Glossary
The glossary draws on the NSW syllabus glossaries, the glossaries developed by the Australian Curriculum, Assessment and Reporting Authority, and the Macquarie Dictionary.
Aboriginal Peoples are the first peoples of Australia and are represented by more than 250 language groups, each associated with a particular Country or territory. Torres Strait Islander Peoples are represented by 5 major island groups, and are associated with island territories to the north of Australia’s Cape York which were annexed by Queensland in 1879.
An Aboriginal and/or Torres Strait Islander person is someone who:
- is of Aboriginal and/or Torres Strait Islander descent
- identifies as an Aboriginal person and/or Torres Strait Islander person, and
- is accepted as such by the Aboriginal and/or Torres Strait Islander community(ies) in which they live.
A recognised dialect of English which is the first, or home language, of many Aboriginal people. It differs from other dialects of English, such as Standard Australian English, in systematic ways including sounds, grammar, words and their meanings, and language use. Aboriginal English is a powerful vehicle for the expression of Aboriginal identity. Aboriginal English is not a target language study option for NSW Aboriginal Languages syllabuses.
Texts that describe landscapes and directions of the tracks forged in lands, waters and skies by Creator Spirits during the Dreaming.
The magnitude or size of a real number, i.e. the distance of the number from the origin on a number line.
Formally, it has the piecewise definition .
The rate at which velocity changes over time.
The extent to which a system, environment or object may be used irrespective of a user’s capabilities or abilities. For example, the use of assistive technologies (AT) to allow people with disability to use computer systems, or the use of icons in place of words to allow young children to use a system.
An angle smaller than a right angle, between 0° and 90°.
Extended in Mathematics Advanced and Extension 1: In circular measure, an angle lying in the interval
A mathematical statement formed by combining numbers and algebraic symbols using arithmetic operations, e.g. .
A fraction in which the numerator and/or the denominator are algebraic expressions.
In trigonometry, refers to using the sine rule to calculate the size of an angle in a triangle where there are two possibilities for the angle, one obtuse and one acute, leading to two possible triangles. This occurs because, for an acute angle , .
A function of the form or has amplitude , that is half the distance between the maximum and minimum values.
Formed by 2 straight lines meeting at a common endpoint, called the vertex. An angle can describe the amount of turn between its 2 arms (lines).
The angle between horizontal and the line of sight from an observer to an object that is lower than the observer.
The angle between horizontal and the line of sight from an observer to an object that is higher than the observer.
The angle a straight line makes with the positive -axis.
A compound interest investment to which payments are made, or a single sum invested from which payments are received, on a regular basis for a fixed period of time.
A part of a circle’s circumference.
Extended in Mathematics Extension 1: A part of a curve.
The distance between two points on a curve. In a circle the length of an arc is given by , where is the arc length, is the radius and is the angle subtended at the centre, measured in radians.
Calculated using , where is the base length and is the perpendicular height. For a triangle with sides and about the angle , the area of the triangle is .
A sequence of numbers in which the difference between any two successive terms of the sequence is constant. Also known as arithmetic sequence.
A sequence of numbers in which the difference between any two successive terms of the sequence is constant. Also known as arithmetic progression.
One of several different arrangements that can be used to model multiplicative situations. It is made by arranging a set of objects, such as counters, into columns and rows. Each column must contain the same number of objects as the other columns, and each row must contain the same number of objects as the other rows.
A device or system whose primary purpose is to maintain or improve an individual's functioning and independence to facilitate participation and enhance overall wellbeing. This includes technologies specifically designed to meet an individual's needs, eg eye gaze technology, as well as more general technologies that can be used by anyone, eg speech-to-text applications. Assistive technology can also be referred to as inclusive technology.
Relationship between pairs of numerical variables e.g. in terms of strength, form and direction.
A straight line (or another curve) that a curve approaches as tends to , or to some particular value.
For example, the curve has an asymptote as tends to , and the curve has asymptotes and as tends to and respectively.
An umbrella term that encompasses the communication methods used to supplement or replace speech or writing. AAC can be unaided, such as gestures, body language and sign language, or aided such as pictures, symbols, objects or speech generating devices.
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A number expressing a central or typical value in a set of data. While it usually refers to the arithmetic mean, that is, the sum of a set of numbers divided by the number of numbers in the set, it may also refer to other measures of centre.
The change in one quantity divided by the corresponding change in another quantity. For a function over the domain , the average rate of change of with respect to is, .
A straight line that divides a shape or curve into two so that one side is a reflection of the other in the given line.
A direction from one point on the Earth’s surface to another. Two types of bearings may be used: compass bearings and true bearings.
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The point at which income from production and cost of production are equal.
