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# Maths A - Glossary

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### Maths A - Glossary

1. 1. 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 taxable income permitted by the Australian Taxation Ofﬁce. Allowable deductions include expenditure incurred in earning income. Allowance — An extra payment made to a worker for working in unfavourable conditions. Angle of depression — The angle through which you must look down from the horizontal to sight an object. Angle of elevation — The angle through which you must look up from the horizontal to sight an object. Annual leave — A period of time that each perma- nent employee is allowed each year for holidays. Annual leave loading — An extra payment of 17 % of the gross pay made to employees when they take their annual leave. Annulus — The area between two circles that have the same centre (concentric). Area — The amount of space within the boundary of a closed ﬁgure. Bar graph — A graph where categorical data are displayed in horizontal bars, with the categories on a vertical axis and quantity on the horizontal axis. Bimodal — A set of scores for which two scores occur most often. Bivariate data — Sets of data containing two vari- ables. Bottom plate — Timber or metal strip at the bottom of a frame. Box-and-whisker-plot — A method of graphically displaying a ﬁve-number summary. The plot is drawn to scale with the box representing the interquartile range and the whiskers representing the range. Within the box the median is also shown. Brace — Sheets of timber, or strips of timber or metal used to provide strength to a frame and help the frame to retain its shape. Budget — A list of a person’s income and expenses. A personal budget is made to try to avoid spending more than is earned. A balanced budget is where income equals expenditure. Building square — A device used by builders to check whether corners of buildings are square. Capacity — The quantity of solid, liquid or gas that a 3-D object could hold. Casual rate — A higher rate of pay to compensate casual workers for the lack of holiday and sick pay. Categorical data — Data which are not numerical and are put into categories such as types of car. Causality — When the occurrence of one variable causes another. For example there is a strong positive relationship between a person’s shirt size and shoe size but one does not cause the other. On the other hand, there is a strong positive relationship between the amount of a Lottery jackpot and the number of tickets sold. In this case, it would seem that one does cause the other. Census — Data gathered from the entire popu- lation. Central tendency — A method for describing a typical score in a data set. There are three measures of central tendency — mean, median and mode. Closed question — One that must be answered within given categories. Column graph — Similar to a bar graph, but the data are displayed in vertical columns. Commission — Payment made to a salesperson. A commission is usually paid as a percentage of sales. Complementary events — Two events that cover all 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 value within a given range. Cosine ratio— The ratio of the adjacent side and hypotenuse in a right-angled triangle. Course — A ‘course of bricks’ is an alternative expression for a ‘row of bricks’. Cumulative frequency — A progressive total of the frequencies. Curing — Allowing concrete to dry slowly to increase its strength. Glossary 1 2 --- MQ Maths A Yr 11 - Glossary Page 555 Thursday, July 5, 2001 8:06 AM
2. 2. 556 G l o s s a r y Cyclic trends — Trends that ﬂuctuate up and down but 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 deducted from an employee’s gross pay before receiving net pay. Dependent variable — A variable whose value responds to changes in the independent variable. Discrete data — Discrete data are where the data can take only certain values, usually whole numbers. Double time — A penalty rate which pays the employee twice the normal hourly rate. Drop — A vertical length. The term is commonly used in wallpapering and curtaining. Effective width — The width of a sheet, taking into account overlap between adjacent sheets. Elevation — A scale drawing of what a building will look like from one side. Enlargement — A ﬁgure is drawn similar to, but larger than the original. The corresponding sides will be in equal ratio and all corresponding angles will be equal. Equally likely outcomes — These occur when each element of the sample space for a probability experiment is equally likely to occur. Event — An occurrence that is being examined in a probability experiment. Exchange rate — The rate at which currencies can be interchanged. Buying rate refers to the rate at which banks will buy the currency from you. Selling rate refers to the rate banks will sell you a currency. Extrapolate — To extend a graph so as to make predictions about future trends. Favourable outcomes — Elements from the sample space that meet the requirement for an event to occur. Five-number summary — A summary of a data set consisting of the lower extreme, lower quartile, median, upper quartile and upper extreme. Floor plan — A plan showing the ﬂoor dimensions of a structure and detailed dimensions of features duch as doors, windows, wall thicknesses and stairs. Footings — Trenches (in the shape of rectangular prisms) dug around the perimeter of a slab, and sometimes within the slab as a support for internal walls. Frequency — The number of times an event occurs. Frequency histogram — A graph suitable for stat- istical (quantitative) data. It is a column graph drawn with scores or class centres on the hori- zontal axis and frequency on the vertical axis. A unit (half column width) space is drawn before the ﬁrst column with no other gaps between columns. Frequency polygon — A line graph often drawn on the same axes as a frequency histogram. The line is drawn from the corner of the axes to the centre of each column. Frequency table — A table displaying statistical data. For ungrouped data the table