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# 2 & 3 Unit (Year 11-12)

## Statement of 2 & 3 Unit Syllabus Topics

1. Basic Arithmetic and Algebra
2. Plane Geometry
3. Probability
4. Real Functions of a Real Variable and Their Geometrical Representation
5. Trigonometric Ratios - Review and Some Preliminary Results
6. Linear Functions and Lines
7. Series and Applications
8. The Tangent to a Curve and the Derivative of a Function
9. The Quadratic Polynomial and the Parabola
10. Geometrical Applications of Differentiation
11. Integration
12. Logarithmic and Exponential Functions
13. The Trigonometric Functions
14. Applications of Calculus to the Physical World
15. Inverse Functions and the Inverse Trigonometric Functions (only at 3 Unit)
16. Polynomials (only at 3 Unit)
17. Binomial Theorem (only at 3 Unit)
18. Permutations, Combinations and Further Probability (only at 3 Unit)

## 2 Unit Course Components

The Mathematics 2 Unit course consists of these components (extracted from the syllabus page 5).

### HSC Course (Year 12)

Basic arithmetic and algebra

Real functions

Trigonometric ratios

Linear functions

The quadratic polynomial and the parabola

Plane geometry - geometrical properties

Tangent to a curve and derivative of a function

Coordinate methods in geometry

Applications of geometrical properties

Geometrical applications of differentiation

Integration

Trigonometric functions

Logarithmic and exponential functions

Applications of calculus to the physical world

Probability

Series and Series applications

## 3 Unit Course Components

The Mathematics 3 Unit course consists of these components (extracted from the syllabus page 6).

### HSC Course (Year 12)

Other inequalities

Circle geometry

Further trigonometry

Angles between two lines

Internal and external division of lines into given ratios

Parametric representation

Permutations and combinations

Polynomials

Harder applications of the Preliminary 2 Unit course

Methods of integration

Primitive of sin2x and cos2x

Equation dN/dt = k(N-P)

Velocity and acceleration as a function of x

Projectile motion

Simple harmonic motion

Inverse functions and inverse trigonometric functions

Induction

Binomial theorem

Further probability

Iterative methods for numerical estimation of the roots of a polynomial equation

Harder applications of HSC 2 unit topics