# year 11-12 MAths

## What our Year 11-12 Maths students will develop

### A deeper level of understanding

All of our material is directly linked to topics from the NSW Board of studies. We start with explaining theory, then start with easier questions and move onto exam style questions

### A fun learning environment

Our lessons are fun, engaging and relaxed. We encourage group discussions, and students are encouraged to ask as many questions as possible!

## What you will recieve

#### Each student at PLATO receives three different books each week which are personalised to each individual!

### Weekly books

We design, print and hand out new books to all students each week. We do not bulk print our materials at the start of each term! Our materials evolve week-to-week, learning from the mistakes of all students and automatically refine to become the ultimate learning tools!

###
Class theory book

The theory books contain the class common questions and notes. There is also a weekly report at the front which is jam-packed with details about each student.

### Personalised homework book

These books contain homework questions which are unique to each student based on their weaknesses or special requests. To learn more about the homework system at PLATO, click here.

### Answer books

At PLATO, we get you ready from as early as Year 6 to organise your mathematical arguments. In English, we learn how to organise text with paragraphs and sentences, and maths is no different! We teach students how to logically present their work, with our proven answer book system!

## What ouR PARENTS recieve

### Weekly reports

Our parents and studnets receive a weekly email report letting them know how their progress has changed, and which topics they are struggling with at the moment

### DIRECT COMMUNICATION

You can contact us directly by SMS or phone call, and speak to your child's tutor directly. No emails, no help desk! Just straight to the point communication!

### Our proven lesson breakdown

### 10 weekly lessons in the school term

## 15 min

###### Weekly quiz

**Weekly quiz on content from the previous week.**

## 30 min

###### Homework help

**We go through any homework related issues, and ensure all students are comfortable.**

## 135 min

###### Lesson

**We teach new material, developing theory, and slowing move up in difficulty until we are answering exam-style questions.**

