maths a - glossary

G l o s s a r y

555

Adjacent

— The side next to the angle used for ref-erence in a right-angled triangle.

Allowable deduction

— A deduction from taxableincome permitted by the Australian TaxationOffice. Allowable deductions include expenditureincurred in earning income.

Allowance

— An extra payment made to a workerfor working in unfavourable conditions.

Angle of depression

— The angle through whichyou must look down from the horizontal to sightan object.

Angle of elevation

— The angle through which youmust look up from the horizontal to sight anobject.

Annual leave

— A period of time that each perma-nent employee is allowed each year for holidays.

Annual leave loading

— An extra payment of17 % of the gross pay made to employees whenthey take their annual leave.

Annulus

— The area between two circles that havethe same centre (concentric).

Area

— The amount of space within the boundaryof a closed figure.

Bar graph

— A graph where categorical data aredisplayed in horizontal bars, with the categorieson a vertical axis and quantity on the horizontalaxis.

Bimodal

— A set of scores for which two scoresoccur most often.

Bivariate data

— Sets of data containing two vari-ables.

Bottom plate

— Timber or metal strip at the bottomof a frame.

Box-and-whisker-plot

— A method of graphicallydisplaying a five-number summary. The plot isdrawn to scale with the box representing theinterquartile range and the whiskers representingthe range. Within the box the median is alsoshown.

Brace

— Sheets of timber, or strips of timber ormetal used to provide strength to a frame andhelp the frame to retain its shape.

Budget

— A list of a person’s income and expenses.A personal budget is made to try to avoidspending more than is earned. A balanced budgetis where income equals expenditure.

Building square

— A device used by builders tocheck whether corners of buildings are square.

Capacity

— The quantity of solid, liquid or gas thata 3-D object could hold.

Casual rate

— A higher rate of pay to compensatecasual workers for the lack of holiday and sickpay.

Categorical data

— Data which are not numericaland are put into categories such as types of car.

Causality

— When the occurrence of one variablecauses another. For example there is a strongpositive relationship between a person’s shirt sizeand shoe size but one does not cause the other.On the other hand, there is a strong positiverelationship between the amount of a Lotteryjackpot and the number of tickets sold. In thiscase, it would seem that one does cause the other.

Census

— Data gathered from the entire popu-lation.

Central tendency

— A method for describing atypical score in a data set. There are threemeasures of central tendency — mean, medianand mode.

Closed question

— One that must be answeredwithin given categories.

Column graph

— Similar to a bar graph, but thedata are displayed in vertical columns.

Commission

— Payment made to a salesperson. Acommission is usually paid as a percentage ofsales.

Complementary events

— Two events that coverall possible outcomes to a probability experi-ment. The sum of the probabilities to comple-mentary events is 1.

Continuous data

— Data which can take any valuewithin a given range.

Cosine ratio

— The ratio of the adjacent side andhypotenuse in a right-angled triangle.

Course

— A ‘course of bricks’ is an alternativeexpression for a ‘row of bricks’.

Cumulative frequency

— A progressive total ofthe frequencies.

Curing

— Allowing concrete to dry slowly toincrease its strength.

Glossary

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Cyclic trends

— Trends that fluctuate up and downbut not according to season.

Data

— Information before it is organised.

Database

— An organised set of data on a popu-lation.

Deduction

— A sum of money that is deductedfrom an employee’s gross pay before receivingnet pay.

Dependent variable

— A variable whose valueresponds to changes in the independent variable.

Discrete data

— Discrete data are where the datacan take only certain values, usually wholenumbers.

Double time

— A penalty rate which pays theemployee twice the normal hourly rate.

Drop

— A vertical length. The term is commonlyused in wallpapering and curtaining.

Effective width

— The width of a sheet, taking intoaccount overlap between adjacent sheets.

Elevation

— A scale drawing of what a buildingwill look like from one side.

Enlargement

— A figure is drawn similar to, butlarger than the original. The corresponding sideswill be in equal ratio and all correspondingangles will be equal.

Equally likely outcomes

— These occur when eachelement of the sample space for a probabilityexperiment is equally likely to occur.

Event

— An occurrence that is being examined in aprobability experiment.

