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Course Outcomes
Mathematics, Mathematics Extension 1 and Mathematics Extension 2

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The current calculus-based 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 standards-referencing 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
Extension 2

Objectives

Preliminary
Outcomes

HSC Outcomes

Preliminary
Outcomes

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 multi-step 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
Outcomes

HSC Outcomes

Preliminary
Outcomes

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


P4

chooses and applies appropriate arithmetic, algebraic, graphical, trigonometric and geometric techniques

H3

manipulates algebraic expressions involving logarithmic and exponential functions


H4

expresses practical problems in mathematical terms based on simple given models


H5

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


E4

uses efficient techniques for the algebraic manipulation required in dealing with questions such as those involving conic sections and polynomials


E5

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


P6

relates the derivative of a function to the slope of its graph


P7

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


H7

uses the features of a graph to deduce information about the derivative


H8

uses techniques of integration to calculate areas and volumes

PE4

uses the parametric representation together with differentiation to identify geometric properties of parabolas


PE5

determines derivatives which require the application of more than one rule of differentiation

HE4

uses the relationship between functions, inverse functions and their derivatives


HE5

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


E7

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



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