# Maths years 11-12 details

- Year 11
- Year 12

### Year 11 Details

- 2U
- 3U

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Algebra

##### Algebra Review

## week 2

#### Algebra

##### Algebra Review

## week 3

#### Functions

##### Domain and Range

## week 4

#### Functions

##### Function Vs Relation and Odd, Even, Neither functions

## week 5

#### Functions

##### Compound Functional Analysis

## week 6

#### Functions

##### Linear functions

## week 7

#### Functions

##### Linear FUNCTIONS

## week 8

#### Functions

##### Quadratics FUNCTIONS

## week 9

#### Functions

##### Cubic Functions

## week 10

#### Functions

##### Absolute Value Functions

*ALGEBRA REVIEW*

*ALGEBRA REVIEW*

*DOMAIN AND RANGE*

*FUNCTION VS RELATION AND ODD, EVEN, NEITHER FUNCTIONS*

*COMPOUND FUNCTIONAL ANALYSIS*

*LINEAR FUNCTIONS*

*LINEAR FUNCTIONS*

*QUADRATICS FUNCTIONS*

*CUBIC FUNCTIONS*

*ABSOLUTE VALUE FUNCTIONS*

## week 1

#### Functions

##### Circles

## week 2

#### Trigonometry

##### Basic trigonometry, the Sine rule, the Cosine rule, and the area rule

## week 3

#### Trigonometry

##### Angles of elevation and depression

## week 4

#### Trigonometry

##### 2D/3D Trigonometry

## week 5

#### Trigonometry

##### Radians

## week 6

#### Trigonometry

##### Trigonometric Identities

## week 7

#### Trigonometry

##### Sketching Trigonometric functions, simplyfing trigonometric equations (including those that reduce to quadratics)

## week 8

#### Introduction to Differentiation

##### Gradients of tangents

## week 9

#### Introduction to Differentiation

##### First principles

## week 10

#### Introduction to Differentiation

##### The Rules of Differentiation

*CIRCLES*

*BASIC TRIGONOMETRY, THE SINE RULE, THE COSINE RULE, AND THE AREA RULE*

*ANGLES OF ELEVATION AND DEPRESSION*

*2D/3D TRIGONOMETRY*

*RADIANS*

*TRIGONOMETRIC IDENTITIES*

*SKETCHING TRIGONOMETRIC FUNCTIONS, SIMPLYFING TRIGONOMETRIC EQUATIONS (INCLUDING THOSE THAT REDUCE TO QUADRATICS)*

*GRADIENTS OF TANGENTS*

*THE RULES OF DIFFERENTIATION*

## week 1

#### Introduction to Differentiation

##### Graphical applications of simple differention

## week 2

#### Introduction to Differentiation

##### Motion

## week 3

#### Logarithms and Exponentials

##### Introducing logarithms

## week 4

#### Logarithms and Exponentials

##### Exponentials

## week 5

#### Logarithms and Exponentials

##### Graphs and applications of exponential and logarithmic functions

## week 6

#### Probability

##### Simple probability and probability trees

## week 7

#### Revision 1

##### Trigonometric Identities and Proofs

## week 8

#### Practice Exam

##### Practice Exam

## week 9

#### Probability and Discrete Probability Distributions

##### Probability and Venn diagrams

## week 10

#### Probability and Discrete Probability Distributions

##### Mean and variance

*GRAPHICAL APPLICATIONS OF SIMPLE DIFFERENTION*

*MOTION*

*INTRODUCING LOGARITHMS*

*EXPONENTIALS*

*GRAPHS AND APPLICATIONS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS*

*SIMPLE PROBABILITY AND PROBABILITY TREES*

*TRIGONOMETRIC IDENTITIES AND PROOFS*

*PRACTICE EXAM*

*PROBABILITY AND VENN DIAGRAMS*

*MEAN AND VARIANCE*

## week 1

## week 2

## week 3

## week 4

## week 5

## week 6

## week 7

## week 8

## week 9

## week 10

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Graphs

##### Graphs 1

## week 2

#### Graphs

##### Graphs 2

## week 3

#### Functions

##### Polynomial Division

## week 4

#### Functions

##### Sums and products of roots of polynomials

## week 5

#### Functions

##### Investigating the multiplicity of a root of a polynomial

## week 6

#### Functions

##### Polynomial Graphing

## week 7

#### Rates of change

##### Particle motion

## week 8

#### Exponential and Logarithms

##### Differentiation of exponentials, and related problems

## week 9

#### Rates of change

##### Describe the rate of change of a physical quantity with respect to time as a derivative

## week 10

#### Rates of change

##### Solve problems involving situations that can be modelled using the exponential model or the modified exponential model and sketch graphs appropriate to such problems

*GRAPHS 1*

*GRAPHS 2*

*POLYNOMIAL DIVISION*

*SUMS AND PRODUCTS OF ROOTS OF POLYNOMIALS*

*INVESTIGATING THE MULTIPLICITY OF A ROOT OF A POLYNOMIAL*

*POLYNOMIAL GRAPHING*

*PARTICLE MOTION*

*DIFFERENTIATION OF EXPONENTIALS, AND RELATED PROBLEMS*

*DESCRIBE THE RATE OF CHANGE OF A PHYSICAL QUANTITY WITH RESPECT TO TIME AS A DERIVATIVE*

*SOLVE PROBLEMS INVOLVING SITUATIONS THAT CAN BE MODELLED USING THE EXPONENTIAL MODEL OR THE MODIFIED EXPONENTIAL MODEL AND SKETCH GRAPHS APPROPRIATE TO SUCH PROBLEMS*