A system that specifies the position of each point in a plane, formed by the intersection of two perpendicular number lines called axes. Each point is represented by an ordered pair of real numbers called the coordinates of the point. The point where the axes meet is called the origin and has coordinates
A formula for the derivative of the composite of two differentiable functions. If is a function of , and is a function of , then the chain rule states that . If is the composite function , then .
A rule for writing a logarithm with a particular base as the ratio of two logarithms with a different base: .
All points equal to a given distance from a fixed point, the centre. When used to describe a shape, a circle includes all points inside the boundary.
The boundary of a circle. The length of the circumference is given by , where is the diameter. Alternatively, it is given by , where is the radius.
A numerical quantity which multiplies a variable in an algebraic expression. For example, 5 is the coefficient of . Variables with no specified coefficient have a coefficient of 1.
The constant difference between successive terms of an arithmetic sequence.
The constant ratio between successive terms of a geometric sequence.
The ways people communicate and the communicative behaviours they use. Communication forms can be non-symbolic and/or symbolic. Non-symbolic forms include sounds, gestures, facial expressions and eye movements. Symbolic forms can be aided or non-aided. Aided forms of symbolic communication include objects, symbols, photographs and drawings. Aided forms can be digital. Non-aided forms of symbolic communication include formal gestures; speech; and signs, such as Key Word Sign.
Angles either side of north or south. For example, a compass bearing of N50°E is found by facing north and moving through an angle of 50° to the east.
All of the outcomes that are not in a given event. All the elements of a set that are not in a given subset.
Two adjacent angles that form a right angle, i.e. the sum of the angles measured in degrees is 90°.
Two mutually exclusive outcomes in a probability experiment, such that where is the probability of event and the probability of event .
Extended in Mathematics Standard and Advanced: Two mutually exclusive events which make up the sample space.
Rearranging a quadratic expression into the form .
When the output of one function becomes the input of a second function.
For example, (read as of of ) is a composite function where the outputs of function are taken as the inputs of function .
The interest earned by investing a sum of money (the principal) when each successive interest payment is added to the principal for calculating the next interest payment.
A function in which all points on a graph between any two given points on the graph lie on or above the chord joining the given points.
A function for which all points on a graph between any two given points on the graph lie on or below the chord joining the given points.
Consideration of whether the knowledge of the occurrence of one event, A, affects the probability of occurrence of another event, B.
Extended in Mathematics Advanced: The probability of an event occurring, given that another event has occurred, notated as (read as ‘probability of given ’).
For a surd , where , , and are real numbers, the conjugate is .
In complex numbers, the conjugate of is . and are complex conjugates.
A fixed numerical value. For example, in the algebraic expression , the number 11 is a constant.
A function that has only one value.
The graph of a continuous function is an unbroken curve. It can be drawn without lifting the pen off the paper.
A continuous random variable is a numerical variable that can take any value along a continuum.
An amount of money that is paid into an annuity. The contribution can be made as a lump sum or as a series of payments.
If one relationship is true, then the opposite is also true.
The converse of a statement ‘If then ' is 'If then '. For example, the converse of Pythagoras’ theorem is that if the sum of the squares of 2 sides of a triangle is equal to the square of the third side, then the triangle is right-angled.
Extended in Mathematics Extension 2: The converse of is or .
The protection provided to the creators of original works and makers of sound recordings and films, that offers a legal framework for the control and reproduction or transmission of their literary, dramatic, artistic or musical works.
For an angle, its cosecant is the reciprocal of its sine, .
In any right-angled triangle, where .
A formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.
The price paid to acquire, produce, accomplish or maintain anything.
For an angle, its cotangent is the reciprocal of its tangent, .
In any right-angled triangle, where .
Country is used to describe a specific area of a nation or clan including physical, linguistic and spiritual features. Aboriginal communities’ cultural associations with their Country may include or relate to languages, cultural practices, knowledge, songs, stories, art, paths, landforms, flora, fauna and minerals. These cultural associations may include custodial relationships with particular landscapes such as land, sea, sky, rivers as well as the intangible places associated with the Dreaming(s). Custodial relationships are extremely important in determining who may have the capacity to authentically speak for their Country.
Place is a space mapped out by physical or intangible boundaries that individuals or groups of Torres Strait Islander Peoples occupy and regard as their own. It is a space with varying degrees of spirituality.
A polynomial function of degree 3, that is, a function of the form .
The customs, habits, beliefs/spirituality, social organisation and ways of life that characterise different groups and communities. Cultural characteristics give a group or individual a sense of who they are and help them make sense of the world in which they live. Culture is a shared system but inherently diverse – there can be individual and group differences within cultures. Everyone has culture – it is a lens through which we see the world.
