# Glossary

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###### ATAR

view_agenda book_2Australian Tertiary Admission Rank

###### Accomplished

view_agenda book_2Highly trained or skilled in a particular activity; perfected in knowledge or training; expert

###### Accuracy

view_agenda book_2For all real numbers \(x, x^2 \geq 0\) (re: real numbers \(x, x^2 \geq 0\))

###### Accurate

view_agenda book_2Precise and exact; to the point; consistent with or exactly conforming to a truth, standard, rule, model, convention or known facts; free from error or defect; meticulous; correct in all details

###### Addition and subtraction of matrices

view_agenda book_2Addition of matrices if A and B are matrices with the same dimensions and the entries of A are \(a_{ij}\), and the entries of B are \(b_{ij}\), then the entries of A + B are \(a_{ij} + b_{ij}\) Subtraction of matrices if A and B are matrices with the same dimensions and the entries of A are \(a_{ij}\), and the entries of B are \(b_{ij}\), then the entries of A − B are \(a_{ij} − b_{ij}\)

###### Addition and subtraction of vectors

view_agenda book_2Given vectors a and b let \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) be directed line segments that represent a and b; they have the same initial point O; the sum of \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) is the directed line segment \(\overrightarrow{OC}\) where C is a point such that OACB is a parallelogram; this is known as the parallelogram rule if \(a = \left(\begin{array}{c} a_1 \end{array} \right)\) and \(b = \left(\begin{array}{c} b_1 \end{array} \right)\), then \(a + b = \left(\begin{array}{c} a_1 + b_1 \end{array} \right)\) in component form if \(a = a_1i + a_2j\) and \(b = b_1i + b_2j\), then \(a + b = (a_1 + b_1)i + (a_2 + b_2)j\) Subtraction of vectors \(a − b = a + (−b)\)

###### Adept

view_agenda book_2Very/highly skilled or proficient at something; expert

###### Adequate

view_agenda book_2Satisfactory or acceptable in quality or quantity equal to the requirement or occasion

###### Algorithm

view_agenda book_2A precisely defined procedure that can be applied and systematically followed through to a conclusion

###### Alternate Segment

view_agenda book_2The word alternate means other; the chord AB divides the circle into two segments and AU is tangent to the circle; angle APB

###### Analyse

view_agenda book_2Dissect to ascertain and examine constituent parts and/or their relationships; break down or examine in order to identify the essential elements, features, components or structure; determine the logic and reasonableness of information; examine or consider something in order to explain and interpret it, for the purpose of finding meaning or relationships and identifying patterns, similarities and differences

###### Angle sum, difference and double-angle identities for sine and cosine ratios

view_agenda book_2Angle sum and difference identities \(\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)\) \(\sin(A - B) = \sin(A)\cos(B) - \sin(B)\cos(A)\) \(\cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B)\) \(\cos(A - B) = \cos(A)\cos(B) + \sin(A)\sin(B)\) Double-angle identities \(\sin(2A) = 2\sin(A)\cos(A)\) \(\cos(2A) = \cos^2(A) - \sin^2(A)\) = 2\cos^2(A) - 1 = 1 - 2\sin^2(A)\)

###### Applied Learning

view_agenda book_2The acquisition and application of knowledge, understanding and skills in real-world or lifelike contexts that may encompass workplace, industry and community situations; it emphasis learning through doing and includes both theory and the application of theory, connecting subject knowledge and understanding with the development of practical skills

###### Applied Subject

view_agenda book_2A subject whose primary pathway is work and vocational education; it emphasises applied learning and community connections; a subject for which a syllabus has been developed by the QCAA with the following characteristics: results from courses developed from Applied syllabuses contribute to the QCE; results may contribute to ATAR calculations

###### Apply

view_agenda book_2Use knowledge and understanding in response to a given situation or circumstance; carry out or use a procedure in a given or particular situation

###### Appraise

view_agenda book_2Evaluate the worth, significance or status of something; judge or consider a text or piece of work

###### Appreciate

view_agenda book_2Recognize or make a judgment about the value or worth of something; understand fully; grasp the full implications of something

###### Appropriate

view_agenda book_2Acceptable; suitable or fitting for a particular purpose, circumstance, context, etc.

###### Apt

view_agenda book_2Suitable to the purpose or occasion; fitting, appropriate

###### Arcosine Function

view_agenda book_2If the domain of the cosine function y = cos(x) is restricted to the interval \([0, \pi]\), a one to one function is formed and so an inverse function exists denoted by \(y = \cos^{-1}(x)\) or arccos(x). The arcosine function is defined by: \(\cos^{-1}: [-1,1] \rightarrow [0, \pi], \cos^{-1}(x) = y\) where \(\cos(y) = x, y \in [0, \pi]\)

###### Arcsine Function

view_agenda book_2If the domain of the sine function y = sin(x) is restricted to the interval \([- \frac{\pi}{2}, \frac{\pi}{2}]\), a one to one function is formed and so an inverse function exists denoted by \(y = \sin^{-1}(x)\) or arcsin(x). The arcsine function is defined by: \(\sin^{-1}: [-1,1] \rightarrow [- \frac{\pi}{2}, \frac{\pi}{2}], \sin^{-1}(x) = y\) where \(\sin(y) = x, y \in [- \frac{\pi}{2}, \frac{\pi}{2}]\)

###### Arctangent Function

view_agenda book_2If the domain of the tangent function y = tan(x) is restricted to the interval \([-\frac{\pi}{2}, \frac{\pi}{2}]\), a one to one function is formed and so an inverse tangent function exists denoted by \(y = \tan^{-1}(x)\) or arctan(x). The arctangent function is defined by: \(\tan^{-1}: \mathbb{R} \rightarrow \left(-\frac{\pi}{2}, \frac{\pi}{2}\right), \tan^{-1}(x) = y\) where \(\tan(y) = x, y \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)

###### Area of Study

view_agenda book_2A division of, or a section within a unit

###### Argue

view_agenda book_2Give reasons for or against something; challenge or debate an issue or idea; persuade, prove or try to prove by giving reasons

###### Argument

view_agenda book_2(Of a complex number) if represented by a point P in the complex plane, then the argument of z, denoted by arg z, is the angle \(\theta\) that OP makes with the positive real axis Ox, with the angle \(\theta\) measured anticlockwise from Ox; the principal value of the argument is the one in the interval \((- \pi, \pi])

###### Aspect

view_agenda book_2A particular part of a feature of something; a facet, phase or part of a whole

###### Assess

view_agenda book_2Measure, determine, evaluate, estimate or make a judgment about the value, quality, outcomes, results, size, significance, nature or extent of something

###### Assessment

view_agenda book_2Purposeful and systematic collection of information about students' achievements

###### Assessment Instrument

view_agenda book_2A tool or device used to gather information about student achievement

###### Assessment Objectives

view_agenda book_2Drawn from the unit objectives and contextualised for the requirements of the assessment instrument (see also 'syllabus objectives', 'unit objectives')

###### Assessment Technique

view_agenda book_2The method used to gather evidence about student achievement, (e.g. examination, project, investigation)

###### Assumptions

view_agenda book_2Conditions that are stated to be true when beginning to solve a problem

###### Astute

view_agenda book_2Showing an ability to accurately assess situations or people; of keen discernment

###### Authoritative

view_agenda book_2Able to be trusted as being accurate or true; reliable; commanding and self-confident; likely to be respected and obeyed

###### Balanced

view_agenda book_2Keeping or showing a balance; not biased; fairly judged or presented; taking everything into account in a fair, well-judged way

###### Basic

view_agenda book_2Fundamental

###### Binomial Theorem

view_agenda book_2The expansion \( (x + y)^n = x^n + (n_1)x^{n-1}y + ... + (n_r)x^{n-r}y^r + ... + y^n \)

###### Calculate

view_agenda book_2Determine or find (e.g. a number, answer) by using mathematical processes; obtain a numerical answer showing the relevant stages in the working; ascertain/determine from given facts, figures or information

###### Cartesian Equation of a Plane

view_agenda book_2When \( \mathbf{n} = \left( b_1, b_2, b_3 \right) \) is a vector normal to a plane in three-dimensional space; the plane consists of all points \( P(x, y, z) \) whose Cartesian equation is \( ax + by + cz + d = 0 \)

