NSW Syllabuses

# Stage 5 outcomes

### Mathematics

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#### Stage 5.2outcomes

##### 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 5.3outcomes

##### 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 5outcomes

##### 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