For a continuous random variable , the cumulative distribution function (CDF), given by the function , is .
The accumulating total of frequencies within an ordered dataset.
A visual representation of data using bars to represent the class boundaries and the cumulative frequencies.
The area of each bar is proportional to the cumulative frequency of the observations up to the end of that class.
A series of straight lines representing the cumulative frequency for a given dataset. Sometimes called the ‘ogive’.
In Aboriginal communities, an individual charged with maintaining and passing on particular elements of cultural significance, eg language, stories, songs, rituals and imagery.
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When referring to deaf people who belong to a linguistic and cultural minority known as the Deaf community, the 'D' may be capitalised in reference to the individual, the group, or the culture in order to accord respect and deference, for example, the Deaf community. When referring simply to audiological status or when cultural affiliation is not known, as in the case of a person with a hearing loss in general, the lowercase 'd', as in 'deaf' is the more common usage.
A cultural identity for people with hearing loss who share a common culture and who usually have a shared sign language.
A unit for measuring an angle. Angles are measured as a proportion of a full turn which is equivalent to 360 degrees, so that one degree, written as is equal to of a full turn.
Comes from Latin, meaning ‘that which gives a name’ [de- “completely”; nomen “name”]. The denominator of a fraction identifies the name of the fractional parts (eg thirds, quarters or fifths).
Extended in 7–10: In the fraction , b is the denominator.
The variable used to represent the output values of a function. A dependent variable is generally represented on the vertical axis of a graph.
The result obtained after differentiation. For the function , the derivative is the gradient function of , and is denoted . The derivative of from first principles is given by . The derivative of with respect to is denoted or .
A function which can be differentiated at each point in its domain.
A function is differentiable at if exists, that is if there is a non-vertical tangent to the graph of at the point .
The process used to find the derivative of a function.
A process of stretching or compressing the graph of a function. This could happen either in the or direction or both.
A proportional relationship where one quantity directly varies with respect to a change in another quantity. This implies that if there is an increase (or decrease) in one quantity then the other quantity will experience a proportionate increase (or decrease).
An umbrella term for any or all of the following components:
- impairments: challenges in body function or structure
- activity limitations: difficulties in executing activities
- participation restrictions: challenges an individual may experience in involvement in life situations. (World Health Organization)
A point at which the graph of a function is broken (not continuous) and the function is undefined.
Specifies the probabilities with which a discrete random variable takes each of its values.
A numerical variable whose values can be listed.
Individual and countable items that can be listed.
Extended in Mathematics Advanced: Also known as a discrete random variable.
In the quadratic expression , the discriminant
Two sets which do not have any common elements.
The change in position of an object, after a period of time, from its original position. Displacement is a vector quantity. The displacement may be positive, negative or zero.
The length between two points. Distance is a positive scalar quantity.
A line graph that relates distance and time, with time on the horizontal axis and distance on the vertical axis.
Different, not equal.
Differences that exist within a group, for example, age, sex, gender, gender expression, sexuality, ethnicity, ability/disability, body shape and composition, culture, religion/spirituality, learning differences, socioeconomic background, values and experiences.
The set of allowable values of in a function or relation.
Extended in Mathematics Advanced, Extension 1 and Extension 2: For a function or relation, it is the set of real numbers on which the function or relation is defined.
The Dreaming has different meanings for different Aboriginal groups. The Dreaming can be seen as the embodiment of Aboriginal creation which gives meaning to everything; the essence of Aboriginal beliefs about creation and spiritual and physical existence. It establishes the rules governing relationships between the people, the land and all things for Aboriginal Peoples. The Dreaming is linked to the past, the present and the future. Where appropriate, refer to Aboriginal names for the Dreaming.
The custodians of knowledge and lore. They are chosen and accepted by their own communities as people who have the permission to disclose cultural knowledge and beliefs. Recognised Elders are highly respected people within Aboriginal communities. Proper consultation with local Aboriginal communities will often direct schools to recognised Elders.
A member of a set. For example, is a member of the set of natural numbers . This relation can be written more concisely as (' is an element of the set ').
The empirical rule for normally distributed random variables is:
- approximately 68% of data will have -scores between −1 and 1
- approximately 95% of data will have -scores between −2 and 2
- approximately 99.7% of data will have -scores between −3 and 3.
The unique set characterised by the property that it has no elements at all.
A type of transformation that increases or decreases the size of an image without changing its shape, depending on the size of the enlargement factor.
If two quantities or mathematical expressions are equal, then the quantities have the same value, or the expressions represent the same mathematical object.
If then either may be substituted for the other.
For and , the ‘=’ sign indicates assignment by definition.