###### Cartesian Equation of a Straight Line

view_agenda book_2Let \( \mathbf{a} = \left( \frac{a_1}{a_2}, a_3 \right) \) be the position vector of any point on a straight line in three-dimensional space and \( \mathbf{d} = \left( \frac{d_1}{d_2}, d_3 \right) \) be any vector with direction along the line; the line consists of all points \( P(x, y, z) \) whose Cartesian equation is \( \frac{x - a_1}{d_1} = \frac{y - a_2}{d_2} = \frac{z - a_3}{d_3} \)

###### Categorise

view_agenda book_2Place in or assign to a particular class or group; arrange or order by classes or categories; classify, sort out, sort, separate

###### Challenging

view_agenda book_2Difficult but interesting; testing one's abilities; demanding and thought-provoking; usually involving unfamiliar or less familiar elements

###### Characteristic

view_agenda book_2A typical feature or quality

###### Clarify

view_agenda book_2Make clear or intelligible; explain; make a statement or situation less confused and more comprehensible

###### Clarity

view_agenda book_2Clearness of thought or expression; the quality of being coherent and intelligible; free from obscurity of sense; without ambiguity; explicit; easy to perceive, understand or interpret

###### Classify

view_agenda book_2Arrange, distribute or order in classes or categories according to shared qualities or characteristics

###### Clear

view_agenda book_2Free from confusion, uncertainty, or doubt; easily seen, heard or understood

###### Clearly

view_agenda book_2In a clear manner; plainly and openly, without ambiguity

###### Coherent

view_agenda book_2Having a natural or due agreement of parts; connected; consistent; logical; orderly; well-structured and makes sense; rational, with parts that are harmonious; having an internally consistent relation of parts

###### Cohesive

view_agenda book_2Characterised by being united, bound together or having integrated meaning; forming a united whole

###### Combinations

view_agenda book_2The number of selections of \(n\) objects taken \(r\) at a time (that is, the number of ways of selecting \(r\) objects out of \(n\) is denoted by \(_nC_r\), and is equal to \(\frac{n!}{r!(n-r)!}\))

###### Comment

view_agenda book_2Express an opinion, observation or reaction in speech or writing; give a judgment based on a given statement or result of a calculation

###### Communicate

view_agenda book_2Convey knowledge and/or understandings to others; make known; transmit

###### Compare

view_agenda book_2Display recognition of similarities and differences and recognise the significance of these similarities and differences

###### Competent

view_agenda book_2Having suitable or sufficient skills, knowledge, experience, etc. for some purpose; adequate but not exceptional; capable; suitable or sufficient for the purpose

###### Competently

view_agenda book_2In an efficient and capable way; in an acceptable and satisfactory, though not outstanding, way

###### Complex

view_agenda book_2Composed or consisting of many different and interconnected parts or factors; compound; composite; characterised by an involved combination of parts; complicated; intricate; a complex whole or system; a complicated assembly of particulars

###### Complex Arithmetic

view_agenda book_2If \(z_1 = x_1 + y_1i\) and \(z_2 = x_2 + y_2i\), then \(z_1 + z_2 = x_1 + x_2 + (y_1 + y_2)i\), \(z_1 - z_2 = x_1 - x_2 + (y_1 - y_2)i\), \(z_1 \times z_2 = x_1x_2 - y_1y_2 + (x_1y_2 + x_2y_1)i\)

###### Complex Conjugate

view_agenda book_2For any complex number \(z = x + yi\), its conjugate is \(\overline{z} = x - yi\)

###### Complex Familiar

view_agenda book_2Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where: relationships and interactions have a number of elements, such that connections are made with subject matter within and/or across the domains of mathematics; and all of the information to solve the problem is identifiable; that is - the required procedure is clear from the way the problem is posed, or - in a context that has been a focus of prior learning. Some interpretation, clarification and analysis will be required to develop responses. These problems can focus on any of the objectives.

###### Complex Number Forms

view_agenda book_2Complex numbers can be expressed in various forms including: \( z = x + yi = r(\cos(\theta) + i\sin(\theta)) = r\text{cis}(\theta) \) where \( r = |z| = \sqrt{x^2 + y^2} \) and \( \arg(z) = \theta \), \( \tan(\theta) = \frac{y}{x} \), \(-\pi < \theta \le \pi \).

###### Complex Plane

view_agenda book_2A geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis; sometimes called the Argand plane.

###### Complex Unfamiliar

view_agenda book_2Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where: relationships and interactions have a number of elements, such that connections are made with subject matter within and/or across the domains of mathematics; and all the information to solve the problem is not immediately identifiable; that is - the required procedure is not clear from the way the problem is posed, and - in a context in which students have had limited prior experience. Students interpret, clarify and analyse problems to develop responses. Typically, these problems focus on objectives 4, 5 and 6.

###### Comprehend

view_agenda book_2Understand the meaning or nature of; grasp mentally.

###### Comprehensive

view_agenda book_2Inclusive; of large content or scope; including or dealing with all or nearly all elements or aspects of something; wide-ranging; detailed and thorough, including all that is relevant.

###### Concise

view_agenda book_2Expressing much in few words; giving a lot of information clearly and in a few words; brief, comprehensive and to the point; succinct, clear, without repetition of information

###### Concisely

view_agenda book_2In a way that is brief but comprehensive; expressing much in few words; clearly and succinctly

###### Conduct

view_agenda book_2Direct in action or course; manage; organise; carry out

###### Confidence Interval

view_agenda book_2Provides a range of values that describe the uncertainty surrounding an estimate

###### Consider

view_agenda book_2Think deliberately or carefully about something, typically before making a decision; take something into account when making a judgment; view attentively or scrutinise; reflect on

###### Considerable

view_agenda book_2Fairly large or great; thought about deliberately and with a purpose

###### Considered

view_agenda book_2Formed after careful and deliberate thought

###### Consistent

view_agenda book_2Agreeing or accordant; compatible; not self-opposed or self-contradictory, constantly adhering to the same principles; acting in the same way over time, especially so as to be fair or accurate; unchanging in nature, standard, or effect over time; not containing any logical contradictions (of an argument); constant in achievement or effect over a period of time

###### Construct

view_agenda book_2Create or put together (e.g. an argument) by arranging ideas or items; display information in a diagrammatic or logical form; make; build

###### Context

view_agenda book_2A group of related situations, phenomena, technical applications and social issues likely to be encountered by students; can provide a meaningful application of concepts in real-world applications; in Specialist Mathematics, a framework for linking concepts and learning experiences that enables students to identify and understand the application of mathematics to their world

###### Contradiction

view_agenda book_2In Specialist Mathematics, assume the opposite (negation) of what you are trying to prove; then proceed through a logical chain of argument until you reach a demonstrably false conclusion; since all the reasoning is correct and a false conclusion has been reached, the only thing that could be wrong is the initial assumption; therefore, the original statement is true

###### Contrapositive

view_agenda book_2The contrapositive of the statement

###### Contrast

view_agenda book_2Display recognition of differences by deliberate juxtaposition of contrary elements; show how things are different or opposite; give an account of the differences between two or more items or situations, referring to both or all of them throughout

###### Controlled

view_agenda book_2Shows the exercise of restraint or direction over; held in check; restrained, managed or kept within certain bounds

###### Convention

view_agenda book_2The generally agreed upon way in which something is done; in a mathematical context this refers to notation, symbols, abbreviations, usage and setting out

###### Converse

view_agenda book_2In Specialist Mathematics, the converse of the statement if \( p \) then \( q \) is if \( q \) then \( p \); symbolically the converse of \( p \rightarrow q \) is: \( q \rightarrow p \); the converse of a true statement need not be true

###### Convert

view_agenda book_2To change into a different form

###### Convincing

view_agenda book_2Persuaded by argument or proof; leaving no margin of doubt; clear; capable of causing someone to believe that something is true or real; persuading or assuring by argument or evidence; appearing worthy of belief; credible or plausible

###### Counter-example

view_agenda book_2An example that demonstrates that a statement is not true

###### Course

view_agenda book_2A defined amount of learning developed from a subject syllabus or alternative sequence

###### Create

view_agenda book_2Bring something into being or existence; produce or evolve from one's own thought or imagination; reorganise or put elements together into a new pattern or structure or to form a coherent or functional whole

###### Creative

view_agenda book_2Resulting from originality of thought or expression; relating to or involving the use of the imagination or original ideas to create something; having good imagination or original ideas

###### Credible

view_agenda book_2Capable or worthy of being believed; believable; convincing

###### Criterion

view_agenda book_2The property or characteristic by which something is judged or appraised

