Level 10A

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Number and Algebra
Measurement and Geometry
Statistics and Probability
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Australian Mathematics Competition (Australian Maths Trust AMT)
Past Maths Competition and Olympiad Papers Archives (Australian Maths Trust AMT)
AMC Past papers: PDF (Australian Maths Trust AMT)

Number and Algebra

Content Description
​Number and Algebra Summary
  • Notes
  • Videos & Interactives
  • Questions
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Real Numbers
Rational and Irrational Numbers, Surds, and Fractional Indices (VCMNA355)
Types of Numbers 
​Fractional Indices
Surds
​Powers Chart

Logarithms (VCMNA356)
Logarithms
​Exponent and Logarithm Laws
The Log (Base 10) Scale

​Patterns and Algebra
Polynomials and the Factor and Remainder Theorems (VCMNA357)
Polynomials
Polynomial Operations
Polynomial Operations with Algebra Tiles
Expanding and Factorising Polynomials
Remainder and Factor Theorems
​
Algorithms and Simulations to Solve Problems (VCMNA358)
Bisection Method 
​​Simulations for Counter-Intuitive Problems ​

​Linear and Non-Linear Relations
Parabolas, Hyperbolas, Circles, and Exponential Functions and Transformations (VCMNA359)
Transformation of the Plane and Functions
Transformations of a Single Parameter
Parabolas / Quadratic Functions
Hyperbolas
Circles
Exponential Functions

Simple Exponential Equations (VCMNA360)
Exponential Equations 
Applications of Exponential Functions 
​
Graphs of Polynomials (VCMNA361)
Sketching Graphs of Polynomial Functions
Graphs of Polynomials 

Factorise Quadratics and Solve Quadratic Equations (VCMNA362)
Manipulating Quadratic Expressions
Quadratic Equations 
​Modelling with Quadratics

Function Notation (VCMNA363)
​Independent and Dependent Variables 
Functions and Function Notation
Domain, and Range ​​

Simultaneous Equations by Systematic Guess-Check-and-Refine (VCMNA364)
​Cobweb Diagrams 
Real Numbers
Rational and Irrational Numbers, Surds, and Fractional Indices (VCMNA355)
Power Tables (Maths Bot)
Irrational Numbers including Surds (Maffs Guru VIdeo)
​​A Note About Surds & Negative Numbers (Eddie Woo Video)
Explaining Tricky Exponents (James Tanton Video)

​What are Surds, and why are they special? (Eddie Woo Video)
Simplifying Surds (Joel Speranza Math Video)
​
​Simplifying Surds
​Adding & Subtracting Surds (Eddie Woo Video)
Adding and Subtracting Surds (Maffs Guru Video)
Adding and subtracting surds (Joel Speranza Math Video)
Multiplying & Dividing Surds (Eddie Woo Video)
Multiplying and Dividing Surds (Maffs Guru Video)
Multiplying surds and the distributive law (Joel Speranza Math Video)
Dividing Surds (Joel Speranza Math Video)
​Rationalising Binomial Denominators (Eddie Woo Video)
Rationalising the Denominator (Maffs Guru Video)
​
Logarithms (VCMNA356)
Power Tables (Maths Bot)
Logarithms, Explained (TED-Ed Video)

​Logarithms
Logarithms and Exponents (Crash Course Video)
​
​Introduction to Logarithms
​Logarithm Laws
Understanding Logarithms - Comparing with Index Laws (Eddie Woo Video)

Understanding Logarithms
Patterns and Algebra
Polynomials and the Factor and Remainder Theorems (VCMNA357)
Why We Care About Quadratics? (Eddie Woo Video)

Algorithms and Simulations to Solve Problems (VCMNA358)
The Monty Hall Problem (Better Explained Article and Simulator)
Monty Hall (GeoGebra Interactive)

​The Monty Hall Problem ​
Derrangements (Numberphile Video)
Monte Carlo Simulation (MarbleScience Video)