Exchange rate

— The rate at which currencies canbe interchanged. Buying rate refers to the rate atwhich banks will buy the currency from you.Selling rate refers to the rate banks will sell youa currency.

Extrapolate

— To extend a graph so as to makepredictions about future trends.

Favourable outcomes

— Elements from thesample space that meet the requirement for anevent to occur.

Five-number summary

— A summary of a data setconsisting of the lower extreme, lower quartile,median, upper quartile and upper extreme.

Floor plan

— A plan showing the floor dimensionsof a structure and detailed dimensions of featuresduch as doors, windows, wall thicknesses andstairs.

Footings

— Trenches (in the shape of rectangularprisms) dug around the perimeter of a slab, andsometimes within the slab as a support forinternal walls.

Frequency

— The number of times an eventoccurs.

Frequency histogram

— A graph suitable for stat-istical (quantitative) data. It is a column graphdrawn with scores or class centres on the hori-zontal axis and frequency on the vertical axis. A

unit (half column width) space is drawn beforethe first column with no other gaps betweencolumns.

Frequency polygon

— A line graph often drawn onthe same axes as a frequency histogram. The lineis drawn from the corner of the axes to the centreof each column.

Frequency table

— A table displaying statisticaldata. For ungrouped data the table will havecolumns for score, tally, frequency and possiblycumulative frequency. For grouped data the scorecolumn will be replaced with a class column anda class centre column.

Fundamental counting principle

— The numberof elements of the sample space for a multi-stageprobability experiment is found by multiplyingthe number of ways each stage can occur. This isthe fundamental counting principle.

Gable roof

— In the shape of an inverted ‘V’ withtwo rectangular surfaces.

Goods and Services Tax

— A tax that is levied onthe price of all items other than fresh food. TheGST is levied at a rate of 10%.

GPS (Global Positioning System)

— A satellitenavigation system accessed by users on land, sea,or in the air, operated by the US Department ofDefense.

Gradient

— The rate of increase (or decrease) inthe dependent variable per one unit increase inthe independent variable.

Great circle

— A circle of the greatest possible dia-meter that can be drawn on the surface of asphere.

Greenwich Mean Time (GMT) —

The standardtime in Greenwich which is used as the basis forcalculating the time in all other parts of theworld.

Greenwich Meridian

— The meridian of longitudefrom which angular distances in the east–westdirection are measured. Using the longitude cal-culated from the Greenwich Meridian, time indifferent places on the Earth’s surface is calcu-lated.

Gross pay

— A person’s earnings before anydeductions are taken out.

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Group certificate

— A statement of gross incomeand the PAYG tax deducted from that incomethroughout the financial year. It is given to theemployee by the employer at the end of eachfinancial year.

Grouped data

— A data set tabulated in smallgroups rather than as individual scores.

Grout

— A mixture rubbed between tiles to provideseparation and to bind them together.

Hip roof

— Generally consists of two trapezium-shaped surfaces and two triangular surfaces.

Histogram

— A column graph which displays thefrequency for a set of scores.

Horizontal

— Level, flat and parallel to the horizonor the ground.

Hypotenuse

— The longest side of a right-angledtriangle. The hypotenuse is opposite the rightangle.

Income

— Money received by a person that is tax-able and is usually in exchange for labour or theresult of an investment.

Income tax

— Tax that is paid on all incomereceived.

Independent variable

— A variable whose valuedoes not depend on the value of another variable.

Indirect tax

— Any tax that is not paid directly tothe government by the taxpayer. For example, theGST is an indirect tax because it is paid to theretailer who then passes it on to the government.

International Date Line

— The meridian of longi-tude opposite to the Greenwich Meridian. TheInternational Date Line is, however, bent for con-venience. When crossing the International DateLine, the date changes.

Interpolate

— Drawing a graph using data found atthe end points.

Interquartile range

— A number that representsthe spread of a data set. The interquartile range iscalculated by subtracting the lower quartile fromthe upper quartile.

King post

— Vertical post from the horizontal tiebeam of a truss to the apex of the truss.

Latitude

— The angular distance of a point on theEarth’s surface either north or south of theequator.

Linear metre

— Length expressed in metres.

Line of best fit

— A line drawn on a scatterplot thatpasses through or is close to as many points aspossible.

Lintel

— A timber or metal strip above a door orwindow.

