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 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.
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).
When a non-zero complex number is represented by a point in the complex plane an argument of , denoted , is an angle that (where is the origin) makes with the positive real axis, with successive pairs differing by .
For the numbers the arithmetic mean is: .
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.
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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The formula for the expansion of a power of a binomial expression:
, when is a positive integer and,, …, are binomial coefficients.
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
The equation of a relation or a function expressed in terms of the Cartesian coordinates 𝑥 and 𝑦. May sometimes be formed from two parametric equations by eliminating the parameter.
A form that expresses a complex number in terms of its real and imaginary parts, , where and are real numbers.
is referred to as the real part of the complex number and is referred to as the imaginary part of the complex number.
The Cauchy–Schwarz inequality for vectors is given by: .
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.
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.
Describes points that lie on the same straight line.
A notation used to represent a vector in two or three dimensions. For example the vectors and can be represented in column vector notation as: and respectively.
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.
Commutativity (commutative property) of addition or multiplication means that two numbers can be added or multiplied in any order and the solution will be the same.
Commutative law, commutativity and turn-around facts are interchangeable terms.
A theorem regarding the complex roots of a polynomial with real coefficients: If is a root of a polynomial equation in one variable with real coefficients, then its complex conjugate is also a root of the polynomial.
A number of the form , where and are real numbers and .
A Cartesian plane in which the real part of a complex number is plotted on the horizontal axis, referred to as the real axis, and the imaginary part on the vertical axis, referred to as the imaginary axis. Sometimes called the Argand plane.
One of the parts of a vector which is parallel to a particular axis or lying in a specified direction.
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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 proposition formed by exchanging the hypothesis and conclusion of a conditional statement and negating both. The contrapositive of the statement ‘if then ’ is ‘if not then not ’. The contrapositive of a true statement is also true.
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.
An instance/example where the proposition is not true, thereby showing the proposition to be false.
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.
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.
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.
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.
Any equation containing the derivative of an unknown function, for example and .
A process of stretching or compressing the graph of a function. This could happen either in the or direction or both.
For a straight line or line segment, a direction vector is a vector whose direction is that of the line or line segment.
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)
In the quadratic expression , the discriminant
Different, not equal.
Multiplication of numbers is distributive over addition because the product of one number with the sum of 2 others equals the sum of the products of the first number with each of the others. For example, the product of 3 with gives the same result as the sum of and :
and
The distributive law is expressed algebraically as follows:
, for all numbers , and .
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.
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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.
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 .
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.
The first language(s) that a person learns to speak.
A push or pull between objects, which may cause one or both objects to change speed, and/or direction of their motion, and/or their shape.
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 .
The th root of the product of numbers. For a set of numbers , the geometric mean is defined as .
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 .
The force of attraction that objects with mass exert on each other.
An identity is a statement involving a variable(s) that is true for all possible values of the variable(s).
A relationship between two propositions where the second is a direct consequence of the first. A statement in the form ‘If then ', or equivalently ' is necessary for ' or ' implies ', represented as or .
The set of all primitives of a continuous function notated . So, where is an arbitrary constant of integration, and .
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.
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.
A function that is to be integrated.
The process of finding the integral of a function. The inverse of differentiation.
A process of transforming the integral of a product of functions into an integral which can be more easily found. It is derived using the product rule for differentiation.
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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.
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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.
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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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 .
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 amount of matter in an object.
A method used to prove a statement involving a natural number is true for all natural numbers larger than some given one.
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.
For a complex number , the modulus, denoted as , is given by .
A complex number expressed in terms of its modulus and argument , i.e. .
If is a statement then the statement ‘not ’ is the negation of . The negation of is denoted by or .
Law 1: an object will remain at rest, or continue moving with the same speed and in the same direction, unless acted upon by a net external force.
Law 2: the acceleration of an object is proportional to the forces applied, that is, .
Law 3: for every action, there is an equal and opposite reaction.
In the fraction , is the numerator. If an object is divided into equal parts, then the fraction represents of these parts all together.
For example, if a line segment is divided into 5 equal parts, each of these parts is one-fifth () of the whole and 3 of these parts taken together corresponds to the fraction .
