Haese Textbook Links

1 Functions

• 1A Exponential Functions 

• 1B Logarithms 

• 1C Logarithmic Functions 

• 1D Trigonometric Functions 

2 Differential Calculus

• 2A First Principles 

• 2B Simple rules of differentiation

• 2C The Chain Rule  

• 2D The Product Rule 

• 2E The Quotient Rule 

• 2F Derivatives of Exponential Functions 

• 2G Derivatives of Logarithmic Functions 

• 2H Derivatives of Trigonometric Functions 

• 2I The Second Derivative 

3 Applications of Differential Calculus

• 3A The equation of a tangent 

• 3B Increasing and Decreasing Functions 

• 3C Stationary Points 

• 3D Inflections & Shape 

• 3E Kinematics 

• 3F Rates of Change 

• 3G Optimisation 

4 Integration

• 4A The area under a curve

  • 4A.2 The definite integral

• 4B Antidifferentiaion

• 4C The Fundamental Theorem of calculus

• 4D Integration

• 4E Rules for Integration

• 4F Integrating f(ax+b)

• 4G Definite integrals

5 Applications of integration

• 5A The area under a curve

• 5B The area between two functions

• 5C Kinematics

• 5D Problem solving by integration

7 Discrete Random Variables

• 7A & 7B Discrete probability distributions 

• 7C Expected value (and fair games) 

• 7D Variance and Standard Deviation 

• 7E Properties of aX+b 

• 7F The Bernoulli distribution 

• 7G The binomial Distribution 

8 Continuous Random Vaiables

9 Sampling and confidence intervals

• 9A Sampling distributions

• 9B Distributions of sample means

• 9C The Central Limit Theorem

• 9D Confidence intervals for means

• 9E Sample Proportions

• 9F Confidence intervals for proportions

10 Number Sequences (Topic 7 in SACE subject outline - included in specialist course)

• 10A Number Sequences

• 10B Arithmetic Sequences

• 10C Geometric Sequences

• 10D Series

• 10E Arithmetic Series

• 10F Geometric Series

1 Mathematical Induction

• 1A The process of induction

• 1B The principle of mathematical induction

2 Real polynomials

• 2A Operations with Polynomials

• 2B Zeros, roots, and factors

• 2C Polynomial equality

• 2D Polynomial Division

• 2E The Remainder Theorem

• 2F The Factor Theorem

• 2G The Fundamental Theorem of Algebra

• 2H Sum and product of roots theorem (Extension) - Not include in SACE outline

• 2I Graphing real Polynomials

• 2J Polynomial equations

3 Functions

• 3A Composite functions

• 3B Inverse functions

• 3C Reciprocal functions

• 3D The Reciprocals of other functions

• 3E Rational functions

• 3F Absolute value functions

4 Complex numbers

• 4A The Complex Plane 

• 4B Modulus and Argument 

• 4C Polar Form 

• 4D Euler's Form  (Not in current outline)

• 4E De Moivre's Theorem 

• 4F Roots of Complex Numbers 

5 Vectors

• 5A Vectors in space

• 5B Operations with vectors in space 

• 5C Vector algebra 

• 5D The vector between two points 

• 5E Parallelism (3D) 

• 5F The scalar product of two vectors  

• 5G The angle between two vectors (3D) 

• 5H Proof using vector geometry (3D)

• 5I The vector product of two vectors 

6 Vector applications

• 6A Area (3D vectors) 

• 6B Lines in 2 and 3 dimensions 

• 6C The angle between two lines 

• 6D Constant velocity problems 

• 6E The shortest distance from a point to a line 

• 6F Intersecting lines 

• 6G Relationships between lines 

• 6H Planes 

• 6I Angles in space 

• 6J Solving 3x3 linear systems 

• 6K Intersecting planes 

7 Integration

8 Rates of change and Differential Equations

• 8A Implicit Differentiation 

• 8B Related Rates

• 8C Differential Equations

• 8D Differential equations of the form dy/dx=f(x)

• 8E Separable Differential Equations

• 8F Slope fields

• 8G Problem solving

• 8H Logistic growth

• 8I Equations of motion

• 8J Simple Harmonic Motion

9 Vector Calculus

• 9A Parametric equations (vector calculus) 

• 9B Pairs of uniformly varying quantities 

• 9C Pairs of non-uniformly varying quantities 

• 9D Bezier Curves  

• 9E Trigonometric parameterisation 

• 9F Arc length of parametric curves 

2 Circle geometry (Topic 8 in SACE subject outline)

• 2A The angle in a semi-circle theorem

• 2B The chord of a circle theorem

• 2C The radius tangent theorem

• 2D The angle at the centre theorem

• 2E Angles subtended by the same arc

• 2F Tangents from an external point

• 2G Angle between tangent and chord

• 2H Cyclic quadrilaterals

• 2I Intersecting chords and secants theorem

3 Vectors

• 3A Vectors and scalars

• 3B Geometric operations with vectors

• 3C Vectors in the plane

• 3D The magnitude of a vector

• 3E Operations with Plane Vectors

• 3F The vector between two points

• 3G Parallelism

• 3H Problems involving vector operations

• 3I The scalar product of two vectors

• 3J The angle between two vectors

• 3K Vector Projection

• 3L Proof using vector geometry

4 Trigonometric functions

4A The general tangent function

4B General trigonometric functions

4C Reciprocal trigonometric functions

4D Solving Trigonometric equations

4E Modelling using trigonometric functions

4F Trigonometric relationships

4G Double angle identities 

4H Angle sum and difference identities

4I Trigonometric equations in quadratic form (Extension-not in outline)

5 Matrices

• 5A Matrix Structure

• 5B Matrix operations and definitions

• 5C Matrix multiplication

• 5D The inverse of a 2x2 matrix

• 5E Simultaneous linear equations

• 5F Translations and lines in 2D

• 5G Linear Transformations

• 5H Rotations about the origin

• 5I Reflections

• 5J Dilations

• 5K Compositions of transformations

• 5L The inverse of a linear transformation

6 Mathematical induction

• 6A The process of induction

• 6B The principle of mathematical induction

• 6C Proof of divisibility

• 6D Proofs for sequences and series

• 6E Proofs for products

• 6F induction with matrices 

• 6G Proof of inequalities (not in SACE subject outline)

7 Real and Complex Numbers

• 7A Interval notation

• 7B Rational numbers

• 7C Division by surds

• 7D Irrational numbers

• 7E The "invention" of imaginery numbers

• 7F complex numbers

• 7G Complex conjugates

• 7H Complex numbers as 2D vectors

• 7I Modulus