Lower extreme

— The lowest score in the data set.

Lower quartile

— The lowest 25% of scores in adata set.

Mean

— The average of a data set, found by total-ling all the scores then dividing by the number ofscores.

Median

— The middle score or the average of thetwo middle scores in a data set.

Medicare levy

— A payment made as part of ourtax system that covers the cost of basic healthcare services. The basic levy is 1.5% of grossincome; however, low income earners pay thelevy at a reduced rate.

Meridian of longitude

— A line on the Earth’s sur-face that runs from the North Pole to the SouthPole. Each meridian of longitude is measured bythe number of degrees east or west it is of theGreenwich Meridian.

Mode

— The score in a data set with the highestfrequency.

Mortar

— A mixture of cement and sand used tobind bricks together (and keep them a fixed dis-tance apart).

Multi-stage event

— This occurs when there ismore than one part to a probability experiment.For example, tossing two coins can be con-sidered as tossing one coin then tossing another,therefore there are two parts to this experiment.

Net pay

— The amount of money actually receivedby the employee after all deductions have beensubtracted from the gross pay.

Nogging

— Horizontal separators between studs ina frame.

Nominal data

— Categorical data which have noorder associated with them.

Non-compliant response

— A response that doesnot fit within the expected responses or categ-ories provided in a questionnaire.

Numerical data

— Data which involve numbers ormeasurements.

Open question

— One that has no guidelineswithin which to answer.

Opposite

— The side opposite to the angle used forreference in a right-angled triangle.

Ordinal data

— Categorical data that are associ-ated with some qualitative scale.

Ordinary rate

— The normal hourly rate for awage earner.

Outcome

— A possible result to a probabilityexperiment.


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Overtime — This is when a person earns more thanthe regular hours each week.

Parallel of latitude — A line on the Earth’s surfaceparallel to the equator. Each parallel of latitude ismeasured in terms of the angular distance eithernorth or south of the equator.

PAYG — Pay As You Go. The method usuallyapplied to the collection of tax.

Payment by piece (Piecework) — Payment for theamount of work completed.

Penalty rate — A higher rate of pay made to aperson who is working overtime.

Per annum — per year.

Percentage chance — The probability of an eventexpressed as a percentage.

Perimeter — The distance around the boundary ofa figure.

Piecework — see Payment by piece.

Pitch — The angle the roof makes with the hori-zontal.

Pitch ratio — The pitch of a roof expressed as atangent ratio in the form 1 : x.

Plumb bob — A device consisting of a length ofstring with a weight attached at one end. It isused to test whether a surface is vertical.

Polygon — A line graph displaying the frequencyfor a set of scores.

Population — An entire group of people or objectsto which a statistical inquiry is applied.

Prism — A solid shape with a constant cross-section.

Probability — A number between 0 and 1 thatdescribes the chance of an event occurring.

Pyramid — A solid shape with a plane shape as itsbase and triangular sides meeting at an apex.

Pythagoras’ theorem — In a right-angled triangle,the square on the hypotenuse is equal to the sumof the squares on the other two sides.

Pythagorean triad or Pythagorean triple — Setsof three numbers which satisfy Pythagoras’theorem.

Qualitative data — Data which do not involvenumbers or measurement.

Quantitative data — Data which can be measured.A numerical value can be assigned to them.

Quartile — 25% of the data set. The upper quartileis the top 25% of the data set and the lower quar-tile is the bottom 25% of the data set.

Questionnaire — A set of questions completed fora statistical investigation.

Rafter — Beam at the top of a truss to which theroof cladding is attached.

Random trends — Those trends which occur ran-domly, caused by external events such as wars,floods.

Range — A number which represents the spread ofa data set. The range is calculated by subtractingthe smallest score from the largest score.

Recording error — Where data have been incor-rectly recorded.

Reduction — A similar figure, drawn smaller insize than the original.

Regression line — A line of best fit that is extrapo-lated to make predictions about data.

Reinforcing mesh — Steel mesh laid in the con-crete in the footings and slab to provide struc-tural strength.

Relative frequency — A number between 0 and 1,usually a decimal, which describes how often anevent has occurred. The relative frequency isfound by dividing the number of times an eventhas occurred by the total number of trials.