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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A correspondence between two sets where each element of one set is paired with one and only one element of another set.
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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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.
A visual representation of the geometric constructions of vector addition and subtraction. For vectors and represented by directed line segments with the same initial point, the sum and difference are the diagonals of a parallelogram.
A quantity that is characteristic of a system.
In statistics, the population mean and the population standard deviation, and are parameters of the population.
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A type of equation that uses a parameter as the independent variable.
For example, and , are a pair of parametric equations, where different values of the parameter will give different points on the number plane.
A way of splitting a rational expression as a sum of two or more simpler rational expressions, for example:
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 flat surface that extends indefinitely. In 3D Cartesian space, the , and planes are referred to as the coordinate planes.
The complex number can be expressed in polar form as: , where is the modulus of the complex number and is its argument expressed in radians. This is also known as modulus-argument form.
An expression made up of non-negative integer powers of the same variable and coefficients combined using addition, subtraction and multiplication.
The vector running from the origin to a fixed point in the plane. A position vector can also be expressed as a function of time, for example , to describe the changing positions of an object, where and are the - and -coordinates of its position at time .
The argument of a non-zero complex number in the interval , denoted as .
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An object initially propelled by an external force, after which the only forces acting on it are gravity and possibly a resistive force due to its motion through a surrounding medium.
The vector component of in the direction of vector is the projection of a vector onto a vector .
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Image long description: Two vector diagrams both representing vectors, each showing two arrows connected at a point. In the first diagram, the angle between the arrows is acute. One arrow is labelled with boldface a, the other with boldface b, with the b arrow as the longer vector, pointing up and to the right. A dotted line perpendicular to arrow b joins the tip of arrow a. There is an arrow drawn on top of arrow b from the vertex, which is labelled proj b a, with a subscripted b and boldface a. In the second diagram the angle between the arrows is obtuse. One arrow is labelled with boldface a and the other with boldface b, with b as the longer vector, pointing up and to the right. A dotted line perpendicular to arrow b joins the tip of arrow a, pointing up and to the left, to an extension of arrow b, pointing down and to the left. The arrow drawn on top of arrow b from the vertex is labelled proj b a with a subscripted b and boldface a.
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 negation of an original statement is assumed but is proven false, usually by deriving a contradiction, so the negation of the original statement cannot be true, that is, the original statement is true.
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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.
An equation of the form , where , and are constants.
Symbols used to specify how many instances of the variable satisfy the statement. and are quantifiers. stands for the phrase ‘for all’, ‘for every’ or ‘for each’. stands for the phrase ‘there exists a’, ‘there is a’ or ‘for some’.
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.
A formula that defines each term of a sequence using a preceding term or preceding terms, for example and defines a geometric sequence with first term and common ratio .
A formula that defines each term of a sequence using a preceding term or preceding terms, for example and defines a geometric sequence with first term and common ratio .
Motion that encounters resisting forces such as air resistance.
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 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 .
The term used to describe real numbers when they are used to multiply (scale) vectors. For example, in , is acting as a scalar.
Also called the dot product. An operation () on two vectors and that outputs a scalar .
The scalar product in two dimensions, for vectors and is . Similarly in three dimensions.
Also, in either two or three dimensions , where is the included angle between and .
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.
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.
Motion in which acceleration is proportional to, and in the opposite direction to, displacement. It is a repetitive movement back and forth through an equilibrium, or central position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.
In three dimensions, lines that do not intersect and are not parallel to each other.
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 theorem to find the limit of a function that is bounded between two other functions: if for all that are near , but not necessarily at , and , then .
A statement is an assertion that is either true or false but not both.
Also referred to as a proposition.
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.
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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In trigonometry, relationships between , and , to the tangent of half the angle. The -formulas are , and where
The constant velocity that a free-falling object approaches as the resistance of the medium through which the object is falling more closely cancels the downward gravitational force.
A theorem describing the relationship between the absolute value of the sum of numbers to the absolute values of those numbers: for real or complex numbers and , or when and are vectors of equal dimension. Geometrically, that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
A circle with a radius of 1 unit.
A quantity having both magnitude and direction.
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 .
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.