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NSW Syllabuses

Stage 5 outcomes

Mathematics

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Stage 5.2
outcomes

A student:
  • selects appropriate notations and conventions to communicate mathematical ideas and solutions

    MA5.2-1WM
  • interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems

    MA5.2-2WM
  • constructs arguments to prove and justify results

    MA5.2-3WM
  • solves financial problems involving compound interest

    MA5.2-4NA
  • recognises direct and indirect proportion, and solves problems involving direct proportion

    MA5.2-5NA
  • simplifies algebraic fractions, and expands and factorises quadratic expressions

    MA5.2-6NA
  • applies index laws to operate with algebraic expressions involving integer indices

    MA5.2-7NA
  • solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques

    MA5.2-8NA
  • uses the gradient-intercept form to interpret and graph linear relationships

    MA5.2-9NA
  • connects algebraic and graphical representations of simple non-linear relationships

    MA5.2-10NA
  • calculates the surface areas of right prisms, cylinders and related composite solids

    MA5.2-11MG
  • applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

    MA5.2-12MG
  • applies trigonometry to solve problems, including problems involving bearings

    MA5.2-13MG
  • calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar

    MA5.2-14MG
  • uses quartiles and box plots to compare sets of data, and evaluates sources of data

    MA5.2-15SP
  • investigates relationships between two statistical variables, including their relationship over time

    MA5.2-16SP
  • describes and calculates probabilities in multi-step chance experiments

    MA5.2-17SP
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Stage 5.3
outcomes

A student:
  • uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

    MA5.3-1WM
  • generalises mathematical ideas and techniques to analyse and solve problems efficiently

    MA5.3-2WM
  • uses deductive reasoning in presenting arguments and formal proofs

    MA5.3-3WM
  • draws, interprets and analyses graphs of physical phenomena

    MA5.3-4NA
  • selects and applies appropriate algebraic techniques to operate with algebraic expressions

    MA5.3-5NA
  • performs operations with surds and indices

    MA5.3-6NA
  • solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations

    MA5.3-7NA
  • uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line

    MA5.3-8NA
  • sketches and interprets a variety of non-linear relationships

    MA5.3-9NA
  • recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems

    MA5.3-10NA
  • uses the definition of a logarithm to establish and apply the laws of logarithms

    MA5.3-11NA
  • uses function notation to describe and sketch functions

    MA5.3-12NA
  • applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids

    MA5.3-13MG
  • applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

    MA5.3-14MG
  • applies Pythagoras’ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions

    MA5.3-15MG
  • proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals

    MA5.3-16MG
  • applies deductive reasoning to prove circle theorems and to solve related problems

    MA5.3-17MG
  • uses standard deviation to analyse data

    MA5.3-18SP
  • investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes

    MA5.3-19SP

Science 

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Stage 5
outcomes

A student:
  • appreciates the importance of science in their lives and the role of scientific inquiry in increasing understanding of the world around them

    SC5-1VA
  • shows a willingness to engage in finding solutions to science-related personal, social and global issues, including shaping sustainable futures

    SC5-2VA
  • demonstrates confidence in making reasoned, evidence-based decisions about the current and future use and influence of science and technology, including ethical considerations

    SC5-3VA
  • develops questions or hypotheses to be investigated scientifically

    SC5-4WS
  • produces a plan to investigate identified questions, hypotheses or problems, individually and collaboratively

    SC5-5WS
  • undertakes first-hand investigations to collect valid and reliable data and information, individually and collaboratively

    SC5-6WS
  • processes, analyses and evaluates data from first-hand investigations and secondary sources to develop evidence-based arguments and conclusions

    SC5-7WS
  • applies scientific understanding and critical thinking skills to suggest possible solutions to identified problems

    SC5-8WS
  • presents science ideas and evidence for a particular purpose and to a specific audience, using appropriate scientific language, conventions and representations

    SC5-9WS
  • applies models, theories and laws to explain situations involving energy, force and motion

    SC5-10PW
  • explains how scientific understanding about energy conservation, transfers and transformations is applied in systems

    SC5-11PW
  • describes changing ideas about the structure of the Earth and the universe to illustrate how models, theories and laws are refined over time by the scientific community

    SC5-12ES
  • explains how scientific knowledge about global patterns of geological activity and interactions involving global systems can be used to inform decisions related to contemporary issues

    SC5-13ES
  • analyses interactions between components and processes within biological systems

    SC5-14LW
  • explains how biological understanding has advanced through scientific discoveries, technological developments and the needs of society

    SC5-15LW
  • explains how models, theories and laws about matter have been refined as new scientific evidence becomes available

    SC5-16CW
  • discusses the importance of chemical reactions in the production of a range of substances, and the influence of society on the development of new materials

    SC5-17CW