Linear and Non-Linear Relations
Parabolas, Hyperbolas, Circles, and Exponential Functions and Transformations (VCMNA359)
The Hyperbola - Understanding the Graph & its Behaviour (Eddie Woo Video)
Transforming Functions ​(Eddie Woo Video)
​Function Transformations (GeoGebra Interactive)
​Application of Completing the Square - Finding a Parabola's Vertex (Eddie Woo Video)
Graphing Circles - Completing the Square (Eddie Woo Video)
​Graphing the Quadratic (Crash Course)​
​
Graphing Parabolas 
Simple Exponential Equations (VCMNA360)

Graphs of Polynomials (VCMNA361)
Cubic Curves (Eddie Woo Video)

Factorise Quadratics and Solve Quadratic Equations (VCMNA362)
Quadratic Equation Problems
​Multiplying rational expressions (Khan Academy Video)
Dividing rational expressions (Khan Academy Video)

A Different Way to Solve Quadratic Equations (Expii Video)
Interpreting a Parabola in Context (Khan Academy Video)
Interpreting Quadratic Model Example (Khan Academy Video)

Straight Up Curriculum Math for the 21st Century
Function Notation (VCMNA363)

Simultaneous Equations by Systematic Guess-Check-and-Refine (VCMNA364)
Intersection Between Lines & Curves
Visualising Function Iteration via Cobwebbing (Math Insight Interactive)
RULER (Read Underline Layout Evaluate Review) Booklet (Tanner Maths)

Real Numbers
Rational and Irrational Numbers, Surds, and Fractional Indices (VCMNA355)
Fractional Indices (Variation Theory)​
Negative and fractional indices (Study Maths)
Fractional Indices (Miss E Resources)
Fractional Indices (Corbettmaths)
Fractional and Negative Indices (Corbettmaths Exam Style)
Powers Puzzle (Starting Points Maths)
Fraction Powers (Starting Points Maths)
Negative and Fractional Indices (MathsHKO)
Index Laws (Corbettmaths Exam Style)

Is this a surd? (Variation Theory)
Introduction to Surds (Purposeful Maths)
Rational and Irrational Numbers (Corbettmaths)
Rational and Irrational Numbers (Corbettmaths Exam Style)
Simplifying Surds (1) (Purposeful Maths)
Simplifying Surds (2) (Purposeful Maths)
Simplifying Surds 1 (Variation Theory)
Simplifying Surds 2 (Variation Theory)
​Simplifying Surds (Interactive Practice)
Surds (MathsHKO)
SURDS (Dr Austin Maths)
Length of a Line Segment as Surds (Variation Theory)
​Adding Surds (Minimally Different)
Adding Surds (Variation Theory)
Adding and subtracting surds (Study Maths)
Squares/Roots using Area (PowerPoint)
Multiplying Surds (Minimally Different)
Multiplying Surds (Variation Theory)
Surds & Rectangles (MathsPad)
Simplifying Dividing Surds (Interactive Practice)
Multiplying and Simplifying Surds (Variation Theory)
Multiplying Surds (Purposeful Maths)
Expanding Brackets with Surds (1) (Purposeful Maths)
Expanding Brackets with Surds (2) (Purposeful Maths)
Multiplying surds (Study Maths)
Surds: mixed operations (Variation Theory)
Surds with Powers (Variation Theory)
Order of Operations: Roots (Variation Theory)
Identifying Conjugates (Variation Theory)
Multiplying Surds in Double Brackets (Variation Theory)
Multiplication of Surds Build Up (Starting Points Maths)
Surds Arithmetic (Corbettmaths Exam Style)
Rationalising the Denominator (Corbettmaths Exam Style)
Surds: Rationalise the Denominator (Variation Theory)
Surds: Rationalise the Denominator 2 (Variation Theory)
Rationalising the Denominator (Starting Points Maths)
Surds (Corbettmaths)
​Surds (Corbettmaths Exam Style)
​Finding Hypotenuses With Surds (Variation Theory)
Averages with Surds (Interwoven Maths)
​Reciprocals (MathsHKO)
Pythagoras and Trigonometry with... (Mixed Questions) (Interwoven Maths)