###### Critical

view_agenda book_2Involving skilful judgement as to truth, merit, etc.; involving the objective analysis and evaluation of an issue in order to form a judgment; expressing or involving an analysis of the merits and faults of a work of literature, music, or art; incorporating a detailed and scholarly analysis and commentary (of a text); rationally appraising for logical consistency and merit

###### Critique

view_agenda book_2Review (e.g., a theory, practice, performance) in a detailed, analytical and critical way

###### Cursory

view_agenda book_2Hasty, and therefore not thorough or detailed; performed with little attention to detail; going rapidly over something, without noticing details; hasty; superficial

###### Cyclic Quadrilateral

view_agenda book_2A quadrilateral whose vertices all lie on a circle

###### De Moivre’s theorem

view_agenda book_2For all integers \(n\), \( \cos(\theta) + i \sin(\theta))^n = \cos(n\theta) + i \sin(n\theta) \), or alternatively if \( z = r\cos(\theta) \) then \( z^n = r^n \cos(n\theta) \)

###### Decide

view_agenda book_2Reach a resolution as a result of consideration; make a choice from a number of alternatives

###### Deduce

view_agenda book_2Reach a conclusion that is necessarily true, provided a given set of assumptions is true; arrive at, reach or draw a logical conclusion from reasoning and the information given

###### Defensible

view_agenda book_2Justifiable by argument; capable of being defended in argument

###### Define

view_agenda book_2Give the meaning of a word, phrase, concept or physical quantity; state meaning and identify or describe qualities

###### Demonstrate

view_agenda book_2Prove or make clear by argument, reasoning or evidence, illustrating with practical example; show by example; give a practical exhibition

###### Derive

view_agenda book_2Arrive at by reasoning; manipulate a mathematical relationship to give a new equation or relationship; in mathematics, obtain the derivative of a function

###### Describe

view_agenda book_2Give an account (written or spoken) of a situation, event, pattern or process, or of the characteristics or features of something

###### Design

view_agenda book_2Produce a plan, simulation, model or similar; plan, form or conceive in the mind; in English, select, organise and use particular elements in the process of text construction for particular purposes; these elements may be linguistic (words), visual (images), audio (sounds), gestural (body language), spatial (arrangement on the page or screen) and multimodal (a combination of more than one)

###### Detailed

view_agenda book_2Executed with great attention to the fine points; meticulous; including many of the parts or facts

###### Determinant

view_agenda book_2For a \(2 \times 2\) matrix, if \(A = \left[ \begin{array}{cc} a & b \\ c & d \end{array} \right]\) the determinant of A denoted as \( \text{det } A = ad - bc \)

###### Determine

view_agenda book_2Establish, conclude or ascertain after consideration, observation, investigation or calculation; decide or come to a resolution

###### Develop

view_agenda book_2Elaborate, expand or enlarge in detail; add detail and fullness to; cause to become more complex or intricate

###### Devise

view_agenda book_2Think out; plan; contrive; invent

###### Differentiate

view_agenda book_2Identify the difference/s in or between two or more things; distinguish, discriminate; recognise or ascertain what makes something distinct from similar things; in mathematics, obtain the derivative of a function

###### Discerning

view_agenda book_2Discriminating; showing intellectual perception; showing good judgment; making thoughtful and astute choices; selected for value or relevance

###### Discriminate

view_agenda book_2Note, observe or recognise a difference; make or constitute a distinction in or between; differentiate; note or distinguish as different

###### Discriminating

view_agenda book_2Differentiating; distinctive; perceiving differences or distinctions with nicety; possessing discrimination; perceptive and judicious; making judgments about quality; having or showing refined taste or good judgment

###### Discuss

view_agenda book_2Examine by argument; sift the considerations for and against; debate; talk or write about a topic, including a range of arguments, factors or hypotheses; consider, taking into account different issues and ideas, points for and/or against, and supporting opinions or conclusions with evidence

###### Disjointed

view_agenda book_2Disconnected; incoherent; lacking a coherent order/sequence or connection

###### Distinguish

view_agenda book_2Recognise as distinct or different; note points of difference between; discriminate; discern; make clear a difference/s between two or more concepts or items

###### Diverse

view_agenda book_2Of various kinds or forms; different from each other

###### Document

view_agenda book_2Support (e.g. an assertion, claim, statement) with evidence (e.g. decisive information, written references, citations)

###### Domains of Mathematics

view_agenda book_2A particular taxonomic classification used to group similar mathematics concepts, ideas, knowledge, understandings and skills; the scope and range of mathematics subject matter

###### Draw Conclusions

view_agenda book_2Make a judgment based on reasoning and evidence

###### Effective

view_agenda book_2Successful in producing the intended, desired or expected result; meeting the assigned purpose

###### Efficient

view_agenda book_2Working in a well-organised and competent way; maximum productivity with minimal expenditure of effort; acting or producing effectively with a minimum of waste, expense or unnecessary effort

###### Element

view_agenda book_2A component or constituent part of a complex whole; a fundamental, essential or irreducible part of a composite entity

###### Elementary

view_agenda book_2Simple or uncompounded; relating to or dealing with elements, rudiments or first principles (of a subject); of the most basic kind; straightforward and uncomplicated

###### Equivalent Statements

view_agenda book_2Statements P and Q are equivalent if \( P \iff Q \) and \( Q \iff P \); the symbol \(\iff\) is used; it is also written as P if and only if Q or P if Q

###### Erroneous

view_agenda book_2Based on or containing error; mistaken; incorrect

###### Essential

view_agenda book_2Absolutely necessary; indispensable; of critical importance for achieving something

###### Evaluate

view_agenda book_2Make an appraisal by weighing up or assessing strengths, implications and limitations; make judgments about ideas, works, solutions or methods in relation to selected criteria; examine and determine the merit, value or significance of something, based on criteria

###### Examination

view_agenda book_2A supervised test that assesses the application of a range of cognitions to one or more provided items such as questions, scenarios and/or problems; student responses are completed individually, under supervised conditions, and in a set timeframe

###### Examine

view_agenda book_2Investigate, inspect or scrutinise; inquire or search into; consider or discuss an argument or concept in a way that uncovers the assumptions and interrelationships of the issue

###### Experiment

view_agenda book_2Try out or test new ideas or methods, especially in order to discover or prove something; undertake or perform a scientific procedure to test a hypothesis, make a discovery or demonstrate a fact

###### Explain

view_agenda book_2Make an idea or situation plain or clear by describing it in more detail or revealing relevant facts; give an account; provide additional information

###### Explicit

view_agenda book_2Clearly and distinctly expressing all that is meant; unequivocal; clearly developed or formulated; leaving nothing merely implied or suggested

###### Explore

view_agenda book_2Look into both closely and broadly; scrutinize; inquire into or discuss something in detail

###### Express

view_agenda book_2Convey, show or communicate (e.g. a thought, opinion, feeling, emotion, idea or viewpoint); in words, art, music or movement, convey or suggest a representation of; depict

###### Extended response

view_agenda book_2An open-ended assessment technique that focuses on the interpretation, analysis, examination and/or evaluation of ideas and information in response to a particular situation or stimulus; while students may undertake some research when writing of the extended response, it is not the focus of this technique; an extended response occurs over an extended and defined period of time

###### Extension subject

view_agenda book_2A two-unit subject for which a syllabus has been developed by QCAA, that is an extension of one or more General or alternative sequence subject/s, studied concurrently with, the final two units of that subject or after completion of, the final two units of that subject

###### Extensive

view_agenda book_2Of great extent; wide; broad; far-reaching; comprehensive; lengthy; detailed; large in amount or scale

###### External assessment

view_agenda book_2Summative assessment that occurs towards the end of a course of study and is common to all schools; developed and marked by the QCAA according to a commonly applied marking scheme

###### External examination

view_agenda book_2A supervised test, developed and marked by the QCAA, that assesses the application of a range of cognitions to multiple provided items such as questions, scenarios and/or problems; student responses are completed individually, under supervised conditions, and in a set timeframe

###### Extrapolate

view_agenda book_2Infer or estimate by extending or projecting known information; conjecture; infer from what is known; extend the application of something (e.g. a method or conclusion) to an unknown situation by assuming that existing trends will continue or similar methods will be applicable

###### Factual

view_agenda book_2Relating to or based on facts; concerned with what is actually the case; actually occurring; having verified existence