An event for which all outcomes have the same probability of occurring. For example, in tossing a fair coin, the outcome ‘head’ and the outcome ‘tail’ are equally likely. In this situation, 𝑃(head)=𝑃(tail)=0.5.
An expression showing the equality of two quantities, using the = sign between them. A mathematical formula asking for a solution so that the two expressions in that variable are equal, for example .
Two things are equivalent if they have the same value.
See Loading , Loading .
Extended in Mathematics Advanced, Extension 1 and Extension 2: Two things are equivalent if they have the same value, function or meaning. For example, and are equivalent. Statements and are equivalent if implies and implies .
An irrational number, , which can be defined in various ways including: and . It has the property .
A function is even if its graph is unchanged under reflection in the -axis.
An even function has the property , for all values of in the domain.
Situations that occur in the everyday context, e.g. having lunch. In the context of probability, the set of possible outcomes.
Extended in 7–10: A subset of the sample space for a random experiment. For example, the set of possible outcomes from tossing 2 coins is , where H represents a 'head' and T is a 'tail'. For example, if is the event 'at least one head is obtained', then
A precise numerical value e.g. as opposed to the approximation .
In statistics, the expected value of a random variable is a measure of the central tendency of its distribution. Also known as the expectation or mean. is calculated differently depending on whether the random variable is discrete or continuous.
A process with an observable result. The results of the experiment are the set of possible outcomes, called the sample space.
Occurs when the rate of change of a mathematical function is negative and proportional to the function’s current value.
A function of the form , where is the independent variable and the base . The graph of an exponential function is an exponential curve.
Occurs when the rate of change of a mathematical function is positive and proportional to the function’s current value.
Two or more numbers or variables connected by operations. For example, , , are all expressions. Expressions do not include an equals sign.
Extended in Mathematics Advanced, Extension 1 and Extension 2: The result of combining numbers, variables and operations in a meaningful way. For example, is an expression, but is not a validly formed expression.
To express a number or algebraic expression as a product. For example, 15 is factorised when expressed as a product: and is factorised when written as a product: .
A value between and .
The first language(s) that a person learns to speak.
The number of times that a particular value occurs in a dataset. For grouped data, it is the number of observations that lie in that group or class interval. For example, when rolling a dice 20 times, ‘the frequency of a 6’ means how many times the number 6 comes up.
A function assigns to each element of one set precisely one element of a second set .
The functions most commonly encountered in elementary mathematics are real functions of real variables. For such functions, the domain are sets of real numbers.
Functions are usually defined by a formula for in terms of . For example, the formula , defines the ‘squaring function’ that maps each real number to its square .
Relates differentiation and integration.
For a continuous function on the interval it has two equivalent forms:
for ,
and
where is any antiderivative of .
The total value of an investment or annuity at the end of a specified term, including all contributions and interest earned.
A straight line in general form is given as , where , and are constants.
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A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed number called the common ratio. Sometimes called a geometric progression (GP).
A geometric series is a sum whose terms form a geometric sequence.
The largest value of the function on its domain.
The smallest value of the function on its domain.
The slope of a line. It is calculated as the gradient of a line segment it contains. If and are two distinct points on a line, the gradient of the line (or line segment ) is given by .
is the gradient–intercept form of a straight line, where is the gradient of the line and is the point at which the line intersects the -axis. is called the -intercept.
A visual representation of statistical data or of a relationship between variables. Ordered pairs of values () that represent the function or relation are plotted to form a graph. Graphs of statistical data include dot plots, box plots, column graphs, divided bar graphs and histograms.
Extended in Mathematics Advanced, Extension 1, Extension 2: For a function , its graph consists of all ordered pairs for in the domain of .
An identity is a statement involving a variable(s) that is true for all possible values of the variable(s).
The set of all primitives of a continuous function notated . So, where is an arbitrary constant of integration, and .
Two events are independent if knowing the outcome of one event tells us nothing about the outcome of the other event.
A variable used to represent values in the domain (input values) of a function. Generally represented on the horizontal axis of a graph.
Also called ‘exponent’. The power to which a number or algebraic expression is to be raised. The index or exponent is written as a superscript. Positive integral exponents indicate the number of times a term is to be multiplied by itself.
The plural of the term index.
An internationally recognised term for the first peoples of a land. In NSW the term Aboriginal person/Peoples is preferred.
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Includes, but is not limited to, objects, sites, cultural knowledge, cultural expression and the arts, that have been transmitted or continue to be transmitted through generations as belonging to a particular Indigenous group or Indigenous people as a whole or their territory.
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A statement that one number or algebraic expression is less than (or greater than) another. There are 4 types of inequalities:
- is less than is written
- is greater than is written
- is less than or equal to is written
- is greater than or equal to is written .
