# Government Standards

## New South Wales Education Standards

Assessment Exam - NESA Mathematics - Stage 5
Working Mathematically eTAP Lesson
Communicating
Uses appropriate terminology, diagrams and symbols in mathematical contexts
NSW.MA5.1-1WM
Signs and Symbols in Mathematics
Selects appropriate notations and conventions to communicate mathematical ideas and solutions
NSW.MA5.2-1WM
Expressing More Relationships Between Numbers
Uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures
NSW.MA5.3-1WM

Problem Solving
Selects and uses appropriate strategies to solve problems
NSW.MA5.1-2WM
Changing Words into Math
Iinterprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems
NSW.MA5.2-2WM
Areas of Triangles
Generalises mathematical ideas and techniques to analyse and solve problems efficiently
NSW.MA5.3-2WM
Setting Up and Solving Equations
Reasoning
Provides reasoning to support conclusions that are appropriate to the context
NSW.MA5.1-3WM
Symbols of Logic

Law of Contraposition
Constructs arguments to prove and justify results
NSW.MA5.2-3WM
Modus Tollens, Negation, Law of Syllogism
Uses deductive reasoning in presenting arguments and formal proofs
NSW.MA5.3-3WM
Direct Proofs

Conditional Proof
Number and Algebra eTAP Lesson
Financial Mathematics
Solves financial problems involving earning, spending and investing money
NSW.MA5.1-4NA
Investment Growth Over Time
Solves financial problems involving compound interest
NSW.MA5.2-4NA
Interest Rate and Loan Length
Ratios and Rates
Recognises direct and indirect proportion, and solves problems involving direct proportion
NSW.MA5.2-5NA
Ratios and Proportions
Draws, interprets and analyses graphs of physical phenomena
NSW.MA5.3-4NA
Seeking Trends with Line Graphs
Algebraic Techniques
Simplifies algebraic fractions, and expands and factorises quadratic expressions
NSW.MA5.2-6NA
Expanding and Reducing Fractions
Selects and applies appropriate algebraic techniques to operate with algebraic expressions
NSW.MA5.3-5NA

Indices
Operates with algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases
NSW.MA5.1-5NA
Integers and the Number Line
Applies index laws to operate with algebraic expressions involving integer indices
NSW.MA5.2-7NA

Surds and Indices
Performs operations with surds and indices
NSW.MA5.3-6NA

Equations
Solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques
NSW.MA5.2-8NA
How to Use Graphs

Graphing Systems of Equations

Solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations
NSW.MA5.3-7NA
Simultaneous Equations

Simultaneous Equations With Strange Solutions
Linear Relationships
Determines the midpoint, gradient and length of an interval, and graphs linear relationships
NSW.MA5.1-6NA
Slope of a Line

Midpoint of a Line Segment
Uses the gradient-intercept form to interpret and graph linear relationships
NSW.MA5.2-9NA
Slope Intercept Form of Equations
Uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line
NSW.MA5.3-8NA
Coordinate Axes and Negative Numbers
Non-Linear Relationships
Graphs simple non-linear relationships
NSW.MA5.1-7NA
Graphing Systems of Equations
Connects algebraic and graphical representations of simple non-linear relationships
NSW.MA5.2-10NA
Graphing Systems of Inequalities
Sketches and interprets a variety of non-linear relationships
NSW.MA5.3-9NA
Substitution

Elimination
Polynomials
Recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems
NSW.MA5.3-10NA
Polynomials
Logarithms
Uses the definition of a logarithm to establish and apply the laws of logarithms
NSW.MA5.3-11NA
Using Logarithms to Model Data
Functions and Other Graphs
Uses function notation to describe and sketch functions
NSW.MA5.3-12NA
Function Notation
Measurement and Geometry eTAP Lesson
Area and Surface Area
Calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms
NSW.MA5.1-8MG
Areas of Rectangles and Parallelograms

Areas of Triangles, Trapezoids and Kites
Calculates the surface areas of right prisms, cylinders and related composite solids
NSW.MA5.2-11MG
Surface Area
Applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids
NSW.MA5.3-13MG
Areas of Regular Polygons

Areas of Circles
Volume
Applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders
NSW.MA5.2-12MG
Cylinders

Polyhedrons, Prisms and Pyramids
Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids
NSW.MA5.3-14MG
Cones

Solids with Curved Surfaces
Numbers of Any Magnitude
Interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures
NSW.MA5.1-9MG
Base Ten Exponents
Right-Angled Triangles (Trigonometry)
Applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression
NSW.MA5.1-10MG
Measuring Angles
Applies trigonometry to solve problems, including problems involving bearings
NSW.MA5.2-13MG
Trigonometric Calculations
Trigonometry and Pythagoras' Theorem
Applies Pythagorasâ€™ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions
NSW.MA5.3-15MG
Definitions - Sine and Cosine

Law of Sines

Law of Cosines
Properties of Geometrical Figures
Describes and applies the properties of similar figures and scale drawings
NSW.MA5.1-11MG
Similar Triangles
Calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar
NSW.MA5.2-14MG
Indirect Measurement with Similar Triangles
Proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals
NSW.MA5.3-16MG
Corresponding Parts
Circle Geometry
Applies deductive reasoning to prove circle theorems and to solve related problems
NSW.MA5.3-17MG
Tangent Properties
Statistics and Probability eTAP Lesson
Single Variable Data Analysis
Uses statistical displays to compare sets of data, and evaluates statistical claims made in the media
NSW.MA5.1-12SP

Uses quartiles and box plots to compare sets of data, and evaluates sources of data
NSW.MA5.2-15SP
Probability Data Plots
Uses standard deviation to analyse data
NSW.MA5.3-18SP
Normal Distributions
Bivariate Data Analysis
Investigates relationships between two statistical variables, including their relationship over time
NSW.MA5.2-16SP
Standard Deviation of Random Variable
Investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes
NSW.MA5.3-19SP
Dependent & Independent Variables
Probability
Calculates relative frequencies to estimate probabilities of simple and compound events
NSW.MA5.1-13SP
Multiple Events
Describes and calculates probabilities in multi-step chance experiments
NSW.MA5.2-17SP
Conditional Probability