Logarithms (VCMNA356)

​Patterns and Algebra
Polynomials and the Factor and Remainder Theorems (VCMNA357)
Factor Theorem (Variation Theory)

Algorithms and Simulations to Solve Problems (VCMNA358)

​Linear and Non-Linear Relations
Parabolas, Hyperbolas, Circles, and Exponential Functions and Transformations (VCMNA359)
Sketching Quadratics (Corbettmaths)
Quadratic Graphs (Corbettmaths Exam Style)​
Graphing Quadratic Equations in Vertex Form (Interactive Practice)
Finding Axis Intercepts (Starting Points Maths)
Exponential Graphs (Corbettmaths Exam Style)
​Exponential Graphs (Corbettmaths Exam Style)
Equation of a Circle (Corbettmaths Exam Style)
​
Simple Exponential Equations (VCMNA360)
​Repeated Percentage Change With Multipliers (Mr Coward Maths)
Growth and decay problems (Boss Maths)

Graphs of Polynomials (VCMNA361)
​Graphing a Cubic Function (Interactive Practice)
Cubic Graphs (Corbettmaths Exam Style)

Factorise Quadratics and Solve Quadratic Equations (VCMNA362)
Completing the Square (Monic) (Variation Theory)
Completing the Square (Non-Monic) (Variation Theory)
​Completing the Square (Corbettmaths)
Completing the Square (Corbettmaths Exam Style)
Completing the Square (Corbettmaths Exam Style)
​​Completing the Square (Interactive Practice)
Multiplies to, Adds to (Positive) (Variation Theory)
Multiplies to, Adds to (Mixed) (Variation Theory)
Factorising into Double Brackets (Positive) (Variation Theory)
Factorising into Double Brackets (Positive 2) (Variation Theory)
Factorising into Double Brackets (Negative) (Variation Theory)
Factorising into Double Brackets (Mixed) (Variation Theory)
Factorising Binomial Products (Interactive Practice)
​Increasingly Difficult Factorisation: Quadratics (Starting Points Maths)
Factorising Quadratics (Corbettmaths Exam Style)
Factorising harder quadratic expressions (Study Maths)
Factorising Quadratics where the Coefficients of x² is not 1 (Variation Theory)
Boxes into Factorising Quadratics (Sam Blatherwick)
Scaffolded Factorisation (ac methd) (Starting Points Maths)
Expanding and Factorising Quadratics (Interwoven Maths Booklet)
Difference of Two Squares - Pattern Spotting (Variation Theory)
Difference of Two Squares (Variation Theory)
HCF and LCM of Algebraic Terms (Swinton Maths)
Simplifying Algebraic Fractions with Quadratics (Variation Theory)
Algebraic Fractions (Corbettmaths)
Simplifying Algebraic Fractions (Corbettmaths)
Factorising Harder Questions (Corbettmaths)
Algebraic Fractions (Corbettmaths Exam Style)
How many brackets? (Variation Theory)
Equations involving Fractions (Advanced) (Corbettmaths Exam Style)
Solve Quadratics by Factorising (Corbettmaths)
Solving Quadratics by Factorising (Corbettmaths Exam Style)
Solving Quadratics by Factorising (Corbettmaths Exam Style)
Solving Quadratics by Completing the Square (Corbettmaths)
Solving Quadratics by Completing the Square (Corbettmaths Exam Style)
Solving Quadratics by Quadratic Formula (Corbettmaths Exam Style)
Using the quadratic formula (Study Maths)
The Quadratic Formula (Andy Lutwyche)
Quadratic Formula (Corbettmaths)
Quadratic Formula (Corbettmaths Exam Style)
Equations: Advanced Fractional (Corbettmaths)
Equations: Cross Multiplication (Corbettmaths)

Function Notation (VCMNA363)

Simultaneous Equations by Systematic Guess-Check-and-Refine (VCMNA364)