Extended in Advanced, Extension 1, Extension 2: An order relation between one number or algebraic expression and another.
Limitless, exceeding any finite amount.
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The rate of change at a particular moment. For a differentiable function, the instantaneous rate of change at a point is its derivative at that point, so it equals the gradient of the tangent to its graph at the point.
A whole number, positive, negative or zero e.g. −3, −2, −1, 0, 1, 2 …
Extended in Advanced, Extension 1, Extension 2: The set of integers is usually denoted by ℤ.
The process of finding the integral of a function. The inverse of differentiation.
Non-material assets such as forms of cultural expression that belong to a particular individual or community. Intellectual property rights refer to the rights that the law grants to individuals for the protection of creative, intellectual, scientific and industrial activity, such as inventions.
See Loading , and Loading
The point at which a curve or function crosses an axis or other curve in a plane. The point at which a curve crosses the -axis is called the -intercept and the point at which a curve crosses the -axis is called the -intercept.
Extended in Advanced and Extension 1: The - and -intercepts are sometimes taken to mean the signed distance from the point at which the curve crosses the axis to the origin, for example, for the line , the -intercept is .
Money paid or received in return for using or lending money.
A percentage at which interest is charged or paid.
For sets and , it is the set of elements that are in both and in . The intersection of and is denoted .
Notation for representing an interval on the real number line by its endpoints. Parentheses and/or square brackets are used respectively to show whether the endpoints are excluded or included.
For , is an open interval, and is a closed interval.
When one variable increases as the other variable decreases. For example, if is said to be ‘inversely proportional’ to , the equation is of the form , where is a constant of variation (or proportion). Also known as inverse proportion.
An allocation of money or capital into an asset or venture which is expected to generate a profit or return.
A number that cannot be expressed as a fraction in the form , where and are integers and is non-zero. The decimal form of irrational numbers does not terminate and is non-recurring.
A communication strategy that incorporates signing with speech. It is used to support language development for people with communication difficulties. Although Key Word Sign uses a simplified form of manual signing, it is different to Auslan, as it is not a signed language.
A key aspect of Aboriginal cultures and values. It includes the importance of all relationships and of being related to and belonging to the land.
An Aboriginal community identified with a common language, both verbal and nonverbal, and with a particular territory. Used in preference to the term ‘tribe’.
The process and range of strategies for increasing knowledge and use of a language that is no longer spoken fluently across all generations in the context of language loss or language dispossession caused by colonisation. Aboriginal Languages and Torres Strait Islander Languages are being revived through community initiatives, linguistic research and school programs. ‘Language revival’ may be used as an overarching term that could also include ‘reclamation’, ‘revitalisation’, ‘renewal’ and ‘reawakening’.
Something that can be represented or modelled by a straight line.
An equation involving linear expressions. The general form of a linear equation in one variable is where and are constants.
is a linear function of if where and are constants.
The graph of a linear function is a straight line, where is the gradient and is the -intercept.
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An amount of money borrowed from a bank or other financial institution.
A local Aboriginal community is constituted by those people who are Aboriginal and who reside in the near locality. Aboriginal communities will have a rich and diverse history that has been seriously affected by dispossession and relations, which sees families with spiritual connection to Country residing beside those who have been forced to move from other locations. The notion of locality is complex and multilayered: schools should seek advice from a range of people and/or organisations representing local interests.
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A point on a function is a local maximum if its function value is larger than the function values near it.
A point on a function is a local minimum if its function value is smaller than the function values near it.
The logarithm of a positive number is the power to which a given number , called the base, must be raised in order to produce the number . The logarithm of , to the base is denoted by .
Algebraically: is equivalent to .
A function, such as , which is the inverse of the exponential function, . Here is the independent variable and is the base of the logarithm.
A scale where successive endpoint values of intervals increase by a constant factor (multiplicatively). Contrast with linear scales in which the increase is a constant amount.
The size or absolute value of a number. For example, +4 and -4 have a magnitude of 4.
Extended in Mathematics Extension 1 and Mathematics Extension 2: For a vector, the magnitude is its length, given by for 2D vectors and for 3D vectors.
The sum of values in a data set divided by the total number of values in the data set. Also called the average.
A statistic that is used to summarise a data set. There are 3 common measures of centre for a data set: mode, median and mean.
The value in a set of ordered data that divides the data into 2 parts. It is frequently called the 'middle value'.
Extended in Mathematics Standard and Advanced: If the number of values in the ordered dataset is even, it is the average of the two middle values. If the number of values in the dataset is odd, the median is the middle value.
One sixtieth of a degree, also equivalent to sixty seconds. Often represented by the sign ( ). For example, (fourteen degrees and twenty five minutes).
The most frequently occurring value in a set of data.