###### Familiar

view_agenda book_2Well-acquainted; thoroughly conversant with; well known from long or close association; often encountered or experienced; common; (of materials, texts, skills or circumstances) having been the focus of learning experiences or previously encountered in prior learning activities

###### Feasible

view_agenda book_2Capable of being achieved, accomplished or put into effect; reasonable enough to be believed or accepted; probable; likely

###### Fluent

view_agenda book_2Spoken or written with ease; able to speak or write smoothly, easily or readily; articulate; eloquent; in artistic performance, characteristic of a highly developed and excellently controlled technique; flowing; polished; flowing smoothly, easily and effortlessly

###### Fluently

view_agenda book_2In a graceful and seemingly effortless manner; in a way that progresses smoothly and readily

###### Formative assessment

view_agenda book_2Assessment whose major purpose is to improve teaching and student achievement

###### Fragmented

view_agenda book_2Disorganised; broken down; disjointed or isolated

###### Frequent

view_agenda book_2Happening or occurring often at short intervals; constant, habitual, or regular

###### Fundamental

view_agenda book_2Forming a necessary base or core; of central importance; affecting or relating to the essential nature of something; part of a foundation or basis

###### General subject

view_agenda book_2A subject for which a syllabus has been developed by the QCAA with the following characteristics: results from courses developed from General syllabuses contribute to the QCE; General subjects have an external assessment component; results may contribute to ATAR calculations

###### Generate

view_agenda book_2Produce; create; bring into existence

###### Hypothesise

view_agenda book_2Formulate a supposition to account for known facts or observed occurrences; conjecture, theorise, speculate; especially on uncertain or tentative grounds

###### ISMG

view_agenda book_2Instrument-specific marking guide; a tool for marking that describes the characteristics evident in student responses and aligns with the identified objectives for the assessment (see

###### Identify

view_agenda book_2Distinguish; locate, recognise and name; establish or indicate who or what someone or something is; provide an answer from a number of possibilities; recognise and state a distinguishing factor or feature

###### Identities for products of sine and cosine ratios

view_agenda book_2\(\cos(A) \cos(B) = \frac{1}{2}(\cos(A - B) + \cos(A + B))\); \(\sin(A) \sin(B) = \frac{1}{2}(\cos(A - B) - \cos(A + B))\); \(\sin(A) \cos(B) = \frac{1}{2}(\sin(A + B) + \sin(A - B))\); \(\cos(A) \sin(B) = \frac{1}{2}(\sin(A + B) - \sin(A - B))\)

###### Illogical

view_agenda book_2Lacking sense or sound reasoning; contrary to or disregarding of the rules of logic; unreasonable

###### Imaginary part of a complex number

view_agenda book_2A complex number \( z \) may be written as \( x + yi \), where \( x \) and \( y \) are real, and \( y \) is the imaginary part of \( z \); it is denoted by \( \Im(z) \)

###### Implement

view_agenda book_2Put something into effect, e.g. a plan or proposal

###### Implication

view_agenda book_2In Specialist Mathematics, if \( P \) then \( Q \) symbol: \( P \Rightarrow Q \)

###### Implicit

view_agenda book_2Implied, rather than expressly stated; not plainly expressed; capable of being inferred from something else

###### Implicit differentiation

view_agenda book_2In Specialist Mathematics, implicit differentiation consists of differentiating each term of an equation as it stands and making use of the chain rule; this can lead to a formula for \( \frac{dy}{dx} \); for example, if \( x^2 + xy^3 - 2x + 3y = 0 \), then \( 2x + x(3y^2) \frac{dy}{dx} + y^3 - 2 + 3 \frac{dy}{dx} = 0 \), and so \( \frac{dy}{dx} = \frac{-2x-y^3+2}{x3y^2+3} \)

###### Improbable

view_agenda book_2Not probable; unlikely to be true or to happen; not easy to believe

###### In-depth

view_agenda book_2Comprehensive and with thorough coverage; extensive or profound; well-balanced or fully developed

###### Inaccurate

view_agenda book_2Not accurate

###### Inappropriate

view_agenda book_2Not suitable or proper in the circumstances

###### Inclusion–exclusion principle

view_agenda book_2Suppose \( A \) and \( B \) are subsets of a finite set \( X \) then \( |A \cup B| = |A| + |B| - |A \cap B| \). Suppose \( A, B \) and \( C \) are subsets of a finite set \( X \) then \( |A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C| \). This result can be generalised to four or more sets

###### Inconsistent

view_agenda book_2Lacking agreement, as one thing with another, or two or more things in relation to each other; at variance; not consistent; not in keeping; not in accordance; incompatible, incongruous

###### Independent

view_agenda book_2Thinking or acting for oneself, not influenced by others

###### Infer

view_agenda book_2Derive or conclude something from evidence and reasoning, rather than from explicit statements; listen or read beyond what has been literally expressed; imply or hint at

###### Informed

view_agenda book_2Knowledgeable; learned; having relevant knowledge; being conversant with the topic; based on an understanding of the facts of the situation (of a decision or judgment)

###### Innovative

view_agenda book_2New and original; introducing new ideas; original and creative in thinking

###### Insightful

view_agenda book_2Showing understanding of a situation or process; understanding relationships in complex situations; informed by observation and deduction

###### Instrument-specific marking guide

view_agenda book_2ISM; a tool for marking that describes the characteristics evident in student responses and aligns with the identified objectives for the assessment (see

###### Integer

view_agenda book_2The numbers \(-\infty,...,-3,-2,-1,0,1,2,3,...\infty\)

###### Integral

view_agenda book_2Adjective: Necessary for the completeness of the whole; essential or fundamental; Noun: In mathematics, the result of integration; an expression from which a given function, equation, or system of equations is derived by differentiation

###### Intended

view_agenda book_2Designed; meant; done on purpose; intentional

###### Internal assessment

view_agenda book_2Assessments that are developed by schools; summative internal assessments are endorsed by the QCAA before use in schools and results externally confirmed contribute towards a student's final result

###### Interpret

view_agenda book_2Use knowledge and understanding to recognise trends and draw conclusions from given information; make clear or explicit; elucidate or understand in a particular way; Bring out the meaning of, e.g., a dramatic or musical work, by performance or execution; bring out the meaning of an artwork by artistic representation or performance; give one's own interpretation of; Identify or draw meaning from, or give meaning to, information presented in various forms, such as words, symbols, pictures or graphs

###### Investigate

view_agenda book_2Carry out an examination or formal inquiry in order to establish or obtain facts and reach new conclusions; search, inquire into, interpret and draw conclusions about data and information

###### Investigation

view_agenda book_2An assessment technique that requires students to research a specific problem, question, issue, design challenge or hypothesis through the collection, analysis and synthesis of primary and/or secondary sources

###### Irrational numbers

view_agenda book_2A real number is irrational if it cannot be expressed as a quotient of two integers

###### Irrelevant

view_agenda book_2Not relevant; not applicable or pertinent; not connected with or relevant to something

###### Isolated

view_agenda book_2Detached, separate, or unconnected with other things; one-off; something set apart or characterised as different in some way

###### Judge

view_agenda book_2Form an opinion or conclusion about; apply both procedural and deliberative operations to make a determination

###### Justified

view_agenda book_2Sound reasons or evidence are provided to support an argument, statement or conclusion

###### Justify

view_agenda book_2Give reasons or evidence to support an answer, response or conclusion; show or prove how an argument, statement or conclusion is right or reasonable

###### Learning area

view_agenda book_2A grouping of subjects, with related characteristics, within a broad field of learning, e.g., the Arts, sciences, languages

###### Linear transformations in two dimensions

view_agenda book_2A linear transformation in the plane is a mapping of the form \(T(x,y) = (ax + by, cx + dy)\); a transformation \(T\) is linear if and only if \(T(ax_{1},y_{1}) + T(bx_{2},y_{2}) = aT(x_{1},y_{1}) + bT(x_{2},y_{2})\); linear transformations include: dilations modelled by the matrix \(\left[ \begin{array}{cc} k & 0 \\ 0 & l \end{array} \right]\), rotations of angle \(\theta\) about the origin modelled by the matrix \(\left[ \begin{array}{cc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array} \right]\), reflections in the line \(y = x\tan(\theta)\) modelled by the matrix \(\left[ \begin{array}{cc} \cos(2\theta) & \sin(2\theta) \\ \sin(2\theta) & -\cos(2\theta) \end{array} \right]\); translations are not linear transformations

