A
Absolute error. Maximum possible error for a measurement, equal to half the precision of the measurement.
Algebraic modelling. Using a function to describe a real life pattern or relationship.
Angle of depression. Angle between the horizontal and the line of sight looking down.
Angle of elevation. Angle between the horizontal and the line of sight looking up.
Annuity. Form of investment involving a series of periodic, equal contributions (payments) made by an individual to an account. See also ordinary annuity
and ordinary annuity due.
Annulus.
Ring-shaped area between two concentric circles.
A=π(R2−r2)
Arc length . Length (l) of a part of the circumference
of a circle. l= × 2πr
angle of depression
angle of elevation
R
r
θ
360
---Area chart.
Type of graph consisting of different ‘areas’ or ‘bands’ each representing a data set over a given period of time.
Asset. Item or resource used by a business to earn income (e.g. machinery or computer equipment).
Asymptote.
Line that a curve gets very close to but never actually touches.
Australian Eastern Standard Time (AEST). Standard time zone for the eastern states of Australia.
Average (or mean). Sum of a set of scores divided by the number of scores. See mean.
B
Bearing (or true bearing). Angle measured from due north in a clockwise direction.z
Box-and-whisker plot (or boxplot). Diagram showing the middle 50% of a set of scores in the box, with lines or ‘whiskers’ extending to the two extremes.
The x-axis is an asymptote for the exponential curve. y
x
A N
B
Bearing of B from A is 215°. 35°
Glossary
C
Capacity. Maximum volume of liquid that can be held by a container, usually measured in mL, L or kL.
Capture–recapture technique. Method of estimating the size of a population by capturing, tagging and releasing a sample, then recapturing a new sample.
Categorical data (or qualitative data). Information or data represented as a category rather than a number (e.g. make of car). See also quantitative data.
Causal relationship. Relationship between two variables, say x and y, where a change in x causes a change in y.
Census. Collection of information about every member of a population.
Changing the subject of a formula. Rearranging a formula so that a different variable is the subject.
Class centre. Midpoint or centre score of a class in a grouped frequency distribution.
Column graph.
Graph consisting of vertical bars of equal width.
Commission. Earnings of a salesperson or agent, usually a percentage of the value of items sold.
Compass radial survey. Survey where a compass is placed in the middle of a field and the true bearing and distance to each corner are measured. See also plane table radial survey.
Complementary events. ‘Opposite’ events (e.g. rolling a 6 and not rolling a 6 with a die). P( ) = 1 −P(E) where is complementary to E.
Compound interest. Interest paid on the sum (principal) invested as well as on any accumulated interest. See also simple interest.
E~ E~
Compounding period. How often interest is calculated (e.g. daily, monthly, quarterly or yearly).
Concentration. Amount of liquid or solid in another liquid or solid expressed as a rate or percentage (e.g. the concentration of salt in water in g/mL).
Continuous data. Quantitative data that can be measured on a scale (such as a person’s height), rather than as distinct values (such as number of children in a family). See also discrete data.
Contribution to an annuity. Periodical payment made by an individual to an annuity.
Correlation. Strength of the relationship between two variables.
Correlation coefficient (r). Measure of the correlation of two variables. –1 <r< 1. Cosine. Ratio in a right-angled triangle:
cos θ=
where θ is an angle. See also sine and tangent.
Cosine rule. Trigonometric rule used for triangle problems involving 3 sides and 1 angle.
c2=a2+b2– 2ab cos C
cos C=
Cubic function.
Function of the form y=ax3.
Cumulative frequency. Sum of the frequencies of a score and all scores below that score.
Cumulative frequency histogram. Histogram where the height of each column represents the cumulative frequency at each score.
side adjacent to θ hypotenuse
---a2+b2–c2 2ab
---Cum. frequency
Cumulative frequency polygon (or ogive). Line graph formed by
joining the ends of the tops of the columns of the cumulative frequency histogram.
D
Data. Facts or information.
Data set. Collection or group of scores.
Daylight saving. Scheme where clocks are turned forward an hour to take advantage of increased hours of daylight in summer.
Deciles. Values that divide a data set into 10 equal parts when the scores are arranged in order. See also
quartiles.
Declining balance method of depreciation. Method of determining the depreciation of an item for tax deductions. The value of the item is reduced each period by a certain percentage, called the declining balance rate. See also straight line method of
depreciation.
