Government Standards



New South Wales Education Standards

Math - Grade 10

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

Solving Quadratic Equations by Graphing
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 Pythagoras’ 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