Measurement and Geometry

Content Description
​Measurement and Geometry Summary​
  • Notes
  • Videos & Interactives
  • Questions
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Using Units of Measurement
Surface Area and Volume of Pyramids, Cones, Spheres, and Composite Solids (VCMMG365)
Surface Area and Volume of Pyramids, Cones, and Spheres
​Composite Solids
​Proof of Cones and Pyramids 
​​Proof of the Volume and Surface Area of Spheres 

​Geometric Reasoning
Circle Theorems (VCMMG366)
Circle Theorems: Radii and Chords
Circle Theorem: Subtended Angles
Circle Theorems: Secants and Tangents (Optional)
Circle Theorems Summary 
​Proofs of and using Circle Theorems 

​Pythagoras and Trigonometry
Sine and Cosine Rules (VCMMG367)
​Sine Rule and Cosine Rule for Non-Right-Angled Triangles 
​​Bearings with Non-Right-Angled Triangles
Area of a Triangle
Area of Regular Polygons

Unit Circle Definitions of Trigonometric Functions and their Graphs (VCMMG368)
​​The Unit Circle and Coterminal Angles
Trigonometric Functions
Periodicity and Symmetry
Evaluating Trigonometric Functions with Exact Values
Sine, Cosine, and Tangent Functions
Applications of Sine and Cosine Functions
​
Solve Simple Trigonometric Equations (VCMMG369)
​​Trigonometric Equations​ 

Pythagoras' Theorem and Trigonometry in Three-Dimensions (VCMMG370)
​Triangles in Three Dimensions 
Using Units of Measurement
Surface Area and Volume of Pyramids, Cones, Spheres, and Composite Solids (VCMMG365)
3 Pyramids = 1 Cube (GeoGebra Interactive)
Cross Sections of Sphere and Cone (GeoGebra Interactive)
Surface Area Cones and Spheres (Joel Speranza Math Video)
Intuition behind Volume of a Pyramid (Khan Academy Video)
Formula for the Volume of a Cone (James Tanton Video)
Finding the Surface Area of Spheres and Hemispheres (Eddie Woo Video)
Volume of a Sphere (Eddie Woo Video)
Volume of a Sphere (Corbettmaths Video)
Cavalieri's Principle in 3D | Volume of a Sphere | (Think Twice Video)
Cavalieri's Principle (Khan Academy)
Volumes of Cones Intuition (Khan Academy)
Volume of tapered solids (Joel Speranza Math Video)
​
​Geometric Reasoning
Circle Theorems (VCMMG366)
Angle at the Centre (GeoGebra Interactive)
Angle in a Semicircle (GeoGebra Interactive)
Angles in the Same Segment (GeoGebra Interactive)
Cyclic Quadrilateral (GeoGebra Interactive)
Angle in the Alternate Segment (GeoGebra Interactive)
Intersecting Chords (GeoGebra Interactive)
Intersecting Secants (GeoGebra Interactive)
​Intersecting Tangents (GeoGebra Interactive)
​
The Angle on the Same Arc Theorem (Joel Speranza Math Video)
Prove the Angle at the Centre Theorem  (Joel Speranza Math Video)
Prove the Angle in a Semi Circle is a Right Angle (Joel Speranza Math Video)
Proving Chord of Circle Theorem (Joel Speranza Math Video)
Proving Tangent to a Circle and the Radius are Perpendicular using Proof by Contradiction (Joel Speranza Math Video)
Proving the Cyclic Quadrilateral Theorem (Joel Speranza Math Video)
​Alternate Segment Theorem Proof (Joel Speranza Math Video)
​Intersecting Chord Theorem Proof (Joel Speranza Math Video)
Proving the tangent secant theorem (Joel Speranza Math Video)
​Equidistant chord Theorem Proof (Joel Speranza Math Video)

Angle Properties 
​Tangents from an External Point are Equal (Eddie Woo Video)

Angle in the Alternate Segment
Intercept Properties
Properties of Tangents (GeoGebra Interactive)

Pythagoras and Trigonometry
Sine and Cosine Rules (VCMMG367)
The Sine Rule
Ambiguous Case (SSA) Illustrator: All Cases (GeoGebra Interactive)
​
​The Cosine Rule
Cosine Rule (GeoGebra Interactive)
​Area of a Triangle - Deriving the Trigonometric Formula (Eddie Woo Video)
​Bearings: Dynamic Illustrator (GeoGebra Interactive)

