Course Outcomes
Mathematics, Mathematics Extension 1 and Mathematics Extension 2
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The current calculusbased mathematics courses will remain unchanged in the introductory years of the New Higher School Certificate. During this time the course content and internal assessment arrangements of 2 Unit, 3 Unit and 4 Unit Mathematics will be maintained. (See Mathematics 2/3 Unit Syllabus and Mathematics 4 Unit Syllabus.) However, under the new HSC structure, the courses will be called Mathematics, Mathematics Extension 1 and Mathematics Extension 2, respectively.
The HSC results of students studying these courses will be reported using the standardsreferencing procedures in place for all Board developed courses under the new structure.
Following are the outcomes developed for the Mathematics, Mathematics Extension 1 and Mathematics Extension 2 courses. The outcomes have been derived from the content of the courses, and together with the content, determine the breadth and depth of study to be undertaken by students.

Mathematics 
Mathematics Extension 1 
Mathematics 

Objectives 
Preliminary 
HSC Outcomes 
Preliminary 
HSC Outcomes 
HSC Outcomes 
Students will develop: 
A student: 
A student: 
A student: 
A student: 
A student: 
appreciation of the scope, usefulness, beauty and elegance of mathematics 
P1 demonstrates confidence in using mathematics to obtain realistic solutions to problems 
H1 seeks to apply mathematical techniques to problems in a wide range of practical contexts 
PE1 appreciates the role of mathematics in the solution of practical problems 
HE1 appreciates interrelationships between ideas drawn from different areas of mathematics 
E1 appreciates the creativity, power and usefulness of mathematics to solve a broad range of problems 
the ability to reason in a broad range of mathematical contexts 
P2 provides reasoning to support conclusions which are appropriate to the context 
H2 constructs arguments to prove and justify results 
PE2 uses multistep deductive reasoning in a variety of contexts 
HE2 uses inductive reasoning in the construction of proofs 
E2 chooses appropriate strategies to construct arguments and proofs in both concrete and abstract settings 
Objectives 
Preliminary 
HSC Outcomes 
Preliminary 
HSC Outcomes 
HSC Outcomes 
Students will develop: 
A student: 
A student: 
A student: 
A student: 
A student: 
skills in applying mathematical techniques to the solution of practical problems 
P3 performs routine arithmetic and algebraic manipulation involving surds, simple rational expressions and trigonometric identities
chooses and applies appropriate arithmetic, algebraic, graphical, trigonometric and geometric techniques 
H3 manipulates algebraic expressions involving logarithmic and exponential functions
expresses practical problems in mathematical terms based on simple given models
applies appropriate techniques from the study of calculus, geometry, probability, trigonometry and series to solve problems 
PE3 solves problems involving permutations and combinations, inequalities, polynomials, circle geometry and parametric representations 
HE3 uses a variety of strategies to investigate mathematical models of situations involving binomial probability, projectiles, simple harmonic motion, or exponential growth and decay 
E3 uses the relationship between algebraic and geometric representations of complex numbers and of conic sections
uses efficient techniques for the algebraic manipulation required in dealing with questions such as those involving conic sections and polynomials
uses ideas and techniques from calculus to solve problems in mechanics involving resolution of forces, resisted motion and circular motion 
Objectives 
Preliminary Outcomes 
HSC Outcomes 
Preliminary Outcomes 
HSC Outcomes 
HSC Outcomes 
Students will develop: 
A student: 
A student: 
A student: 
A student: 
A student: 
understanding of the key concepts of calculus and the ability to differentiate and integrate a range of functions 
P5 understands the concept of a function and the relationship between a function and its graph
relates the derivative of a function to the slope of its graph
determines the derivative of a function through routine application of the rules of differentiation 
H6 uses the derivative to determine the features of the graph of a function
uses the features of a graph to deduce information about the derivative
uses techniques of integration to calculate areas and volumes 
PE4 uses the parametric representation together with differentiation to identify geometric properties of parabolas
determines derivatives which require the application of more than one rule of differentiation 
HE4 uses the relationship between functions, inverse functions and their derivatives
applies the chain rule to problems including those involving velocity and acceleration as functions of displacement HE6 determines integrals by reduction to a standard form through a given substitution 
E6 combines the ideas of algebra and calculus to determine the important features of the graphs of a wide variety of functions
uses the techniques of slicing and cylindrical shells to determine volumes E8 applies further techniques of integration, including partial fractions, integration by parts and recurrence formulae, to problems 
Objectives 
Preliminary Outcomes 
HSC Outcomes 
Preliminary Outcomes 
HSC Outcomes 
HSC Outcomes 
Students will develop: 
A student: 
A student: 
A student: 
A student: 
A student: 
the ability to interpret and communicate mathematics in a variety of forms 
P8 understands and uses the language and notation of calculus 
H9 communicates using mathematical language, notation, diagrams and graphs 
PE6 makes comprehensive use of mathematical language, diagrams and notation for communicating in a wide variety of situations 
HE7 evaluates mathematical solutions to problems and communicates them in an appropriate form 
E9 communicates abstract ideas and relationships using appropriate notation and logical argument 
© Board of Studies 2000
Published by Board of Studies NSW
GPO Box 5300
Sydney 2001
Australia
ISBN 0 7313 4490 1
99655