# Changes to Mathematics in 2018 Digested For You

Do words such as *Bernoulli, Interval Estimate, Sample Proportion, Confidence Interval, or Matrices* sound familiar?

In 2018, the Board of Studies will be implementing certain changes to the NSW Syllabus (Stage 6) for students beginning Year 11 for all Mathematics levels. If you have been wondering what is planned for the future of mathematics this article provides a summary of each notable change.

If you are reading this as a current student or a graduate from any of these courses it is always nice to how things will change. For those currently in Year 9 and planning to take on any of these courses in 2018, I’m sure some light reading never hurt.

**Summary of Changes for 2 Unit Mathematics**

**Year 11 (NEW)**

- Trigonometry and Radians * NEW
- Trigonometric Functions
- Functions
- Logarithms and Exponentials
- Series and Sequences
- Introduction to Differentiation
- Descriptive Statistics * NEW
- Probability * NEW
- Probability Distributions * NEW
- Matrix Operations * NEW

**Year 12 ****(NEW)**

- Trigonometric Identities and Proofs
- Graphing Techniques * NEW
- Differential Calculus
- Integral Calculus
- Annuities
- Bivariate Data Analysis * NEW
- The Normal Distribution * NEW
- Matrix Applications * NEW

**Year 11 (OLD)**

- Basic Algebra & Arithmetic
- Plane Geometry
- Real Functions
- Trigonometry
- Linear Functions
- Introductory Calculus
- The Quadratic Function
- Locus & Parabola
- Series & Applications
- Coordinate Methods in Geometry
- Applications of Geometrical Properties

**Year 12 (OLD)**

- Geometrical Applications of Calculus
- Integration
- Trigonometric Functions
- Exponential & Logarithm Functions
- Applications of Calculus to the Physical World & Rates
- Probability

## Notable Changes:

**Binomial Expansion (Probability) – ****Topic moved from 3 Unit! **

Binomial Expansion, originally an Extension 1 topic is now a technique used for determining probability distributions.

**Trigonometry and Radians – ****Topic moved from Year 12 to 11!**

2 Unit students should also expect to learn the relationships of Radian form in trigonometry in Year 11, which as per the old syllabus used to be taught in Year 12.

**Matrices – ****New Topic! **

Students will now be learning Matrices starting from the 2 Unit level.

**Statistics – ****New Topic! **

A continuation topic of statistics will be introduced at the 2 Unit level extending on from Year 9 and 10.

**Introduction to Differentiation – ****Topic moved from Year 12 to 11! **

This introductory calculus topic remains largely the same with the exception that Rates of Change theory is now a requirement in interpreting the differential function. Basically, Rates of Change theory is now taught in Year 11.

**Summary of Changes for 3 Unit Mathematics**

**Year 11 (NEW)**

- Inverse Trigonometric Functions and Graphs * NEW
- Further Work with Functions
- Polynomials
- Related Rates of Change * NEW
- Permutations and Combinations

**Year 12 (NEW)**

- Trigonometric Equations
- Further Calculus Skills
- Exponential Growth and Decay
- Volumes and Solids of Revolution * NEW
- Sampling and Estimates * NEW

**Year 11 (OLD)**

- Basic Algebra & Arithmetic including Other Inequalities
- Plane Geometry
- Further Geometry & Circle Geometry
- Real Functions
- Trigonometry
- Further Trigonometry, Radian Measurement, and General Solutions
- Linear Functions Including Interval Division and Angle Between 2 Lines
- Introductory Calculus
- The Quadratic Function, Locus & The Parabola
- Parametric Representation
- Polynomials
- Permutations & Combinations
- Series & Applications
- Coordinate Methods in Geometry
- Applications of Geometrical Properties
- Integration

**Year 12 (OLD)**

- Integration by Substitution
- Proof by Induction
- Trigonometric Functions Including Primitive of sin2x and cos2x
- Exponential & Logarithm Functions
- Inverse Functions
- Applications of Calculus to the Physical World & Rates
- Binomial Theorem
- Probability
- Further Probability

## Notable Changes:

**Inverse Trigonometry and Graphs – ****Moved from Year 12 to Year 11!**

The topic has remained largely untouched with the only major change that it is taught as a part of the preliminary HSC course in Year 11.

**Further Work with Functions – ****Moved from 4U! **

With the extension theory remaining largely the same, the introduction of *graphical relationships* *of functions* (a chapter in this topic) has taken away the requirement of a curve sketching topic in Ext. 2 Mathematics.

**Volumes of Solids of Revolutions – ****Moved from 2U and 4U! **

The introduction of this topic in Year 12 for 3U has taken away the requirement for 2U and 4U students to learn Volumes and their relationship with integral calculus in their respective courses.

**Sampling and Estimates – ****New Topic! **

This is the extension topic for statistics.

**Summary of Changes for 4 Unit Mathematics**

**Year 12 (NEW)**

- The Nature of Proof * NEW
- Deductive Proof * NEW
- Proof by Mathematical Induction * NEW
- Vectors * NEW
- Mechanics * NEW
- Advanced Calculus Skills
- Introduction to Complex Numbers
- Using Complex Numbers

**Year 12 (OLD)**

- Complex Numbers
- Polynomials
- conics
- Integration
- Volumes
- Graphs
- Mechanics
- Harder Extension 1 Topics

## Notable Changes:

**Proofs – Renamed Harder Ext 1 + Mathematical Induction – ****Moved from 3U! **

The three proof headings ‘The Nature of Proof’, ‘Deductive Proof’ and ‘Proof by Mathematical Induction’ are not foreign to students who have studied 4U or planning to study.

‘The Nature of Proof’ was originally taught under Harder Ext 1.

‘Deductive Proof’ is basically Circle Geometry.

‘Proof by Mathematical Induction’ is now an exclusive 4U topic.

**Vectors – ****New Topic! **

This topic acts as the extension to Matrices for the 2U theory. It is almost an extension to the complex numbers vectors topic as it adds a plethora of theory to finding and representing direction with magnitude.

**Integration + Conics – ****Removed Topic! **

Integration techniques which were exclusive to 4U have been removed alongside the entire topic of conics.

**Mechanics – New Sub-Topics!**

The 4 Unit Mechanics course has expanded to include Simple Harmonic Motion and Projectile Motion theory originally taught in 3 Unit. This has taken away the requirement at the 2 Unit and 3 Unit level to have an understanding of motion and calculus in terms of displacement, velocity and acceleration.

**Final comments**

These reforms come as a blessing to the determined minds of many mathematical academics across NSW, however, many students may feel that these changes have made the courses ‘harder’ and more ‘complicated’ which will probably exist as a grey area for the coming years.

It can be assumed that the entire mathematics course has been shifted around with many topics that were previously exclusive to certain Extension Units being applied to the Mathematics Advanced (2U) course. The largest change has been the introduction of Statistics through all Mathematic levels.

Personally, I welcome these changes as they add necessary challenges to prepare students for the Mathematics they will likely learn in University or the real world.

## See the full changes here!

The Board of Studies, Teaching and Educational Standards NSW (BOSTES) is currently developing new Stage 6 syllabuses for English, Mathematics, and much more!

Consultation on the draft syllabuses is now open.

**By Martin S Phabmixay**

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