Extended in 7–10: There can be more than one mode. When there are 2 modes, the dataset is said to be bimodal.
A mathematical, conceptual or physical representation that describes, simplifies, clarifies or provides an explanation of the structure, workings or relationships within an object, system or idea. Models can provide a means of testing and predicting behaviour within limited conditions. Models may be physical or exist in digital form.
An event that consists of two or more simple experiments. For example, tossing a coin three times (repeated trials), or both tossing a coin and rolling a dice (possible outcomes would be H and 5, T and 2).
Two events which cannot have simultaneous outcomes in the same chance experiment.
For example, when a fair coin is tossed twice, the events 'HH' and 'TT' cannot occur at the same time and are, therefore, mutually exclusive.
In a Venn diagram, as shown below, mutually exclusive events do not overlap.
Extended in Mathematics Advanced: For a random experiment two events and are mutually exclusive if , that is, they cannot occur simultaneously.
A logarithm to the base . The logarithm of to the base is denoted as or .
In calculus, the normal to a curve at a given point is the straight line that is perpendicular to the tangent to the curve at a given point .
A type of continuous distribution whose graph looks like this:
Image long description: The horizontal x-axis is labelled from 100 to 200 in increments of 20 from left to right. The y-axis is labelled from 0 to 50 in increments of 10 from the bottom to the top. Along the x-axis is a series of columns that rise to a peak halfway along the axis and fall back towards 0 on the far right of the x-axis. An orange ‘bell curve’ is laid over the peaks of the columns.
The mean, median and mode are equal and the scores are symmetrically arranged either side of the mean.
The graph of a normal distribution is often called a ‘bell curve’ due to its shape.
A variable which varies according to the normal distribution.
A function whose graph is unchanged under rotation of about the origin.
An odd function has the property , for all values of in the domain.
Taking place away from Aboriginal land or Country of origin.
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Taking place on Aboriginal land or Country of origin.
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Possible result from an experiment or trial.
Each Aboriginal Language is recognised as belonging to a particular geographical area and thus to the people who can claim a connection to that area. Aboriginal community members acquire ownership of their language(s) at birth. Language proficiency is not essential for ownership.
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The graph of . The point is called the vertex of the parabola and the -axis is the axis of symmetry of the parabola.
Some other parabolas are the graphs of where .
Two distinct lines, rays, or line segments in the same plane that have no points of intersection and so necessarily have the same gradient (slope).
The symbol is used to express that one line, ray, or line segment is parallel to another.
The th partial sum of a sequence is the sum of the first terms of the sequence: , for all whole numbers .
A function is periodic with period if , for all , that is, the function repeats itself after each interval of length .
For example, and have period .
Two lines, rays, line segments, vectors, planes or other objects that intersect at a 90° angle (a right angle).
A function which is defined differently for different parts of the domain. For example,
A point on a curve where the concavity changes. At a point of inflection, the tangent exists and crosses the curve.
For a function , a primitive is a function whose derivative is . Primitive and antiderivative are synonyms.
The chance of something happening shown on a scale from 0 and 1 (inclusive). For example, the probability that a fair coin toss will come up ‘heads’ is 0.5.
For a random variable , the probability density function (PDF), , is a function that describes the likelihood that the random variable takes a particular value, that is .
For a random variable , the probability distribution is the set of values taken by the random variable, together with the probabilities that .
A rule for the derivative of the product of two differentiable functions: If where and are both functions of , then , or if then .
A rigorous mathematical argument that demonstrates the truth of a given statement or proposition. A mathematical statement that has been established by means of a proof is called a theorem.
The appropriate ways of behaving, communicating and showing respect for diversity of history and culture. This involves appreciation of the knowledge, standing and status of people within the local Aboriginal community and the school community. Protocols inevitably vary between communities, and between people within a community. In establishing a partnership between schools and Aboriginal communities, it is especially important that protocols are acknowledged and respected.
The square of the length of the hypotenuse, , of a right-angled triangle equals the sum of the squares of the lengths of the other 2 sides, and , such that .
A quarter of a circle.
Any one of the four parts into which the Cartesian plane is divided by the - and -axes. Thus, the first or positive quadrant consists of those points with and .
An equation of the form , where , and are constants.
An expression of the form , where , and are constants.
The roots of a quadratic equation where are given by the quadratic formula:
.
A function of the form , where , and are constants.
An inequality reducible to inequalities of the form , where , and are constants.
The values that divide an ordered dataset into 4 (approximately) equal parts. There are 3 quartiles. The first, the lower quartile , divides off (approximately) the lower 25% of data values. The second quartile is the median. The third quartile, the upper quartile , divides off (approximately) the upper 25% of data values.