###### Logical

view_agenda book_2Rational and valid; internally consistent; reasonable; reasoning in accordance with the principles/rules of logic or formal argument; characterised by or capable of clear, sound reasoning; (of an action, decision, etc.) expected or sensible under the circumstances

###### Logically

view_agenda book_2According to the rules of logic or formal argument; in a way that shows clear, sound reasoning; in a way that is expected or sensible

###### Logistic Equation

view_agenda book_2The logistic equation has applications in a range of fields, including biology, biomathematics, economics, chemistry, mathematical psychology, probability, and statistics. One form of this differential equation is: \(\frac{dy}{dt} = ay - by^2\) (where \(a > 0\) and \(b > 0\)). The general solution of this is: \(y = \frac{be^{at}}{b+c e^{at}}\), where \(C\) is an arbitrary constant

###### Magnitude of a Vector

view_agenda book_2The magnitude of a vector \( \vec{a} \) is the length of any directed line segment that represents \( \vec{a} \); it is denoted by \( |\vec{a}| \); this can be represented in two dimensions by \( |\vec{a}| = \sqrt{a_1^2 + a_2^2} \) and in three dimensions by \( |\vec{a}| = \sqrt{a_1^2 + a_2^2 + a_3^2} \)

###### Make Decisions

view_agenda book_2Select from available options; weigh up positives and negatives of each option and consider all the alternatives to arrive at a position

###### Manipulate

view_agenda book_2Adapt or change to suit one's purpose

###### Mathematical Model

view_agenda book_2A depiction of a situation that expresses relationships using mathematical concepts and language, usually as an algebraic, diagrammatic, graphical or tabular representation

###### Mathematical Modelling

view_agenda book_2Involves: formulating a mathematical representation of a problem derived from within a real-world context; using mathematics concepts and techniques to obtain results; interpreting the results by referring back to the original problem context; revising the model (where necessary)

###### Matrix

view_agenda book_2A matrix is a rectangular array of elements or entries displayed in rows and columns; a square matrix has the same number of rows and columns; a column matrix (or vector) has only one column; a row matrix (or vector) has only one row

###### Matrix Algebra

view_agenda book_2For a 2 by 2 matrix if \( A \), \( B \), and \( C \) are \( 2 \times 2 \) matrices, \( I \) the \( 2 \times 2 \) (multiplicative) identity matrix and \( 0 \) the \( 2 \times 2 \) zero matrix then: \( A + B = B + A \) (commutative law for addition), \( (A + B) + C = A + (B + C) \) (associative law for addition), \( A + 0 = A \) (additive identity), \( A + (-A) = 0 \) (additive inverse), \( (AB)C = A(BC) \) (associative law for multiplication), \( AI = A = IA \) (additive identity), \( A^{-1} = A^{-1}A = I \) (multiplicative inverse), \( A(B + C) = AB + AC \) (left distributive law), \( (B + C)A = BA + CA \) (right distributive law)

###### Matrix Multiplication

view_agenda book_2Matrix multiplication is the process of multiplying a matrix by another matrix; the product \( AB \) of two matrices \( A \) and \( B \) with dimensions \( m \times n \) and \( p \times q \) is defined if \( n = p \); if it is defined, the product \( AB \) is an \( m \times q \) matrix and it is computed as shown in the following example: \(\left[ \begin{array}{ccc} 1 & 8 & 6 \\ 2 & 5 & 7 \end{array} \right] \left[ \begin{array}{cc} 1 & 10 \\ 1 & 3 \\ 1 & 4 \end{array} \right] = \left[ \begin{array}{cc} 94 & 34 \\ 151 & 63 \end{array} \right]\), the entries are computed as shown \( 1 \times 6 + 8 \times 1 + 10 \times 2 = 94 \), \( 1 \times 10 + 8 \times 3 + 0 \times 4 = 34 \), \( 2 \times 6 + 5 \times 1 + 7 \times 12 = 151 \), \( 2 \times 10 + 5 \times 3 + 7 \times 4 = 63 \), the entry in row \( i \) and column \( j \) of the product \( AB \) is computed by

###### Mental Procedures

view_agenda book_2A domain of knowledge in Marzano's taxonomy, and acted upon by the cognitive, metacognitive and self-systems; sometimes referred to as 'procedural knowledge'; there are three distinct phases to the acquisition of mental procedures — the cognitive stage, the associative stage, and the autonomous stage; the two categories of mental procedures are skills (single rules, algorithms and tactics) and processes (macroprocedures).

###### Methodical

view_agenda book_2Performed, disposed or acting in a systematic way; orderly; characterised by method or order; performed or carried out systematically.

###### Minimal

view_agenda book_2Least possible; small, the least amount; negligible.

###### Modify

view_agenda book_2Change the form or qualities of; make partial or minor changes to something.

###### Modulus of a Complex Number

view_agenda book_2If \( z \) is a complex number and \( z = x + iy \) then the modulus of \( z \) is the distance of \( z \) from the origin in the Argand plane; the modulus of \( z \) denoted by \( |z| \) is \( \sqrt{x^2 + y^2} \).

###### Momentum

view_agenda book_2The momentum \( p \) of a particle is the vector quantity \( p = mv \) where \( m \) is the mass and \( v \) is the velocity

###### Multimodal

view_agenda book_2Uses a combination of at least two modes (e.g., spoken, written), delivered at the same time, to communicate ideas and information to a live or virtual audience, for a particular purpose; the selected modes are integrated so that each mode contributes significantly to the response

###### Multiplication by a scalar

view_agenda book_2Let \( \mathbf{a} \) be a non-zero vector and \( k \) a positive real number (scalar); then the scalar multiple of \( \mathbf{a} \) by \( k \) is the vector \( k\mathbf{a} \), which has magnitude \( |k|\|\mathbf{a}\| \) and the same direction as \( \mathbf{a} \); if \( k \) is a negative real number, then \( k \) has magnitude \( |k|\|\mathbf{a}\| \) but is directed in the opposite direction to \( \mathbf{a} \) (see negative of a vector)

###### Multiplication principle

view_agenda book_2Suppose a choice is to be made in two stages; if there are \( a \) choices for the first stage and \( b \) choices for the second stage, no matter what choice has been made at the first stage, then there are \( ab \) choices altogether; if the choice is to be made in \( n \) stages and if for each \( i \), there are \( a_i \) choices for the \( i^{th} \) stage then there are \( a_1a_2 \ldots a_n \) choices altogether

###### Multiplicative identity matrix

view_agenda book_2A multiplicative identity matrix is a square matrix in which all the elements in the leading diagonal are ones and the remaining elements are zeros. Identity matrices are designated by the letter \( I \); there is an identity matrix for each order of square matrix; when clarity is needed, the order is written with a subscript: \( I_n \)

###### Multiplicative inverse

view_agenda book_2Multiplicative inverse of a square matrix: the inverse of a square matrix \( A \) is written as \( A^{-1} \) and has the property that \( A A^{-1} = A^{-1} A = I \) where \( I \) is the identity matrix; not all square matrices have an inverse; a matrix that has an inverse is said to be invertible. Multiplicative inverse of a 2 × 2 matrix: the inverse of the matrix \( A = \left[ \begin{array}{cc} a & b \\ c & d \end{array} \right] \) is \( A^{-1} = \frac{1}{det A} \left[ \begin{array}{cc} d & -b \\ -c & a \end{array} \right] \), when \( det A \neq 0 \).