Retainer — A fixed payment usually paid tosomeone receiving commission. They receive theretainer regardless of the number of sales made.

Roof truss — Frame providing shape and strengthfor a roof.

Royalty — A royalty is a payment made to theowner of a copyright such as a musician orauthor. The royalty is usually a percentage ofsales.

Salary — A form of payment where a person ispaid a fixed amount to do their job. A salary isusually based on an annual amount divided intoweekly or fortnightly instalments.

Sample — When data are gathered from a portionof the population, that is taken to be represen-tative of the whole population.

Sample space — A list of all possible outcomes toa probability experiment.

Scale factor — A number by which the side lengthson the first of two similar figures is multiplied byto obtain the measurements on the second of thefigures.

Scatterplot — A graph that shows two variables,one on each axis, and their relationship by plot-ting the points generated by each data pair.

Score — Each piece of quantitative data is a score.

Seasonal trend — A trend that fluctuates with thechanging seasons.


G l o s s a r y 559Sector — The area between any two radii of a

circle.Sector graph — A graph where a circle is cut into

sectors. Each sector then represents a section ofthe data set. Each sector is the same proportionof the circle as the part of the data set it rep-resents.

Secular trend — A trend that appears to eitherincrease or decrease steadily over time, with nomajor changes of direction.

Sill — Timber of metal strip below a window.Similar (figures) — Two or more figures with cor-

responding angles equal and corresponding sidesin the same ratio.

Sine ratio — The ratio of the opposite side and thehypotenuse in a right-angled triangle.

Site plan — A plan showing the boundaries of ablock of land and the position of the structure onthe lot.

Slab — Foundations for a structure.Small circle — A circle that is drawn on the surface

of a sphere that is of a smaller diameter than agreat circle.

Sphere — A closed surface consisting of points inspace that are a fixed distance, the radius, from agiven point, the centre.

Spirit level — A device, usually constructed of alu-minium, containing a vial of liquid with an airbubble. It can be used to determine whether asurface is horizontal and whether a surface isvertical.

Standard deviation — A measure of the spread ofa data set. The standard deviation is found on acalculator using either the population standarddeviation or the sample standard deviation.

Statistics — Numerical facts compiled to describe adata set.

Stem-and-leaf-plot — A method of displaying adata set where the first part of a number iswritten in the stem and the second part of thenumber is written in the leaves.

Studs — Vertical strips of timber or metal in aframe.

Summary statistic — A number such as the mean,median or mode which describes a data set.

Survey plan — A plan showing all boundaries ofblocks of land and the position of roadways.

Tangent ratio — The ratio of the opposite side andthe adjacent side in a right-angled triangle.

Taxable income — The amount of income uponwhich the amount of tax due is calculated. Tax-able income is calculated by subtracting anyallowable tax deductions from the total grossincome.

Three-dimensional — Can be described usingthree measurements (for example a length, awidth and a height).

Tie beam — Beam at the base of a truss.

Time and a half — A penalty rate where theemployee is paid 1 times the normal hourlyrate.

Time series — Bivariate data where one of the vari-ables is time.

Top plate — Timber or metal strip at the top of aframe.

Tree diagram — A method of listing the samplespace to a multi-stage probability experiment.The diagram branches once for each stage of theexperiment at each level showing all possibleoutcomes to each stage.

Trend line — A straight line used to represent atime series.

Trial — The number of times a probability experi-ment has been conducted.

Trigonometry — A branch of mathematics in whichsides and angles of triangles are calculated.

Two-dimensional — Can be described using twomeasurements (for example a length and awidth).

Upper extreme — The highest score in a data set.

Upper quartile — The highest 25% of scores in adata set.

Value Added Tax — Similar to the GST, a VAT islevied in many countries on the cost of goodsand services. The rate of VAT varies fromcountry to country.

Volume — The amount of space contained in, oroccupied by, a 3-D object.

Wage — A form of payment that is based on anhourly rate.

Water level — A device consisting of a length ofclear hose filled with water. It can be used toestablish levels between two poins which areseparated by some distance.

y-intercept — The value of y when a functioncrosses the vertical axis.

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MQ Maths A Yr 11 - Glossary 59 Thursday, July 5, 2001 8:06 AM

maths a - glossary

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