Deductions, allowable. Amounts subtracted from a person’s yearly income in order to determine their taxable income (such as work expenses, donations).
Deductions from pay. Amounts taken out of a person’s gross pay (e.g. union fees, superannuation, income tax).
Deferred payment. Payment made for goods after an interest-free period has elapsed (e.g. ‘buy now and pay nothing for 6 months’).
Dependent variable. Pronumeral that depends on another for its value. For example, if y = 3x + 5, y is the dependent variable as its value depends on the value of x. See also independent variable.
Cum. frequency
Score 100%
Depreciation. Loss in value of assets due to wear and tear, age, etc.
Depreciation schedule. Table showing the decreasing value of an asset during its expected life. It is used by a business to record allowable tax deductions.
Direct variation (or direct proportion). Relationship between two variables (say x and y) by an equation of the form y = kx, where k is the constant of variation. See also inverse variation.
Discrete data. Quantitative data that can be counted (such as number of pets). See also continuous data.
Divided bar graph. Graph representing the parts of a whole population by a rectangle divided into proportionately sized sections. See also sector graph.
Dividend. Share of profits in a company paid to each shareholder.
Dividend yield. Percentage return on an investment.
Dividend yield = × 100%
Dot plot. Way of representing a small data set to see the whole distribution. For example, temperatures of 10 hospital patients:
See also stem-and-leaf plot.
E
Ellipse. Oval-shaped plane figure with area A =πab.
Equator. 0° latitude, the great circle running around the middle of the Earth. The latitude of any point on the Earth’s surface is measured north or south of the Equator.
W T B C
dividend per share market value of share
---36 37 38 39 40 41 42 °C
Event. In probability, one or more outcomes. For example, the event, throwing an even number with a die, contains the three outcomes {2, 4, 6}.
Expected outcome. In probability, the number of times an event is expected to occur.
Exponent. Index or power. For example, 5 is the exponent in x5.
Exponential decay. Decrease of a quantity according to the exponential function y = b(ax) where 0 , a , 1. Exponential function. Function of the form y = b(ax).
Exponential growth. Increase of a quantity according to the exponential function y = b(ax) where a . 1. Extrapolate. To estimate the value of a quantity that is outside the given range of values. See also
interpolate.
Extremes, upper and lower. Highest and lowest scores in a data set.
F
Field diagram. Surveyor’s sketch showing the measurements of a field or block of land found from an offset survey.
Financial expectation. Expected amount of money to be returned, found by multiplying every financial outcome by its probability and adding them together.
Five-number summary. Lower extreme, lower quartile, median, upper quartile and upper extreme of a data set. These five numbers are used to draw a box plot.
24 40 32 25 0
16
Exponential growth Exponential decay
Flat rate interest. See simple interest.
Flat rate loan. Loan where simple interest is charged on the amount borrowed for the term of the loan. See also reducing balance loan.
Frequency. Number of times a score or group of scores occurs in a data set.
Frequency distribution. Table or graph showing all scores in a data set and their frequencies.
Frequency histogram. Histogram where the height of each column represents the frequency of a single score or group of scores.
Frequency polygon. Line graph formed by joining the midpoints of the tops of the columns of the frequency histogram.
Fuel consumption. Rate at which fuel is used by a vehicle, usually measured in L/100 km.
Function. Relationship between two variables, (e.g. y = 3x − 5).
Future value of an annuity. Total value of the annuity at the end of the specified term. See also
present value of an annuity.
G
Goods and services tax (GST). Tax a consumer pays on any purchased item or service (e.g. buying a car, hiring a painter).
Gradient. Slope of a line. Gradient = .
Graphics calculator. Calculator that includes a screen for displaying graphs. It also has statistical and financial functions.
Frequency
Score
Frequency
Score
Great circle. Circle formed when a slice is taken through the centre of the Earth. The Equator and all meridians of longitude are great circles. See also small
circle.
Greenwich Mean Time (GMT). Time at the Greenwich meridian (0º longitude) from which other times in the world are measured.
Greenwich meridian. Meridian of longitude (0º longitude) that passes through Greenwich in London. The longitude of any point on the Earth’s surface is measured east or west of this meridian.
Gross pay (or gross wage). Person’s pay before tax is deducted.
Grouped data. Data that has been put into classes. Data is grouped when the spread of data is large or when there is a large number of scores.
Guess, check and refine. Method of solving equations by guessing the answer, testing the answer and improving on it.