## week 1

#### Probability and Statistics

##### Probability Revision

## week 2

#### Probability and Statistics

##### Conditional probability

## week 3

#### Probability and Statistics

##### Discrete probability distributions

## week 4

#### Permutations and Combinations

##### Working with CombinatoricsThe binomial expansion and Pascals triangle

## week 5

#### Permutations and Combinations

##### Factorial problems

## week 6

#### Exam

##### Practice Exam

## week 7

#### Polynomials

##### Review before rates of change, including their derivatSums of roots and multiple root theoremives

## week 8

#### Permutations and Combinations

##### Permutations and Combinations

## week 9

#### Calculus

##### Calculus 2U11

## week 10

#### Trigonometry

##### Trigonometric Functions

*PROBABILITY REVISION*

*CONDITIONAL PROBABILITY*

*DISCRETE PROBABILITY DISTRIBUTIONS*

*WORKING WITH COMBINATORICSTHE BINOMIAL EXPANSION AND PASCALS TRIANGLE*

*FACTORIAL PROBLEMS*

*PRACTICE EXAM*

*REVIEW BEFORE RATES OF CHANGE, INCLUDING THEIR DERIVATSUMS OF ROOTS AND MULTIPLE ROOT THEOREMIVES*

*REVIEW BEFORE RATES OF CHANGE, INCLUDING THEIR DERIVATSUMS OF ROOTS AND MULTIPLE ROOT THEOREMIVES*

*CALCULUS 2U11*

*TRIGONOMETRIC FUNCTIONS*

## week 1

#### Further work with functions

##### Inverse functions

## week 2

#### Trigonometry

##### Inverse Trigonometry (Equations)

## week 3

#### Trigonometry

##### Inverse Trigonometry (Graphs)

## week 4

#### Calculus

##### Rates of change with respect to time

## week 5

#### Calculus

##### Exponential growth and decay

## week 6

#### Calculus

##### Related rates of change

## week 7

#### Trigonometry

##### Compound Angles 1

## week 8

#### Trigonometry

##### Compound Angles 2

## week 9

#### Trigonometry

##### Solving trigonometric equations

## week 10

#### Higher differentiation

##### Understanding the first derivatie

*INVERSE FUNCTIONS*

*INVERSE TRIGONOMETRY (EQUATIONS)*

*INVERSE TRIGONOMETRY (GRAPHS)*

*RATES OF CHANGE WITH RESPECT TO TIME*

*EXPONENTIAL GROWTH AND DECAY*

*RELATED RATES OF CHANGE*

*COMPOUND ANGLES 1*

*COMPOUND ANGLES 2*

*SOLVING TRIGONOMETRIC EQUATIONS*

*UNDERSTANDING THE FIRST DERIVATIE*

## week 1

#### Calculus

##### An Introduction to Calculus

## week 2

#### Calculus

##### Calculating with derivatives

## week 3

#### Functions

##### Further work with functions 1

## week 4

#### Functions

##### Further work with functions 2

## week 5

#### Trigonometric Functions

##### Trigonometric Functions and Identities

## week 6

#### Trigonometric Functions

##### Further Trigonometric Identities

## week 7

#### Functions

##### Inverse functions and Parametric Equations

## week 8

#### Trigonometric Functions

##### Inverse Trigonometric Functions (Graphs)

## week 9

#### Trigonometric Functions

##### Inverse Trigonometric Functions (Algebra)

## week 10

#### Exponential and Logarithmic Functions

##### Logarithms and Exponentials 1

*AN INTRODUCTION TO CALCULUS*

*CALCULATING WITH DERIVATIVES*

*FURTHER WORK WITH FUNCTIONS 1*

*FURTHER WORK WITH FUNCTIONS 2*

*TRIGONOMETRIC FUNCTIONS AND IDENTITIES*

*FURTHER TRIGONOMETRIC IDENTITIES*

*INVERSE FUNCTIONS AND PARAMETRIC EQUATIONS*

*INVERSE TRIGONOMETRIC FUNCTIONS (GRAPHS)*

*INVERSE TRIGONOMETRIC FUNCTIONS (ALGEBRA)*

*LOGARITHMS AND EXPONENTIALS 1*

### Year 12 Details

- 2U
- 3U
- 4U

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Integration

##### Further Areas Under the Curve

## week 2

#### Functions

##### Graphing Techniques 1

## week 3

#### Graphs

##### Graphing Techniques 2

## week 4

#### Calculus

##### Particle Motion

## week 5

#### Calculus

##### The graphs of particle motion

## week 6

#### Trigonometry

##### Sketching trigonometric graphs

## week 7

#### Trigonometry

##### Solving Trigonometric Equations

## week 8

#### Logarithmic and Exponentials

##### Problem solving with exponentials and logarithms

## week 9

#### Statistics

##### Understanding Frequency (empirical) probabilities

## week 10

#### Statistics

##### Conditional Probabilities

## week 11

#### Statistics

##### Discrete Probability Distributions

## week 12

#### Descriptive Statistics and Bivariate Data Analysis

##### Data (grouped and ungrouped) and summary statistics

*FURTHER AREAS UNDER THE CURVE*

*GRAPHING TECHNIQUES 1*

*GRAPHING TECHNIQUES 2*

*PARTICLE MOTION*

*THE GRAPHS OF PARTICLE MOTION*

*SKETCHING TRIGONOMETRIC GRAPHS*

*SOLVING TRIGONOMETRIC EQUATIONS*

*PROBLEM SOLVING WITH EXPONENTIALS AND LOGARITHMS*

*UNDERSTANDING FREQUENCY (EMPIRICAL) PROBABILITIES*

*CONDITIONAL PROBABILITIES*

*DISCRETE PROBABILITY DISTRIBUTIONS*