will have columns for score, tally, frequency and possibly cumulative frequency. For grouped data the score column will be replaced with a class column and a class centre column. Fundamental counting principle — The number of elements of the sample space for a multi-stage probability experiment is found by multiplying the number of ways each stage can occur. This is the fundamental counting principle. Gable roof — In the shape of an inverted ‘V’ with two rectangular surfaces. Goods and Services Tax — A tax that is levied on the price of all items other than fresh food. The GST is levied at a rate of 10%. GPS (Global Positioning System) — A satellite navigation system accessed by users on land, sea, or in the air, operated by the US Department of Defense. Gradient — The rate of increase (or decrease) in the dependent variable per one unit increase in the independent variable. Great circle — A circle of the greatest possible dia- meter that can be drawn on the surface of a sphere. Greenwich Mean Time (GMT) — The standard time in Greenwich which is used as the basis for calculating the time in all other parts of the world. Greenwich Meridian — The meridian of longitude from which angular distances in the east–west direction are measured. Using the longitude cal- culated from the Greenwich Meridian, time in different places on the Earth’s surface is calcu- lated. Gross pay — A person’s earnings before any deductions are taken out. 1 2 --- MQ Maths A Yr 11 - Glossary Page 556 Thursday, July 5, 2001 8:06 AM
3. 3. G l o s s a r y 557 Group certiﬁcate — A statement of gross income and the PAYG tax deducted from that income throughout the ﬁnancial year. It is given to the employee by the employer at the end of each ﬁnancial year. Grouped data — A data set tabulated in small groups rather than as individual scores. Grout — A mixture rubbed between tiles to provide separation and to bind them together. Hip roof — Generally consists of two trapezium- shaped surfaces and two triangular surfaces. Histogram — A column graph which displays the frequency for a set of scores. Horizontal — Level, ﬂat and parallel to the horizon or the ground. Hypotenuse — The longest side of a right-angled triangle. The hypotenuse is opposite the right angle. Income — Money received by a person that is tax- able and is usually in exchange for labour or the result of an investment. Income tax — Tax that is paid on all income received. Independent variable — A variable whose value does not depend on the value of another variable. Indirect tax — Any tax that is not paid directly to the government by the taxpayer. For example, the GST is an indirect tax because it is paid to the retailer who then passes it on to the government. International Date Line — The meridian of longi- tude opposite to the Greenwich Meridian. The International Date Line is, however, bent for con- venience. When crossing the International Date Line, the date changes. Interpolate — Drawing a graph using data found at the end points. Interquartile range — A number that represents the spread of a data set. The interquartile range is calculated by subtracting the lower quartile from the upper quartile. King post — Vertical post from the horizontal tie beam of a truss to the apex of the truss. Latitude — The angular distance of a point on the Earth’s surface either north or south of the equator. Linear metre — Length expressed in metres. Line of best ﬁt — A line drawn on a scatterplot that passes through or is close to as many points as possible. Lintel — A timber or metal strip above a door or window. Lower extreme — The lowest score in the data set. Lower quartile — The lowest 25% of scores in a data set. Mean — The average of a data set, found by total- ling all the scores then dividing by the number of scores. Median — The middle score or the average of the two middle scores in a data set. Medicare levy — A payment made as part of our tax system that covers the cost of basic health care services. The basic levy is 1.5% of gross income; however, low income earners pay the levy at a reduced rate. Meridian of longitude — A line on the Earth’s sur- face that runs from the North Pole to the South Pole. Each meridian of longitude is measured by the number of degrees east or west it is of the Greenwich Meridian. Mode — The score in a data set with the highest frequency. Mortar — A mixture of cement and sand used to bind bricks together (and keep them a ﬁxed dis- tance apart). Multi-stage event — This occurs when there is more 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 received by the employee after all deductions have been subtracted from the gross pay. Nogging — Horizontal separators between studs in a frame. Nominal data — Categorical data which have no order associated with them. Non-compliant response — A response that does not ﬁt within the expected responses or categ- ories provided in a questionnaire. Numerical data — Data which involve numbers or measurements. Open question — One that has no guidelines within which to answer. Opposite — The side opposite to the angle used for reference in a right-angled triangle. Ordinal data — Categorical data that are associ- ated with some qualitative scale. Ordinary rate — The normal hourly rate for a wage earner. Outcome — A possible result to a probability experiment. MQ Maths A Yr 11 - Glossary Page 557 Thursday, July 5, 2001 8:06 AM