H
Hectare. Land measure equal to the area of a square 100 m by 100 m. 1 ha = 10 000 m2.
Hyperbolic function. Function of the form y = .
Graph is a hyperbola.
Hypotenuse. Longest side of a right-angled triangle; side opposite the right angle.
I
Income tax. Money paid to the government from income earned.
a x
---Hypotenuse
Independent variable. Pronumeral whose values do not depend on any other pronumeral. For example, if A =πr2, r is the independent variable. See also
dependent variable.
Instalment. See repayment.
Interest. Money earned on an investment or paid on a loan.
International Date Line. Imaginary line that runs north–south through the Pacific Ocean and is approximately the 180ºE or 180ºW meridian. A day is either gained or lost when this line is crossed.
Interpolate. To estimate the value of a quantity that is within the given range of values. See also extrapolate.
Interquartile range. Difference between the third and first quartiles of a data set (Q3− Q1). It is a measure of the spread of the data.
Inverse variation (or inverse proportion).
Relationship between two variables (say x and y) by an equation of the form y = , where k is the constant of variation. See also direct variation.
K
Knot. Speed on water of 1 nautical mile per hour. 1 knot = 1 M/h = 1.852 km/h.
L
Latitude. Angular distance of a point on the Earth’s surface north or south of the Equator (0° latitude).
Line of best fit (or regression line). Straight line that best represents a set of points.
Linear function. Function of the form y = mx + b, whose graph is a straight line.
Linear modelling. Using a linear function to approximate a real-life situation.
Longitude. Angular distance of a point on the Earth’s surface east or west of the Greenwich meridian (0° longitude).
M
Mean . Arithmetic average of a set of scores.
Mean =
= =
Median. Middle score of a data set when scores are arranged in ascending order. If there are two middle scores, the median is the average of the two.
Median regression line. Line of best fit relating the medians of each third of a set of points that have a high correlation.
Meridian of longitude. Great semicircle running down the Earth’s surface from the North Pole to the South Pole, measured east or west of the Greenwich meridian (0° longitude).
Minute. Measure of time or angle size. of an hour where 1 h = 60 min or of a degree where 1° = 60′.
Mode. Score(s) with the highest frequency. If each score has the same frequency, there is no mode.
Modelling. Using mathematics to describe a real-life pattern or relationship.
Multistage event. Set of outcomes resulting from two or more experiments. For example, a two-stage event occurs when you toss a coin and roll a die.
N
Nautical mile. Distance used in navigation. Abbreviation is M or nM. 1 M = 1.852 km.
Normal distribution. Statistical distribution that is symmetrical about the mean.
x
sum of scores number of scores
---x Σx n --- Σfx
Σf
---1 60 ---1
60
---Numerical data. See quantitative data.
O
Offset survey (or traverse survey). Survey carried out by a
surveyor by measuring along a traverse line joining two corners of a field as well as measuring the offsets. It is used to find the area and perimeter of the field. See also field diagram.
Ogive. See cumulative frequency polygon.
Ordered selection. Selection of items where the order is important (e.g. choosing a captain and vice-captain of a cricket team).
Ordinary annuity. Annuity where the payment is made at the end of each compounding period.
Ordinary annuity due. Annuity where the payment is made at the beginning of each compounding period.
Outcome. One result in an experiment. For example, getting a 6 is an outcome when a die is rolled. See also
event.
Outlier. Any score in a data set that lies away from the rest of the scores. For example, 10 is an outlier in the data set {0, 0, 1, 2, 2, 3, 4, 4, 4, 5, 10}.
Overtime. Time worked beyond usual working hours, usually paid at a higher rate. See also wage.
P
Parabola. U-shaped graph of a quadratic function. See also quadratic function.
Parallel of latitude. Small circle running across the Earth’s surface, measured north or south of the Equator (0° latitude).
Offset
PAYE tax. Pay As You Earn tax, which is tax paid in instalments each payday rather than as a lump sum at the end of the financial year. See also tax refund.
Percentage error. Maximum possible error for a measurement, expressed as a percentage.
Percentage error = × 100%.
Periodic payment. Payment made by an individual to a loan or an annuity each compounding period.
Pie chart. See sector graph.
Piecewise linear function. Function comprised of two or more different linear functions. Its graph is made up of separate lines or ‘pieces’.
Piecework. Earnings calculated on the number of items or pieces produced (e.g. for making shirts).
