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 |