*DATA (GROUPED AND UNGROUPED) AND SUMMARY STATISTICS*

## week 1

#### Descriptive Statistics and Bivariate Data Analysis

##### Bivariate Data Analysis

## week 2

#### Revision 1

##### Integration of Trigonometric Functions, and Area under the curve

## week 3

#### Revision 2

##### Applications of the second derivative

## week 4

#### Revision 3

##### Prove trigonometric identities

## week 5

#### Statistics

##### Continuous Random Variables

## week 6

#### Statistics

##### The Normal Distribution

## week 7

#### Exam

##### Practice Trial Exam

## week 8

#### Sequences and Series

##### Review of AP and GP

## week 9

#### Sequences and Series

##### Financial Mathematics 1 (Compound Interest)

## week 10

#### Sequences and Series

##### Financial Mathematics 2 (Annuities)

## week 11

#### Sequences and Series

##### Financial Mathematics 3 (Reducing balance)

## week 12

#### Trigonometry

##### Solve problems involving the use of trigonometry in two and three dimensions

*BIVARIATE DATA ANALYSIS*

*INTEGRATION OF TRIGONOMETRIC FUNCTIONS, AND AREA UNDER THE CURVE*

*APPLICATIONS OF THE SECOND DERIVATIVE*

*PROVE TRIGONOMETRIC IDENTITIES*

*CONTINUOUS RANDOM VARIABLES*

*THE NORMAL DISTRIBUTION*

*PRACTICE TRIAL EXAM*

*REVIEW OF AP AND GP*

*FINANCIAL MATHEMATICS 1 (COMPOUND INTEREST)*

*FINANCIAL MATHEMATICS 2 (ANNUITIES)*

*FINANCIAL MATHEMATICS 3 (REDUCING BALANCE)*

*SOLVE PROBLEMS INVOLVING THE USE OF TRIGONOMETRY IN TWO AND THREE DIMENSIONS*

## week 1

#### Graphs

##### Revision of graphing techniques

## week 2

#### Exam

##### Practice Trial Exam

## week 3

#### Financial Mathematics

##### Surprise! 😀

## week 4

#### Revision

##### Linear functions and discrete probability revision

## week 5

#### Class requested revision

##### Applications of exponentials

## week 6

#### Class requested revision

##### Trigonometric Functions and Graphs

## week 7

#### Calculus

##### Optimisation Problems

## week 8

#### Class requested revision

##### Domain/Range, PDF/CDF, Probability

## week 9

#### Revision

##### Harder bearings and z-score

## week 10

#### Exam

##### Practice Trial Exam

## week 11

#### Exam

##### Practice Trial Exam

## week 12

#### Exam

##### Practice Trial Exam

*REVISION OF GRAPHING TECHNIQUES*

*PRACTICE TRIAL EXAM*

*SURPRISE! :-D*

*LINEAR FUNCTIONS AND DISCRETE PROBABILITY REVISION*

*APPLICATIONS OF EXPONENTIALS*

*TRIGONOMETRIC FUNCTIONS AND GRAPHS*

*OPTIMISATION PROBLEMS*

*DOMAIN/RANGE, PDF/CDF, PROBABILITY*

*HARDER BEARINGS AND Z-SCORE*

*PRACTICE TRIAL EXAM*

*PRACTICE TRIAL EXAM*

*PRACTICE TRIAL EXAM*

## week 1

#### Sequences and Series

##### Arithmetic Series

## week 2

#### Sequences and Series

##### Geometric Series

## week 3

#### Sequences and Series

##### Financial Applications 1

## week 4

#### Sequences and Series

##### Financial Applications 2

## week 5

#### Calculus

##### Rules of Differentiation

## week 6

#### Calculus

##### Understanding the first derivative

## week 7

#### Calculus

##### Understanding the second derivative

## week 8

#### Calculus

##### Optimisation Problems

## week 9

#### Calculus

##### Rules of Integral Calculus

## week 10

#### Calculus

##### The Trapezoidal Rule and similar problems

## week 11

#### Calculus

##### Definite Integrals

## week 12

#### Exam

##### Practice Trial Exam

*ARITHMETIC SERIES*

*GEOMETRIC SERIES*

*FINANCIAL APPLICATIONS 1*

*FINANCIAL APPLICATIONS 2*

*RULES OF DIFFERENTIATION*

*UNDERSTANDING THE FIRST DERIVATIVE*

*UNDERSTANDING THE SECOND DERIVATIVE*

*OPTIMISATION PROBLEMS*

*RULES OF INTEGRAL CALCULUS*

*THE TRAPEZOIDAL RULE AND SIMILAR PROBLEMS*

*DEFINITE INTEGRALS*

*PRACTICE TRIAL EXAM*

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Calculus

##### Area between curves

## week 2

#### Calculus

##### ODEs 1

## week 3

#### Calculus

##### Solving ODEs

## week 4

#### Calculus

##### Solving ODEs using the separation of variables

## week 5

#### Calculus

##### Sketch ODEs

## week 6

#### Calculus

##### Applications of ODEs to the real world

## week 7

#### Projectile Motion

##### Understand the concept of a projectile

## week 8

#### Projectile Motion

##### Apply calculus to the equations of motion to solve problems involving projectiles

## week 9

#### Statistics

##### Discrete Probability Distributions

## week 10

#### Projectile Motion

##### Projectile 1

## week 11

#### Polynomials

##### Polynomial Revision 1

## week 12

#### Exam

##### Practice Trial

*AREA BETWEEN CURVES*

*ODES 1*

*SOLVING ODES*

*SOLVING ODES USING THE SEPARATION OF VARIABLES*

*SKETCH ODES*

*APPLICATIONS OF ODES TO THE REAL WORLD*