###### Narrow

view_agenda book_2Limited in range or scope; lacking breadth of view; limited in amount; barely sufficient or adequate; restricted

###### Negation

view_agenda book_2If \( P \) is a statement then the statement

###### Nuanced

view_agenda book_2Showing a subtle difference or distinction in expression, meaning, response, etc.; finely differentiated; characterised by subtle shades of meaning or expression; a subtle distinction, variation or quality; sensibility to, awareness of, or ability to express delicate shadings, as of meaning, feeling, or value

###### Objectives

view_agenda book_2See

###### Observation

view_agenda book_2Data or information required to solve a mathematical problem and/or develop a mathematical model; empirical evidence

###### Obvious

view_agenda book_2Clearly perceptible or evident; easily seen, recognised or understood

###### Optimal

view_agenda book_2Best, most favourable, under a particular set of circumstances

###### Organise

view_agenda book_2Arrange, order; form as or into a whole consisting of interdependent or coordinated parts, especially for harmonious or united action

###### Organised

view_agenda book_2Systematically ordered and arranged; having a formal organisational structure to arrange, coordinate and carry out activities

###### Outstanding

view_agenda book_2Exceptionally good; clearly noticeable; prominent; conspicuous; striking

###### Parametric equation of a straight line

view_agenda book_2When \( a = \left(\frac{a_1}{a_2}\right) \) is the position vector of a point on a straight line in three-dimensional space and \( d = \left(\frac{d_1}{d_2}\right) \) is any vector with direction along the line; the line consists of all points \( P(x, y, z) \) whose parametric form is given by \( x = a_1 + kd_1, y = a_2 + kd_2, z = a_3 + kd_3 \) for some real number \( k \)

###### Partial

view_agenda book_2Not total or general; existing only in part; attempted, but incomplete

###### Particular

view_agenda book_2Distinguished or different from others or from the ordinary; noteworthy

###### Pascal’s triangle

view_agenda book_2A triangular arrangement of binomial coefficients in which the \( n^{th} \) row consists of the binomial coefficient \((n \choose r)\); for \( 0 \leq r \leq n \), each interior entry is the sum of the two entries above it, and the sum of the entries in the \( n^{th} \) row is \( 2^n \)

###### Perceptive

view_agenda book_2Having or showing insight and the ability to perceive or understand; discerning (see also 'discriminating')

###### Performance

view_agenda book_2An assessment technique that requires students to demonstrate a range of cognitive, technical, creative and/or expressive skills and to apply theoretical and conceptual understandings, through the psychomotor domain; it involves student application of identified skills when responding to a task that involves solving a problem, providing a solution or conveying meaning or intent; a performance is developed over an extended and defined period of time

###### Permutations

view_agenda book_2A permutation of n objects is an arrangement or rearrangement of n objects (order is important); the number of arrangements of n objects is \( n! \); the number of permutations of n objects taken r at a time is denoted \( P_r^n \), where \( P_r^n = \frac{n!}{(n-r)!} = n \times (n - 1) \times (n - 2) \times ... \times (n - r + 1) \)

###### Persuasive

view_agenda book_2Capable of changing someone's ideas, opinions or beliefs; appearing worthy of approval or acceptance; (of an argument or statement) communicating reasonably or credibly (see also

###### Perusal time

view_agenda book_2Time allocated in an assessment to reading items and tasks and associated assessment materials; no writing is allowed; students may not make notes and may not commence responding to the assessment in the response space/book

###### Pigeon-hole principle

view_agenda book_2If there are n pigeon holes and n + 1 pigeons to go into them, then at least one pigeon hole must get two or more pigeons

###### Planning time

view_agenda book_2Time allocated in an assessment to planning how to respond to items and tasks and associated assessment materials; students may make notes but may not commence responding to the assessment in the response space/book; notes made during planning are not collected, nor are they graded or used as evidence of achievement

###### Polished

view_agenda book_2Flawless or excellent; performed with skilful ease

###### Precise

view_agenda book_2Definite or exact; definitely or strictly stated, defined or fixed; characterised by definite or exact expression or execution

###### Precision

view_agenda book_2Accuracy; exactness; exact observance of forms in conduct or actions

###### Predict

view_agenda book_2Give an expected result of an upcoming action or event; suggest what may happen based on available information

###### Probability density function

view_agenda book_2The probability density function (pdf) of a continuous random variable is the function that when integrated over an interval gives the probability that the continuous random variable having that pdf lies in that interval; the probability density function is therefore the derivative of the (cumulative probability) distribution function

###### Problem-solving strategies

view_agenda book_2May include estimating, identifying patterns, guessing and checking, working backwards, using diagrams, considering similar problems and organising data

###### Procedural vocabulary

view_agenda book_2Instructional terms used in a mathematical context (e.g. calculate, convert, determine, identify, justify, show, sketch, solve, state).

###### Procedure

view_agenda book_2A list of sequential steps that are used to solve a problem or perform a task

###### Product

view_agenda book_2An assessment technique that focusses on the output or result of a process requiring the application of a range of cognitive, physical, technical, creative and/or expressive skills, and theoretical and conceptual understandings; a product is developed over an extended and defined period of time

###### Proficient

view_agenda book_2Well advanced or expert in any art, science or subject; competent, skilled or adept in doing or using something

###### Project

view_agenda book_2An assessment technique that focusses on a problem-solving process requiring the application of a range of cognitive, technical and creative skills and theoretical understandings; the response is a coherent work that documents the iterative process undertaken to develop a solution and includes written paragraphs and annotations, diagrams, sketches, drawings, photographs, video, spoken presentations, physical prototypes and/or models; a project is developed over an extended and defined period of time

###### Propose

view_agenda book_2Put forward (e.g. a point of view, idea, argument, suggestion) for consideration or action

###### Prove

view_agenda book_2Use a sequence of steps to obtain the required result in a formal way

###### Psychomotor Procedures

view_agenda book_2A domain of knowledge in Marzano's taxonomy, and acted upon by the cognitive, metacognitive and self-systems; these are physical procedures used to negotiate daily life and to engage in complex physical activities; the two categories of psychomotor procedures are skills (foundational procedures and simple combination procedures) and processes (complex combination procedures)

###### Purposeful

view_agenda book_2Having an intended or desired result; having a useful purpose; determined; resolute; full of meaning; significant; intentional

###### Pythagorean Identities

view_agenda book_2\(\cos^2(A) + \sin^2(A) = 1\), \(\tan^2(A) + 1 = \sec^2(A)\), \(\cot^2(A) + 1 = \csc^2(A)\)

###### QCE

view_agenda book_2Queensland Certificate of Education

###### Qualitative Statements

view_agenda book_2Statements relating to a quality or qualities; of a non-numerical nature

###### Quantifiers

view_agenda book_2For all (for each)

###### Quantitative Analysis

view_agenda book_2Use of mathematical measurements and calculations, including statistics, to analyse the relationships between variables; may include use of the correlation coefficient, coefficient of determination, simple residual analysis or outlier analysis

###### Random Sample

view_agenda book_2A set of data in which the value of each observation is governed by some chance mechanism that depends on the situation; the most common situation in which the term random sample is used refers to a set of independent and identically distributed observations

###### Rarely

view_agenda book_2Infrequently; in few instances

###### Rational function

view_agenda book_2A function such that \( f(x) = \frac{g(x)}{h(x)} \) where \( g(x) \) and \( h(x) \) are polynomials; usually \( g(x) \) and \( h(x) \) are chosen so as to have no common factor of degree greater than or equal to one, and the domain of \( f \) is usually taken to be \( R \setminus \{x : h(x) = 0\} \)

###### Rational numbers

view_agenda book_2A real number is rational if it can be expressed as a quotient of two integers; otherwise, it is called irrational; all rational numbers can be expressed as decimal expansions that are either terminating or eventually recurring

###### Real numbers

view_agenda book_2The numbers generally used in mathematics, in scientific work and in everyday life are the real numbers; they can be pictured as points on a number line, with the integers evenly spaced along the line, and a real number a to the right of a real number b if \( a > b \); a real number is either rational or irrational; the set of real numbers consists of the set of all rational and irrational numbers; every real number has a decimal expansion; rational numbers are the ones whose decimal expansions are either terminating or eventually recurring

###### Realise

view_agenda book_2Create or make (e.g. a musical, artistic or dramatic work); actualise; make real or concrete; give reality or substance to

###### Reasonable

view_agenda book_2Endowed with reason; having sound judgment; fair and sensible; based on good sense; average; appropriate, moderate

###### Reasonableness of solutions

view_agenda book_2To justify solutions obtained with or without technology using everyday language, mathematical language or a combination of both; may be applied to calculations to check working, or to questions that require a relationship back to the context

###### Reasoned

view_agenda book_2Logical and sound; based on logic or good sense; logically thought out and presented with justification; guided by reason; well-grounded; considered

###### Recall

view_agenda book_2Remember; present remembered ideas, facts or experiences; bring something back into thought, attention or into one's mind

###### Reciprocal trigonometric functions

view_agenda book_2Sec(A) = \(\frac{1}{\cos(A)}\), \(\cos(A) \neq 0\)\ncosec(A) = \(\frac{1}{\sin(A)}\), \(\sin(A) \neq 0\)\ncot(A) = \(\frac{\cos(A)}{\sin(A)}\), \(\sin(A) \neq 0\)