Plane table radial survey. Survey where a table is placed in the middle of a field and the angle and distance to each corner are measured. See also
compass radial survey.
Population. All of the items under investigation, from which a sample is surveyed. See also sample.
Precision. The precision of a measuring device is how exact you can make a measurement using the device. For example, a protractor has a precision of 1°. The precision of a measured value is how exact that value is expressed. For example, a length measured as 12.4 cm has a precision of 0.1 cm.
Present value of an annuity. Single amount of money that, if invested today at the given compound interest rate, would produce the same amount as that obtained by a series of regular contributions to the annuity. See also future value of an annuity.
Principal. Original amount of money invested for the purpose of earning interest.
absolute error measurement
---Prism. Solid with a uniform cross-section.
Probability. Measure of how likely an event E is to occur, written P(E). It ranges from impossible [P(E) = 0] to certain [P(E) = 1].
Probability tree diagram. Tree diagram in which probabilities are listed on the branches of every stage.
Proportional to. In the same ratio as. If y is proportional to x, we say x and y have a direct linear variation. See direct variation.
Pythagoras’ theorem. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides.
Q
Quadrant. Quarter of a circle.
Quadratic. Algebraic expression in which the highest power of the variable is 2 (e.g. 3x2− 4x + 6).
Quadratic function. Function of the form y = ax2+ bx + c.
Graph is a parabola.
Qualitative data. See categorical data.
Quality control. Ways of ensuring that manufactured items are of the same quality (e.g. testing the life of batteries).
Quantitative data (or numerical data). Data that can be counted or measured. It can be discrete or continuous. See also categorical data.
c
a b c2= a2+ b2
Quartiles, upper and lower. Upper or third quartile (Q3) is the median of the upper half of a data set. Lower or first quartile (Q1) is the median of the lower half of a data set.
Quartiles. Values that divide a data set into 4 equal parts when the scores are arranged in order. The 2nd quartile (Q2) is called the median. See also deciles.
R
Radar chart. Display of data on a circular grid that shows changes over a certain period or cycle.
Random sample. Sample for which every member of a population has an equal chance of selection.
Range. Difference between the highest score and lowest score in a data set.
Rate. Relationship between two quantities with different units. For example, a tree’s growth rate can be measured in cm/year.
Ratio. Relationship between quantities that are measured in the same units (e.g. 200 cm : 40 cm = 5 : 1).
Raw score. Score before it has been standardised. See also z-score.
Reducing balance loan. Loan in which interest is charged on the amount still owing rather than the principal borrowed. See also flat rate loan.
Regression line. See line of best fit.
Relative frequency. Ratio used to estimate the probability of a score or event.
Relative frequency of a score =
Repayment (or instalment). Amount paid regularly to pay off a loan.
Royalty. Agreed portion of the sale of an item. For example, a writer is paid a royalty for every book sold.
frequency of score total frequency
---S
Salary. Fixed earnings quoted as a yearly amount, but paid weekly, fortnightly or monthly. See also wage.
Salvage value. Value of an asset at a particular time in its useful life.
Sample. Group of items selected from a population to represent the population. The sample size is the number of items in a sample.
Sample space. Set of all possible outcomes of a probability experiment or game.
Scatterplot (or scattergram). Graph consisting of a series of points showing the correlation of two variables.
Scientific notation. Way of writing very large or very small numbers (e.g. 98 000 000 = 9.8 × 107).
Second. Measure of time or angle size: of a minute where 1 min = 60 s or 1′= 60″.
Sector. Part of the area of a circle bounded by an arc and two radii. A piece of ‘pie’.
Sector graph (or pie chart). Graph representing the parts of a whole population by a circle divided into proportionately sized sectors. See also divided bar graph.
Significant figures. Meaningful digits in a numeral that tell ‘how many’. For example, 98 000 000 has two significant figures, 9 and 8.
Similar figures. Figures that have the same shape but not necessarily the same size. Matching sides are in the same ratio.
Simple interest (or flat rate interest). Interest calculated on the original sum of money (principal) invested or borrowed. See also compound interest.
1 60
Simpson’s rule. Method for finding the approximate area of an irregular-shaped block.
A ≈ (df+ 4dm+ dl)
Simulation. Using a method to model or represent a real situation (e.g. tossing a coin to simulate the sex of a baby, where H = boy and T = girl).