Unit Circle Definitions of Trigonometric Functions and their Graphs (VCMMG368)
The Unit Circle Model (GeoGebra Interactive)
​Ferris Wheel: Modelling with Trigonometric Functions (GeoGebra ​Interactive)

Solve Simple Trigonometric Equations (VCMMG369)

Pythagoras' Theorem and Trigonometry in Three-Dimensions (VCMMG370)

Using Units of Measurement
Surface Area and Volume of Pyramids, Cones, Spheres, and Composite Solids (VCMMG365)
Surface Area - Cone (mathworksheets4kids)
Surface Area of a Cone (Corbettmaths)
Surface Area of a Cone (Corbettmaths Exam Style)
Surface Area - Square Pyramid (mathworksheets4kids)
Surface Area of a Sphere (Corbettmaths)
Surface Area of a Sphere (Corbettmaths Exam Style)
Surface Area - Mixed Shapes (mathworksheets4kids)
Volume of a Pyramid (Variation Theory)
Volume of pyramids (Study Maths)
Volume - Pyramids (mathworksheets4kids)
Volume of a Pyramid (Corbettmaths)
Volume of a Pyramid (Corbettmaths Exam Style)
Volume - Rectangular Pyramid 1 (mathworksheets4kids)
Volume - Rectangular Pyramid 2 (mathworksheets4kids)
Volume of a Cone (Variation Theory)
Volume of cones (Study Maths)
Volume - Cone 1 (mathworksheets4kids)
Volume - Cone 2 (mathworksheets4kids)
Volume - Cone 3 (mathworksheets4kids)
Volume of a Cone (Corbettmaths)
Volume of a Cone (Corbettmaths Exam Style)
Volume - Cones and Pyramids (mathworksheets4kids)
Volume of spheres (Study Maths)
Volume of a Sphere (Corbettmaths)
Volume of a Sphere (Corbettmaths Exam Style)
Volume - Sphere & Hemisphere (mathworksheets4kids)
Volume - Mixed Shapes 1 (mathworksheets4kids)
Volume - Mixed Shapes 2 (mathworksheets4kids)
Volume - Composite Shapes 1 (mathworksheets4kids)
Volume - Composite Shapes 2 (mathworksheets4kids)
Volume - Composite Shapes 3 (mathworksheets4kids)​
Backwards Volumes (Starting Points Maths)
Interwoven Volume and Surface Area Completion Tables (Interwoven Maths)

​​Geometric Reasoning
Circle Theorems (VCMMG366)
Parts of the Circle (Corbettmaths)
Parts of the Circle (CorbettmathsExam Style)
Introducing Circle Theorems (Interwoven Maths)
Subtending Angles (Mathematical Musings)
Circle Theorems: Angle at the Centre (Variation Theory)
Circle Theorems: Angle in a Semicircle (Variation Theory)
Circle Theorems: Cyclic Quadrilaterals (Variation Theory)
Circle Theorems (Corbettmaths)
Circle Theorems (Corbettmaths Exam Style)
Circle Theorems (Corbettmaths Exam Style)
Circle Theorems (MathsHKO)
CanFigureIt Geometry: Proofs Simplified (Interactive Practice - Free Login)
Geometric Proof (Corbettmaths Exam Style)
Pythagoras' with Circle Theorems (Go Teach Maths)
Circle Theorems - Mixed (Go Teach Maths)
Angles - Mixed (Go Teach Maths)
Solving Linear Equations from Circle Theorems (Interwoven Maths)
Solving Further Equations with Circle Theorems (Interwoven Maths)
Interleaving Circle Theorems 1 (Mr Draper Maths)
Circle Theorems with... (no diagrams!) (Interwoven Maths)
Intersecting Chord and Secant Theorems (Dr Frost Maths)