###### Recognise

view_agenda book_2Identify or recall particular features of information from knowledge; identify that an item, characteristic or quality exists; perceive as existing or true; be aware of or acknowledge

###### Refined

view_agenda book_2Developed or improved so as to be precise, exact or subtle

###### Reflect on

view_agenda book_2Think about deeply and carefully

###### Rehearsed

view_agenda book_2Practised; previously experienced; practised extensively

###### Related

view_agenda book_2Associated with or linked to

###### Relevance

view_agenda book_2Being related to the matter at hand

###### Relevant

view_agenda book_2Bearing upon or connected with the matter in hand; to the purpose; applicable and pertinent; having a direct bearing on

###### Repetitive

view_agenda book_2Containing or characterised by repetition, especially when unnecessary or tiresome

###### Reporting

view_agenda book_2Providing information that succinctly describes student performance at different junctures throughout a course of study

###### Representatively sample

view_agenda book_2In this syllabus, a selection of subject matter that accurately reflects the intended learning of a topic

###### Resolve

view_agenda book_2In the Arts, consolidate and communicate intent through a synthesis of ideas and application of media to express meaning

###### Routine

view_agenda book_2Often encountered, previously experienced; commonplace; customary and regular; well-practised; performed as part of a regular procedure, rather than for a special reason

###### Rudimentary

view_agenda book_2Relating to rudiments or first principles; elementary; undeveloped; involving or limited to basic principles; relating to an immature, undeveloped or basic form

###### Safe

view_agenda book_2Secure; not risky

###### Sample mean

view_agenda book_2The arithmetic average of the sample values

###### Scalar (dot) product

view_agenda book_2Let \(a = (a_1, a_2, a_3)\) and \(b = (b_1, b_2, b_3)\), \(a \cdot b = a_1b_1 + a_2b_2 + a_3b_3\) is the scalar (dot) product; when expressed in \(i, j, k\) notation, \(a = a_1i + a_2j + a_3k\) and \(b = b_1i + b_2j + b_3k\) then \(a \cdot b = a_1b_1 + a_2b_2 + a_3b_3\); the scalar (dot) product has the following geometric interpretation: \(a \cdot b = |a||b|\cos(θ)\) where \(θ\) is the angle between \(a\) and \(b\); note \(|a| = \sqrt{a \cdot a}\)

###### Scalar multiplication

view_agenda book_2The process of multiplying a matrix by a scalar (number); in general, for the matrix A with entries \(a_{ij}\), the entries of \(kA\) are \(ka_{ij}\)

###### Secure

view_agenda book_2Sure; certain; able to be counted on; self-confident; poised; dependable; confident; assured; not liable to fail

###### Select

view_agenda book_2Choose in preference to another or others; pick out

###### Sensitive

view_agenda book_2Capable of perceiving with a sense or senses; aware of the attitudes, feelings or circumstances of others; having acute mental or emotional sensibility; relating to or connected with the senses or sensation

###### Sequence

view_agenda book_2Place in a continuous or connected series; arrange in a particular order

###### Show

view_agenda book_2Provide the relevant reasoning to support a response

###### Significant

view_agenda book_2Important; of consequence; expressing a meaning; indicative; includes all that is important; sufficiently great or important to be worthy of attention; noteworthy; having a particular meaning; indicative of something

###### Simple

view_agenda book_2Easy to understand, deal with and use; not complex or complicated; plain; not elaborate or artificial; may concern a single or basic aspect; involving few elements, components or steps

###### Simple Familiar

view_agenda book_2Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where: relationships and interactions are obvious and have few elements; and all of the information to solve the problem is identifiable; that is – the required procedure is clear from the way the problem is posed, or – in a context that has been a focus of prior learning. Students are not required to interpret, clarify and analyse problems to develop responses. Typically, these problems focus on objectives 1, 2 and 3.

###### Simple Harmonic Motion

view_agenda book_2Used to model oscillations in two dimensions; occurs when the acceleration is proportional to displacement but in opposite directions modelled by \( \frac{d^2x}{dt^2} = -\omega^2x \) where \( \omega \) represents the angular frequency; the equations for simple harmonic motion with amplitude A, phase \( \alpha \) or \( \beta \), velocity \( v \), period T and frequency F include: displacement \( x = A \sin(\omega t + \alpha) \) or \( x = A \cos(\omega t + \beta) \) velocity \( v^2 = \omega^2(A^2 - x^2) \) period \( T = \frac{2\pi}{\omega} \) frequency \( f = \frac{1}{T} \)

###### Simplistic

view_agenda book_2Characterised by extreme simplification, especially if misleading; oversimplified

###### Simpson’s rule

view_agenda book_2A formula for approximating the integral of a function; \( \int_a^b f(x) dx \approx \frac{w}{3} [f(x_0) + 4f(x_1) + f(x_2) + ...] + [2f(x_2) + f(x_4) + ...] + f(x_n) \) where the interval [\( a, b \)] of the function \( f(x) \) is divided into an even number \( n \) of equal strips of width \( w \).

###### Sketch

view_agenda book_2Execute a drawing or painting in simple form, giving essential features but not necessarily with detail or accuracy; in mathematics, represent by means of a diagram or graph; the sketch should give a general idea of the required shape or relationship and should include features

###### Skilled

view_agenda book_2Having or showing the knowledge, ability or training to perform a certain activity or task well; having skill; trained or experienced; showing, involving or requiring skill

###### Skillful

view_agenda book_2Having technical facility or practical ability; possessing, showing, involving or requiring skill; expert, dexterous; demonstrating the knowledge, ability or training to perform a certain activity or task well; trained, practised or experienced

###### Slope Field

view_agenda book_2Slope field (direction or gradient field) is a graphical representation of the solutions of a linear first-order differential equation in which the derivative at a given point is represented by a line segment of the corresponding slope

###### Solution

view_agenda book_2The result of a mathematical process undertaken to answer or resolve a problem

###### Solve

view_agenda book_2Find an answer to, explanation for, or means of dealing with (e.g. a problem); work out the answer or solution to (e.g. a mathematical problem); obtain the answer/s using algebraic, numerical and/or graphical methods

###### Sophisticated

view_agenda book_2Of intellectual complexity; reflecting a high degree of skill, intelligence, etc.; employing advanced or refined methods or concepts; highly developed or complicated

###### Specific

view_agenda book_2Clearly defined or identified; precise and clear in making statements or issuing instructions; having a special application or reference; explicit, or definite; peculiar or proper to something, as qualities, characteristics, effects, etc.

###### Sporadic

view_agenda book_2Happening now and again or at intervals; irregular or occasional; appearing in scattered or isolated instances

###### Statement

view_agenda book_2A sentence or assertion

###### Straightforward

view_agenda book_2Without difficulty; uncomplicated; direct; easy to do or understand

###### Structure

view_agenda book_2Verb: give a pattern, organisation or arrangement to; construct or arrange according to a plan; Noun: in languages, arrangement of words into larger units, e.g. phrases, clauses, sentences, paragraphs and whole texts, in line with cultural, intercultural and textual conventions

###### Structured

view_agenda book_2Organised or arranged so as to produce a desired result

###### Subject

view_agenda book_2A branch or area of knowledge or learning defined by a syllabus or alternative sequence; school subjects are usually based in a discipline or field of study (see also

###### Subject

view_agenda book_2A branch or area of knowledge or learning defined by a syllabus; school subjects are usually based in a discipline or field of study (see also

###### Subject Matter

view_agenda book_2The subject-specific body of information, mental procedures and psychomotor procedures that are necessary for students' learning and engagement within that subject

###### Substantial

view_agenda book_2Of ample or considerable amount, quantity, size, etc.; of real worth or value; firmly or solidly established; of real significance; reliable; important; worthwhile

###### Substantiated

view_agenda book_2Established by proof or competent evidence

###### Subtended Angle

view_agenda book_2The angle made by a line, arc or object at a given point

###### Subtle

view_agenda book_2Fine or delicate in meaning or intent; making use of indirect methods; not straightforward or obvious

###### Successful

view_agenda book_2Achieving or having achieved success; accomplishing a desired aim or result

###### Succinct

view_agenda book_2Expressed in few words; concise; terse; characterised by conciseness or brevity; brief and clear

###### Sufficient

view_agenda book_2Enough or adequate for the purpose

###### Suitable

view_agenda book_2Appropriate; fitting; conforming or agreeing in nature, condition, or action

###### Summarise

view_agenda book_2Give a brief statement of a general theme or major point(s); present ideas and information in fewer words and in sequence