A formula for the derivative of the ratio of two differentiable functions. If , where and are both functions of then the quotient rule states that , or if then .
A unit of angular measure frequently used in mathematics.
1 radian is the angle between two radii of a circle which cut off on the circumference an arc equal to the radius.
The size of an angle subtended by an arc of a circle in radian (or circular) measure is given by the ratio .
Radian measure is frequently employed in mathematics. For example, in the formulas of differentiation for trigonometric function; the values of relate to radian measure.
A variable whose possible values are outcomes of a statistical experiment or a random phenomenon.
The set of values of the dependent variable for which a function is defined.
For a function, the relative change in a function’s value to a change in . Instantaneous rate of change is measured by its derivative.
For example, the velocity of a moving object is the rate of change of its position over time.
An element of the infinite set of numbers {, where and are integers and zero}. It may be expressed in decimal form, eg and
A number which can be represented by a point on a number line. The set of real numbers is the set of all rational and irrational numbers.
If is any real number then the reciprocal of that number will be . For example, the reciprocal of 4 is .
A reducing balance loan is a compound interest loan where the loan is repaid by making regular payments and the interest paid is calculated on the amount still owing (the reducing balance of the loan) after each payment is made.
A type of transformation that decreases the size of an image by a factor without changing its shape.
A transformation of a shape formed by creating a mirror image on the other side of a given line.
An association between the elements of one set and the elements of another set . It may be represented as a set of ordered pairs , where is in , is in and is related to .
Given by the ratio , where is the frequency of occurrence of a particular data value or group of data values in a dataset and is the number of data values in the dataset.
A set amount, paid at regular intervals over the period of a loan, to pay off a loan.
A term used commonly in NSW Aboriginal communities to refer to the way an individual treats others. Showing respect occurs in many ways, such as waiting to speak, listening and demonstrating understanding, not asking too many direct questions, ensuring that people are not made to feel uncomfortable or uneasy, and generally showing regard for others’ ideas, beliefs and culture.
The total income generated from normal business operations, such as from the sale of items produced.
The solution to an equation. For example, has roots and .
A turn about a point through a specified angle. For example, a rotation about the origin through an anticlockwise angle of 45° transforms the line into the line .
A subset of a population used to estimate characteristics of the population. For example, a randomly selected group of 8-year-olds (sample) selected to estimate the height of 8-year-olds in Australia (population).
The straight line passing through 2 points on the graph of a function.
For an angle, the secant is the reciprocal of its cosine, .
In any right-angled triangle,
where
.
The derivative of the first derivative. It is denoted by: , or .
The plane figure enclosed by 2 radii or a circle and the arc between them.
A plane figure enclosed by a chord and the arc joining the endpoints of a chord.
Half of a circle.
An enumerated list of elements: , , …, , …where is referred to as the th term.
In a sequence, repetitions are allowed and order matters. The length (possibly infinite) of the sequence is the number of terms in it.
The sum of the terms of an infinite sequence. The notation is used for the series corresponding to the sequence
A collection of objects or elements, usually specified by listing its elements, e.g. ; by describing it in words, e.g. ‘the set of primes’; or by using a rule such as .
Extended in Mathematics Advanced, Extension 1 and Extension 2: A collection of distinct, unordered objects, referred to as members or elements of the set.
Hand signs (or hand talk) used to supplement or replace oral language. Signs form part of nonverbal communication for Aboriginal and Torres Strait Islander Peoples and may be used by people who are hearing, or d/Deaf or hard of hearing. Aboriginal and Torres Strait Islander Sign Languages may be used in some areas. Some Sign Languages may be associated with sacred ceremonial practices.
The use of words, graphic designs and/or symbols used to communicate a message, eg information signs, plaques, warning signs, road signs, signs that show direction.
In any right-angled triangle, where .
Relates the lengths of the sides of a triangle to the sines of its angles: .
The absolute value of an object’s velocity. It represents how fast the object is moving. For an object moving along the -axis, average speed is calculated as . If its position at time is the instantaneous speed is .
A measure of the variability or spread of a dataset. It gives an indication of the degree to which the individual data values are spread around their mean.
Extended in Mathematics Standard and Advanced: For a random variable, the standard deviation is the square root of its variance.
It provides a measure of the spread of the probability density function.
A stationary point on the graph of a differentiable function is a point where .
A stationary point could be classified as a local or global maximum or minimum or a horizontal point of inflection.
is a subset of set if every member of set is a member of set and is written as , i.e. ‘ is a subset of ’. If there are elements of not in , then is a proper subset of , written .
The process of replacing a variable in an algebraic expression, formula, equation or function consistently by a particular value, another variable, expression or function.
Simultaneous equations can be solved using substitution by isolating one variable in one equation and using its value to replace that variable in another equation.