Circle Theorems
​​Pythagoras and Trigonometry
Sine and Cosine Rules (VCMMG367)
​Sine Rule: Finding Missing Sides (Minimally Different)
Sine Rule: Missing Sides (mathworksheets4kids)
Sine Rule: Missing Angles (mathworksheets4kids)
Sine Rule: Mixed (mathworksheets4kids)
Sine Rule (Corbettmaths)
​Cosine Rule: Missing Sides (mathworksheets4kids)
Cosine Rule: Missing Angles (mathworksheets4kids)
Cosine Rule: Missing Angles (Variation Theory)
Cosine Rule (Corbettmaths)
Cosine rule (Study Maths)
Cosine Rule (Variation Theory)
Sine and Cosine Rule Match Up (Starting Points Maths)
​Enough Information for Non-right Angled Triangles (Miss E Resources)
Area of a Triangle using Included Angle (mathworksheets4kids)​
Area of a Triangle - Trigonometry (Variation Theory)
Area of any Triangle (Corbettmaths)
Area of a Scalene Triangle - Heron's Formula (mathworksheets4kids)​
Sine Rule, Cosine Rule, and Area of any Triangle (Corbettmaths Exam Style)
Advanced Trigonometry (MathsHKO)
Trigonometry (Maths Bot Interactive Practice)

Unit Circle Definitions of Trigonometric Functions and their Graphs (VCMMG368)
Coordinates on the unit circle (Mr Coward Maths)
Graphing Trig Functions (Interactive Practice)
Graphing Trig Equations 2 (Interactive Practice)​​​​​
Graphs of Trigonometric Functions (Corbettmaths)
Trigonometric Graphs (Corbettmaths Exam Style)
Trigonometric Graphs (Corbettmaths Exam Style)

Solve Simple Trigonometric Equations (VCMMG369)
Exact Trig Values (Corbettmaths)
Exact Trig Values in Degrees (Corbettmaths Exam Style)

Pythagoras' Theorem and Trigonometry in Three-Dimensions (VCMMG370)
​Pythagoras in three dimensions (Study Maths)
3D Pythagoras (Corbettmaths)
3D Pythagoras (Corbettmaths Exam Style)
3D Trigonometry (Corbettmaths)
3D Trigonometry (Corbettmaths Exam Style)
3D Pythagoras and Trigonometry (Corbettmaths Exam Style)
Finding Hypotenuses With Overlapping Triangles (Variation Theory)

Statistics and Probability

​Content Description
​Statistics and Probability Summary
  • Notes
  • Videos & Interactives
  • Questions
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Chance
Planning and Implementation of Studies (VCMSP371)​
3 Ways to Spot a Bad Statistic (TED Video)
​Misleading Graphs (Venngage Article)
​How to spot a misleading graph (TED-Ed Video)
Misleading Graphs (Eddie Woo Video)
Misleading Graphs (Corbettmaths Video)
Sampling Methods (GeoGebra Interactive)
Simulators (MathsWhiteboard Interactives)
​​
​Data Representation and Interpretation
Mean and Standard Deviations (VCMSP372)
​Dot Plot - How a Data Value Affects Statistics (GeoGebra Interactive)
Characterising a Dataset - Discussing outliers (Eddie Woo Video)
​
Scatterplots and Lines of Best Fit (VCMSP373)
Fitting Equations to Data (Crash Course Video)
Chance
Planning and Implementation of Studies (VCMSP371)​
​Random Sampling (Corbettmaths Exam Style)
Stratified Sampling (Variation Theory)
Stratified Sampling (Corbettmaths)
​Stratified Sampling (Corbettmaths Exam Style)

​Data Representation and Interpretation
Mean and Standard Deviations (VCMSP372)
Standard Deviation from a Summary Table (Variation Theory)
Standard Deviation from a List (Variation Theory)
Standard Deviation Word Problems (Starting Points Maths)

Scatterplots and Lines of Best Fit (VCMSP373)
Identifying an Appropriate Line of Best Fit (Variation Theory)
Lines of Best Fit (Worksheet)
Three-Median Line (VCAA Exam Questions)