###### Summative Assessment

view_agenda book_2Assessment whose major purpose is to indicate student achievement; summative assessments contribute towards a student

###### Superficial

view_agenda book_2Concerned with or comprehending only what is on the surface or obvious; shallow; not profound, thorough, deep or complete; existing or occurring at or on the surface; cursory; lacking depth of character or understanding; apparent and sometimes trivial

###### Supported

view_agenda book_2Corroborated; given greater credibility by providing evidence

###### Sustained

view_agenda book_2Carried on continuously, without interruption, or without any diminishing of intensity or extent

###### Syllabus

view_agenda book_2A document that prescribes the curriculum for a course of study

###### Syllabus Objectives

view_agenda book_2Outline what the school is required to teach and what students have the opportunity to learn; described in terms of actions that operate on the subject matter; the overarching objectives for a course of study (see also

###### Symbolise

view_agenda book_2Represent or identify by a symbol or symbols

###### Synthesise

view_agenda book_2Combine different parts or elements (e.g. information, ideas, components) into a whole, in order to create new understanding

###### Systematic

view_agenda book_2Done or acting according to a fixed plan or system; methodical; organised and logical; having, showing, or involving a system, method, or plan; characterised by system or method; methodical; arranged in, or comprising an ordered system

###### Technical vocabulary

view_agenda book_2Terms that have a precise mathematical meaning (e.g., categorical data, chain rule, decimal fraction, imaginary number, log laws, linear regression, sine rule, whole number); may include everyday words used in a mathematical context (e.g., capacity, differentiate, evaluate, integrate, order, property, sample, union)

###### Test

view_agenda book_2Take measures to check the quality, performance or reliability of something

###### There exists

view_agenda book_2Symbol \(\exists\)

###### Thorough

view_agenda book_2Carried out through, or applied to the whole of something; carried out completely and carefully; including all that is required; complete with attention to every detail; not superficial or partial; performed or written with care and completeness; taking pains to do something carefully and completely

###### Thoughtful

view_agenda book_2Occupied with, or given to thought; contemplative; meditative; reflective; characterised by or manifesting thought

###### Topic

view_agenda book_2A division of, or sub-section within a unit; all topics/sub-topics within a unit are interrelated

###### Unclear

view_agenda book_2Not clear or distinct; not easy to understand; obscure

###### Understand

view_agenda book_2Perceive what is meant by something; grasp; be familiar with (e.g. an idea); construct meaning from messages, including oral, written and graphic communication

###### Uneven

view_agenda book_2Unequal; not properly corresponding or agreeing; irregular; varying; not uniform; not equally balanced

###### Unfamiliar

view_agenda book_2Not previously encountered; situations or materials that have not been the focus of prior learning experiences or activities

###### Unit

view_agenda book_2A defined amount of subject matter delivered in a specific context or with a particular focus; it includes unit objectives particular to the unit, subject matter and assessment direction

###### Unit objectives

view_agenda book_2Drawn from the syllabus objectives and contextualised for the subject matter and requirements of a particular unit; they are assessed at least once in the unit (see also

###### Unit vector

view_agenda book_2A vector with magnitude 1; given a vector \( \mathbf{a} \) the unit vector in the same direction as \( \mathbf{a} \) is \( \frac{\mathbf{a}}{|\mathbf{a}|} \); this vector is often denoted as \( \hat{\mathbf{a}} \)

###### Unrelated

view_agenda book_2Having no relationship; unconnected

###### Use

view_agenda book_2Operate or put into effect; apply knowledge or rules to put theory into practice

###### Vague

view_agenda book_2Not definite in statement or meaning; not explicit or precise; not definitely fixed, determined or known; of uncertain, indefinite or unclear character or meaning; not clear in thought or understanding; couched in general or indefinite terms; not definitely or precisely expressed; deficient in details or particulars; thinking or communicating in an unfocused or imprecise way

###### Valid

view_agenda book_2Sound, just or well-founded; authoritative; having a sound basis in logic or fact (of an argument or point); reasonable or cogent; able to be supported; legitimate and defensible; applicable

###### Variable

view_agenda book_2Adjective: Apt or liable to vary or change; changeable; inconsistent; (readily) susceptible or capable of variation; fluctuating, uncertain. Noun: In mathematics, a symbol, or the quantity it signifies, that may represent any one of a given set of number and other objects

###### Variety

view_agenda book_2A number or range of things of different kinds, or the same general class, that are distinct in character or quality; (of sources) a number of different modes or references

###### Vector

view_agenda book_2In Specialist Mathematics, the term vector is used to describe a physical quantity like velocity or force that has a magnitude and direction; a vector is an entity \( \mathbf{a} \) which has a given length (magnitude) and a given direction; if \( \overrightarrow{AB} \) is a directed line segment with this length and direction, then we say that \( \overrightarrow{AB} \) represents \( \mathbf{a} \)

###### Vector (cross) product

view_agenda book_2When expressed in \( i, j, k \) notation, \( \mathbf{a} = a_1 \mathbf{i} + a_2 \mathbf{j} + a_3 \mathbf{k} \) and \( \mathbf{b} = b_1 \mathbf{i} + b_2 \mathbf{j} + b_3 \mathbf{k} \) then \( \mathbf{a} \times \mathbf{b} = (a_2b_3 - a_3b_2) \mathbf{i} + (a_3b_1 - a_1b_3) \mathbf{j} + (a_1b_2 - a_2b_1) \mathbf{k} \); the vector (cross) product has the following geometric interpretation; let \( \mathbf{a} \) and \( \mathbf{b} \) be two non-parallel vectors then \( \lvert \mathbf{a} \times \mathbf{b} \rvert \) is the area of the parallelogram defined by \( \mathbf{a} \) and \( \mathbf{b} \) and \( \mathbf{a} \times \mathbf{b} \) is normal to this parallelogram

###### Vector equation of a plane

view_agenda book_2Let \( \mathbf{a} \) be the position vector of a point on a plane and \( \mathbf{n} \) be any vector normal to the plane; the plane consists of all points \( \mathbf{P} \) whose position vector \( \mathbf{r} \) is given by \( \mathbf{r \cdot n} = \mathbf{a \cdot n} \)

###### Vector equation of a straight line

view_agenda book_2Let \( \mathbf{a} \) be the position vector of a point on a straight line and \( \mathbf{d} \) be any vector with direction along the line; the line consists of all points \( \mathbf{P} \) whose position vector \( \mathbf{r} \) is given by \( \mathbf{r} = \mathbf{a} + k\mathbf{d} \) for some real number \( k \)

###### Vector function

view_agenda book_2In this course, a vector function is one that depends on a single real number parameter t, often representing time, producing a vector \( \mathbf{r}(t) \) as the result; in terms of the standard unit vectors \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) the-dimensional space, the vector-valued functions of this specific type are given by expressions such as \( \mathbf{r}(t) = f(t)\mathbf{i} + g(t)\mathbf{j} + h(t)\mathbf{k} \) where f(t), g(t) and h(t) are real valued functions giving coordinates

###### Vector projection

view_agenda book_2When \( \mathbf{a} \) and \( \mathbf{b} \) are two vectors and \( \theta \) is the angle between them; the projection of a vector \( \mathbf{a} \) on a vector \( \mathbf{b} \) is the vector \( \| \mathbf{a} \| \cos(\theta) \mathbf{b} \) where \( \mathbf{b} \) is the unit vector in the direction of \( \mathbf{b} \); the projection of a vector \( \mathbf{a} \) on a vector \( \mathbf{b} \) is \( \mathbf{a} \cdot \mathbf{b} \) where \( \mathbf{b} \) is the unit vector in the direction of \( \mathbf{b} \); this projection is also given by \( \frac{\mathbf{a} \cdot \mathbf{b}}{\| \mathbf{b} \|} \mathbf{b} \)

###### Verify

view_agenda book_2To ascertain the truth or correctness of, especially by examination or comparison

###### Wide

view_agenda book_2Of great range or scope; embracing a great number or variety of subjects, cases, etc.; of full extent

###### With expression

view_agenda book_2In words, art, music or movement, conveying or indicating feeling, spirit, character, etc.; a way of expressing or representing something; vivid, effective or persuasive communication

###### \(\forall\)

view_agenda book_2For all \(\forall\) real numbers \(x, x^2 \geq 0\) (re: real numbers \(x, x^2 \geq 0\))