Mathematics+BOS+Outcomes

These are the official Board of Studies (BOS) Outcomes. The BOS Outcomes are much higher level than the topic outcomes used in our topic content descriptions. Official assessment is aligned to the BOS Outcomes.


 * **Objectives** || **Mathematics - Preliminary Outcomes** |||| **Mathematics Extension 1 Preliminary Outcomes** ||
 * //Appreciation of the scope, usefulness, beauty and elegance of mathematics.// || **P1** Demonstrates confidence in using mathematics to obtain realistic solutions to problems. || **PE1** Appreciates the role of mathematics in the solution of practical problems. ||
 * //The ability to reason in a broad range of mathematical contexts.// || **P2** Provides reasoning to support conclusions which are appropriate to the context. || **PE2** Uses multi-step deductive reasoning in a variety of contexts. ||
 * //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. || **PE3** Solves problems involving permutations and combinations, inequalities, polynomials, circle geometry and parametric representations. ||
 * //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. || **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. ||
 * //The ability to interpret and communicate mathematics in a variety of forms.// || **P8** Understands and uses the language and notation of calculus. || **PE6** Makes comprehensive use of mathematical language, diagrams and notation for communicating in a wide variety of situations. ||
 * **Objectives** || **Mathematics - HSC Outcomes** || **Mathematics Extension 1 HSC Outcomes** ||
 * //Appreciation of the scope, usefulness, beauty and elegance of mathematics.// || **H1** Seeks to apply mathematical techniques to problems in a wide range of practical contexts || **HE1** Appreciates interrelationships between ideas drawn from different areas of mathematics. ||
 * //The ability to reason in a broad range of mathematical contexts.// || **H2** Constructs arguments to prove and justify results. || **HE2** Uses inductive reasoning in the construction of proofs. ||
 * //Skills in applying mathematical techniques to the solution of practical problems.// || **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. || **HE3** Uses a variety of strategies to investigate mathematical models of situations involving binomial probability, projectiles, simple harmonic motion, or exponential growth and decay. ||
 * //Understanding of the key concepts of calculus and the ability to differentiate and integrate a range of functions.// || **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. || **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. ||
 * //The ability to interpret and communicate mathematics in a variety of forms.// || **H9** Communicates using mathematical language, notation, diagrams and graphs. || **HE7** Evaluates mathematical solutions to problems and communicates them in an appropriate form. ||