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.
and are functions of time that describe the acceleration of an object in the -direction and -direction respectively. is an acceleration vector in two dimensions.
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 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).
A part of a circle’s circumference.
Extended in Mathematics Extension 1: A part of a curve.
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.
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.
See Loading
A discrete probability distribution of a Bernoulli random variable.
Represents the result of a Bernoulli trial. It takes two possible values, a value of 1 representing ‘success’ (with probability ) and a value of 0 representing ‘failure’ (with probability ).
An experiment with only two possible outcomes, often labelled ‘success’ (with probability ) and ‘failure’ (with probability ).
The coefficient of the term in the expansion of . It is written as or where and is given by .
In Pascal’s triangle, the uppermost row is row 0. The entries in row are the binomial coefficients or where of the expansion of .
The discrete probability distribution of the number of successes in a sequence of independent Bernoulli trials, each of which yields success with probability .
The algebraic expansion of a power of a binomial expression. For example, is the binomial expansion of .
Performance of a fixed number of Bernoulli trials.
An algebraic expression with two terms. For example, is a binomial expression in the two terms and .
Represents the number of successes in independent Bernoulli trials.
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 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 .
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.
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.
A selection of distinct objects from distinct objects, where order is not important. The number of such combinations is given by , the binomial coefficient or.
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.
One of the parts of a vector which is parallel to a particular axis or lying in a specified direction.
See Loading
Notation used to express a vector in terms of unit vectors. For example, vectors and can be expressed in component form as and as respectively, where is a unit vector in the -direction, is a unit vector in the -direction, and is a unit vector in the -direction.
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 .
A fixed numerical value. For example, in the algebraic expression , the number 11 is a constant.
A two-dimensional plane formed by two perpendicular number lines, intersecting at the origin. The -plane, the -plane and the -plane are the three coordinate planes.
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.
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.
In Aboriginal communities, an individual charged with maintaining and passing on particular elements of cultural significance, eg language, stories, songs, rituals and imagery.
See Loading
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.
The highest power of that appears in a polynomial .
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 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 .
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.
A part of a line between two endpoints, with fixed length and a direction.
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)
Specifies the probabilities with which a discrete random variable takes each of its values.
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.
Represents the displacement from one point to another.
The length between two points. Distance is a positive scalar quantity.
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 number that is divided or distributed in a division problem. For example, in , 12 is the dividend.
A number which is divided into another number.
In polynomials, is the result of dividing a polynomial by a divisor , that is not the zero polynomial, with quotient and remainder .
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.
See Loading
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 ').
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 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 .
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.
A precise numerical value e.g. as opposed to the approximation .
The number of times that a particular event or outcome is predicted to occur using theoretical probability.
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.
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.
If is a polynomial and for some number , then is divisible by . The factor theorem can be used to obtain factors of a polynomial.
The product of the first positive integers is denoted by , read as ‘ factorial’, that is, , with the definition that .
A value between and .
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 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 .
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).
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.
See Loading
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.
See Loading
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.
See Loading
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 .
is the inverse function of if the relationships and hold.
reverses or undoes the effect of the function .
An inverse function exists for any one-to-one function and has domain the range of the function.
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’.
The coefficient of the term involving the highest power in a polynomial.
The term involving the highest power in a polynomial.
Something that can be represented or modelled by a straight line.
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.
See Loading
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.
See Loading
A common S-shaped curve with the equation where , and are constants, and is the carrying capacity.
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.
The sum of values in a data set divided by the total number of values in the data set. Also called the average.
A point on a line segment or interval that divides the segment into 2 equal parts.
Let and be points in the Cartesian plane. Then the midpoint of line segment has coordinates .
This can be seen from the congruent triangles below.
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.
A polynomial in which the coefficient of the leading term is 1.
If one event has possible outcomes and a second independent event has possible outcomes, then there is a total of possible outcomes for the two combined events.
The number of times a particular number is a zero for a given polynomial or a root for a polynomial equation.
An angle bigger than a right angle (90°) but smaller than a straight angle (2 right angles, or 180°).
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.
See Loading
Taking place on Aboriginal land or Country of origin.
See Loading
A correspondence between two sets where each element of one set is paired with one and only one element of another set.
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.
See Loading
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.
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.
See Loading
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 triangular figure with rows of numbers starting and ending with 1, where each interior number is equal to the sum of the two numbers immediately above it.
See Loading
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 .
An arrangement of distinct objects taken from distinct objects where order is important, where . The number of such permutations is denoted by , and is given by .
Two lines, rays, line segments, vectors, planes or other objects that intersect at a 90° angle (a right angle).
A point on a curve where the concavity changes. At a point of inflection, the tangent exists and crosses the curve.
An expression made up of non-negative integer powers of the same variable and coefficients combined using addition, subtraction and multiplication.
The complete set of individuals, objects, places, etc, that we want information about.
Extended in Mathematics Standard and Mathematics Extension 1: In statistics it is the entire dataset from which a statistical sample may be drawn.
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 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 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 .
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 .
.
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 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 expression of the form , where , and are constants.
A function of the form , where , and are constants.
The result of dividing one number or algebraic expression by another.
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.
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.
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 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 .
The part 'left over' when dividing a number into equal groups. The remainder forms part of the next group.
Extended in 7–10: The amount left over when one number or algebraic quantity is divided by another . If is divisible by , then the remainder is 0. For example, when 68 is divided by 11, the remainder is 2, because 68 can be expressed as .
Extended in Mathematics Extension 1: What is left over after a division. When division of a polynomial by a non-zero polynomial gives , where the degree of is less than the degree of , then is the remainder.
A rule to determine the remainder when one polynomial is divided by a linear polynomial . The remainder is equal to .
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 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 sum of the values in a sample of data, divided by the total number of values in the sample, denoted .
The distribution of a sample statistic over all samples of the same size.
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 .
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.
A graphical representation of the tangent lines to the solutions of a first-order differential equation.
A statement is an assertion that is either true or false but not both.
Also referred to as a proposition.
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.
See Loading
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.
See Loading
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 .
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 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.
For vector addition, when two vectors are represented as two sides of a triangle, the third side represents the resultant vector:
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 vector with a magnitude of 1.
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.
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 .
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 polynomial which has all coefficients equal to zero.
The vector of magnitude 0, namely in two dimensions and in three dimensions. Denoted as When handwritten, it is expressed as , to be distinguished from the number 0.