4. 4. 558 G l o s s a r y Overtime — This is when a person earns more than the regular hours each week. Parallel of latitude — A line on the Earth’s surface parallel to the equator. Each parallel of latitude is measured in terms of the angular distance either north or south of the equator. PAYG — Pay As You Go. The method usually applied to the collection of tax. Payment by piece (Piecework) — Payment for the amount of work completed. Penalty rate — A higher rate of pay made to a person who is working overtime. Per annum — per year. Percentage chance — The probability of an event expressed as a percentage. Perimeter — The distance around the boundary of a 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 a tangent ratio in the form 1 : x. Plumb bob — A device consisting of a length of string with a weight attached at one end. It is used to test whether a surface is vertical. Polygon — A line graph displaying the frequency for a set of scores. Population — An entire group of people or objects to which a statistical inquiry is applied. Prism — A solid shape with a constant cross- section. Probability — A number between 0 and 1 that describes the chance of an event occurring. Pyramid — A solid shape with a plane shape as its base and triangular sides meeting at an apex. Pythagoras’ theorem — In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Pythagorean triad or Pythagorean triple — Sets of three numbers which satisfy Pythagoras’ theorem. Qualitative data — Data which do not involve numbers 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 quartile is 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 for a statistical investigation. Rafter — Beam at the top of a truss to which the roof 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 of a data set. The range is calculated by subtracting the smallest score from the largest score. Recording error — Where data have been incor- rectly recorded. Reduction — A similar ﬁgure, drawn smaller in size 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 an event has occurred. The relative frequency is found by dividing the number of times an event has occurred by the total number of trials. Retainer — A ﬁxed payment usually paid to someone receiving commission. They receive the retainer regardless of the number of sales made. Roof truss — Frame providing shape and strength for a roof. Royalty — A royalty is a payment made to the owner of a copyright such as a musician or author. The royalty is usually a percentage of sales. Salary — A form of payment where a person is paid a ﬁxed amount to do their job. A salary is usually based on an annual amount divided into weekly or fortnightly instalments. Sample — When data are gathered from a portion of the population, that is taken to be represen- tative of the whole population. Sample space — A list of all possible outcomes to a probability experiment. Scale factor — A number by which the side lengths on the ﬁrst of two similar ﬁgures is multiplied by to obtain the measurements on the second of the ﬁgures. 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 the changing seasons. MQ Maths A Yr 11 - Glossary Page 558 Thursday, July 5, 2001 8:06 AM
5. 5. G l o s s a r y 559 Sector — 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 of the data set. Each sector is the same proportion of the circle as the part of the data set it rep- resents. Secular trend — A trend that appears to either increase or decrease steadily over time, with no major changes of direction. Sill — Timber of metal strip below a window. Similar (ﬁgures) — Two or more ﬁgures with cor- responding angles equal and corresponding sides in the same ratio. Sine ratio — The ratio of the opposite side and the hypotenuse in a right-angled triangle. Site plan — A plan showing the boundaries of a block of land and the position of the structure on the 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 a great circle. Sphere — A closed surface consisting of points in space that are a ﬁxed distance, the radius, from a given point, the centre. Spirit level — A device, usually constructed of alu- minium, containing a vial of liquid with an air bubble. It can be used to determine whether a surface is horizontal and whether a surface is vertical. Standard deviation — A measure of the spread of a data set. The standard deviation is found on a calculator using either the population standard deviation or the sample standard deviation. Statistics — Numerical facts compiled to describe a data set. Stem-and-leaf-plot — A method of displaying a data set where the ﬁrst part of a number is written in the stem and the second part of the number is written in the leaves. Studs — Vertical strips of timber or metal in a frame. Summary statistic — A number such as the mean, median or mode which describes a data set. Survey plan — A plan showing all boundaries of blocks of land and the position of roadways. Tangent ratio — The ratio of the opposite side and the adjacent side in a right-angled triangle. Taxable income — The amount of income upon which the amount of tax due is calculated. Tax- able income is calculated by subtracting any allowable tax deductions from the total gross income. Three-dimensional — Can be described using three measurements (for example a length, a width and a height). Tie beam — Beam at the base of a truss. Time and a half — A penalty rate where the employee is paid 1 times the normal hourly rate. Time series — Bivariate data where one of the vari- ables is time. Top plate — Timber or metal strip at the top of a frame. Tree diagram — A method of listing the sample space to a multi-stage probability experiment. The diagram branches once for each stage of the experiment at each level showing all possible outcomes to each stage. Trend line — A straight line used to represent a time series. Trial — The number of times a probability experi- ment has been conducted. Trigonometry — A branch of mathematics in which sides and angles of triangles are calculated. Two-dimensional — Can be described using two measurements (for example a length and a width). Upper extreme — The highest score in a data set. Upper quartile — The highest 25% of scores in a data set. Value Added Tax — Similar to the GST, a VAT is levied in many countries on the cost of goods and services. The rate of VAT varies from country to country. Volume — The amount of space contained in, or occupied by, a 3-D object. Wage — A form of payment that is based on an hourly rate. Water level — A device consisting of a length of clear hose ﬁlled with water. It can be used to establish levels between two poins which are separated by some distance. y-intercept — The value of y when a function crosses the vertical axis. 1 2 --- MQ Maths A Yr 11 - Glossary Page 559 Thursday, July 5, 2001 8:06 AM