ad absurdum Proof by contradiction Result of Being true because of previous information and logic Looking back over work and understanding it Right Hand Side Approximately Way of doing something If S is the set of all sets that are not members of themselves, then does S belong to S ? Revision RHS Roughly Rule Russell’s paradox 101 Sets, Logic, Proofs and Genera Satisfy Selfreferential Sentence Set Show Simplest form Simplify Solution Solve Special case State Statement Statistically Sufficient Symbol Technique Theorem There exists Therefore Thus Works in an equation or statement Statement that refers to itself, often resulting in a paradox Symbols (normally words) written in a certain order that make sense Collection of distinct objects Prove Expression with the smallest numbers and fewest symbols Write with fewer symbols and smaller numbers Answer with working Get a solution Case involving a specific instance of something Say or write an answer without showing working Sentence which is either true or false Using statistics Statement A in ‘A implies B’ Mark(s) which represent something Way of doing something Proposition to be proved using hypotheses and axioms There is Consequently Therefore 102 Sets, Logic, Proofs and Genera Transfinite cardinal True Truth value Undefined Understand Union Universal set Unsolved problem Vacuously true Venn diagram WLOG Working(s) Work out Write down Zeno’s paradoxes Cardinal used to measure sizes of infinite sets Factually correct, based on current knowledge True or false Meaningless Make sense of Set composed of the collection of all elements in a number of sets Set consisting of everything under discussion Problem that has been neither proven nor disproven Automatically true Diagram showing all possible logical relations between a fixed number of sets Without Loss of Generality; considering a specific class of cases which is essentially representative of the general situation Intermediate step(s) in a calculation before the answer Get an answer to Write an answer without showing working Paradoxes envisaged by Zeno that attempt to show that motion is an illusion 103 Epilogue This vocabulary book is meant to represent a step towards addressing the numeracy and literacy issues surrounding mathematics’ place in the Curriculum for Excellence. Hopefully, by discussing concepts not found in traditional course syllabi, ample opportunities for enriching the learning experience will make themselves manifest. M. Patel (June 2011) An educational system isn't worth a great deal if it teaches young people how to make a living but doesn't teach them how to make a life (Unknown) 104

Maths Vocabulary Book: Scottish Secondary School Curriculum S1-S6

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