Simultaneous equations. Two equations that must be solved at the same time. The solution must satisfy both equations. For example, y = 3x − 5 and y = 2x have the solution x = 5, y = 10.
Sine. Ratio in a right-angled triangle:
sin θ=
where θ is an angle. See also cosine and tangent.
Sine rule. Trigonometric rule used for triangle problems involving 2 sides and the 2 angles opposite them.
= =
Sinking fund. Any annuity where you ‘sink’ regular amounts of money into an account to reach a target (e.g. the sinking fund for a block of units to have a certain sum of money for repairs at some future date).
Skewness. Shape of a statistical distribution when most of the data is either low (positively skewed) or high (negatively skewed). The tail indicates the direction of the skew.
Small circle. Circle formed when a slice is taken through the Earth but not through its centre. All parallels of latitude are small circles except for the Equator. See also great circle.
Speed. Rate at which an object travels (e.g. km/h).
Speed =
Standard deviation. Statistical measure of the spread of a set of scores. Symbol σn is used for the standard
h 3
---side oppositeθ hypotenuse
---a sin A --- b
sin B --- c
sin C
---Negatively skewed Positively skewed
distance time
---deviation of a population and symbol σn − 1 is used for the standard deviation of a sample.
Standardised score. See z-score.
Statistics. Collection, tabulation and displaying of data for the purpose of analysis.
Stem-and-leaf plot. Way of displaying a small data set. For example, 12 scores in a test:
See also dot plot.
Stepwise linear function (or step graph). Function whose graph consists
of two or more separate line segments forming ‘steps’ (e.g. postage rates).
Straight line method of depreciation. Method of determining the depreciation of an item for tax deductions. The value of the item is reduced by the same amount each year. See also declining balance
method of depreciation.
Stratified sample. Sample consisting of a percentage of items from each ‘stratum’ or ‘layer’ of a population. For example, a stratified sample from a population of 35% children and 65% adults should contain 35% children and 65% adults.
Summary statistic. Calculated value giving a measure of the central tendency (e.g. mean) or spread of a distribution (e.g. standard deviation).
Superannuation fund. Type of annuity where money is invested for a person’s retirement.
Survey (land). Measurements and calculations involved in finding the area and perimeter of a field.
Survey (statistical). Gathering information for statistical purposes.
4 5 6 7 8
2 5
0 2 8 5 | 8 means 58.
Systematic sample. Sample chosen by using a set pattern (e.g. taking every 10th person in a phone book).
T
Tangent. Ratio in a right-angled triangle:
tan θ=
where θ is an angle. See also cosine and sine.
Tax refund. Amount by which the amount of PAYE tax already paid exceeds the amount of tax due; paid to the taxpayer after completion of a tax return.
Tax return. Form completed at the end of a financial year to account for income earned, deductions and tax already paid; used to calculate tax refund.
Taxable income. Income after allowable deductions and on which tax due is calculated.
Term of a loan. Period allowed for the loan to be fully repaid.
Time zone. Zone of about 15° longitude in which the time is the same for all places.
Time-and-a-half. Wages paid at 1.5 times the normal rate (e.g. for working on Saturday).
Traverse survey. See offset survey.
Tree diagram. Way of listing all possible outcomes of a multistage event. See also probability tree
diagram.
Trigonometry. Branch of maths dealing with the relationships between the sides and angles of triangles.
True bearing. See bearing.
U
Unbiased sample. Sample that is representative of the entire population.
side oppositeθ side adjacent toθ
---Unitary method. Way of calculating an amount by first finding the value of one unit, then multiplying.
Unordered selection. Selection of items where the order is not important (e.g. choosing 3 students to represent a school).
V
Value-added tax (VAT). Tax on goods or services used in some countries, similar to the GST in Australia.
Variable. Pronumeral that can take a range of values (that is, not a constant).
Vertical intercept (or y-intercept). Value at which a straight line cuts the vertical axis. For example, the vertical intercept of this graph is 3.
Volume. Amount of space occupied by a solid, measured in cubic units (e.g. m3).
W
Wage. Amount earned by an employee for a set number of working hours, usually paid weekly. See also overtime and salary.
Y
y-intercept. See vertical intercept.
Z
z-score (or standardised score). Score in a standard normal distribution (mean 0 and standard deviation 1). For example, a z-score of −2 means the raw score is 2 standard deviations below the mean.
z = See also raw score.
y
x
−1 3
2
1 2 −2−1
1