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Extended in Mathematics Extension 1 and Extension 2: Integration by substitution is a method used for evaluating integrals. The substitution could be expressed as a function of the variable of integration, or with the variable of integration as the subject of the substitution.
In geometry, an angle subtended by an arc or interval is the angle whose 2 rays pass through the endpoints of the arc or interval. A possible synonym for ‘subtends’ is ‘makes’.
Notation used to express a sum. For example, the sum can be represented using summation notation as . Also known as sigma notation.
A numerical expression involving one or more irrational roots of numbers.
Extended in Mathematics Advanced: An irrational root of a number; for example and .
More generally sums involving rational multiples of surds are sometimes also referred to as surds; for example, .
A type of assistive technology that enables people with cognitive and/or physical disability to access a range of devices, including computers and communication devices. Switches can be activated by touch, or triggered without contact, such as through eye gaze, sound or blowing.
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A line that intersects a circle at just one point. It touches the circle at that point of contact but does not pass inside it.
Extended in Mathematics Advanced, Extension 1 and Extension 2: For a curve at a given point the tangent can be described intuitively as the straight line that ‘just touches’ the curve at that point. At the curve has ‘the same direction’ as the tangent. In this sense it is the best straight-line approximation to the curve at point . For a differentiable function the tangent to its graph at the point has slope .
The ratio of the length of the altitude, , of a right-angled triangle to the length of its base, , for a given base angle, theta, .
In any right-angled triangle, , where ° °.
A procedure or set of procedures that changes the size and/or shape of an image. A transformation operates on points in the plane to change aspects, such as the position, size or shape of curves and other figures.
Translations, reflections, rotations, dilations, enlargements are all examples of transformations.
A type of transformation that moves a shape (or all the points in a plane) by the same amount to the left or right, or up or down.
A method of approximating the area of an irregular shape, or a region bounded by a curve and an axis, by slicing the area up into trapeziums (trapezia) of equal height.
A diagram consisting of line segments (edges) connected to points (vertices) like the branches of a tree. It shows the relationship between sets, events, or the set of outcomes of a multi-step random experiment.
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A single performance of a random experiment. Successive trials refers to repeated performances of the same experiment each of which will therefore have the same set of possible outcomes (sample space).
When there are only two possible outcomes they are known as Bernoulli trials.
The relationship between the angles and sides of right-angled triangles. The 3 basic trigonometric ratios are sine, cosine and tangent.
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Measured in degrees clockwise from true north and written with 3 digits to specify the direction.
For example, the direction of north is specified °T, east is specified as °T, south is specified as °T and north-west is specified as °T.
Points at which the gradient of the graph of a function changes direction, so the function has either a local minimum or local maximum at those points.
A common way of displaying the two-way frequency distribution that arises when a group is categorised according to 2 criteria.
A probability distribution in which all values of the random variable are equally likely.
For sets and , the union is the set of elements which are in or or both and is written as , i.e. ‘ union ’.
The universal set for a particular problem or context contains all elements involved in the problem.
Things that are measurable or observable that are expected to either change over time or between individual observations. They are often designated by symbols, such as , and , to represent members of a set.
For example, the variable could represent an unspecified real number.
Something measurable or observable that is expected to change either over time or between individual observations.
For example, the age of students, their hair colour or a playing field's length or its shape.
In statistics, the variance of a random variable is a measure of the spread of its distribution. is calculated differently depending on whether the random variable is discrete or continuous.
The rate of change of an object's position with respect to time. It is a vector quantity, meaning it has both magnitude and direction. The SI units for velocity are metres per second (ms-1).
Extended in Mathematics Advanced, Extension 1, Extension 2: A particle moving along the -axis whose position at time is has velocity .
Graphical representations, using several typically overlapping circles, showing elements of sets in relation to properties or attributes. They are drawn for some specified universal set.
Where 2 straight sides of a two-dimensional shape meet.
Extended in 7–12: A vertex is a point in the plane where lines meet and do not extend beyond, or a point in space where several edges meet. A vertex can also refer to a node in a network. It is also the turning point of a parabola.
Determines whether a relation or graph is also a function. If a vertical line intersects or touches a graph at more than one point, then the graph is not a function.
The amount of space occupied by an object.
Any of the positive integers or 0.
Yarning circles are an important cultural practice for Aboriginal and Torres Strait Islander Peoples to learn within the collective group. Knowledge and information are shared in harmony and respect with all individuals.
A -score is a statistical measurement of how many standard deviations a raw score is above or below the mean. A -score can be positive or negative, indicating whether it is above or below the mean, or zero. Also known as a standardised score.
A point in the domain of a function where the value of the function is zero. A solution of the equation .