Product description

## Details

- Units 3 and 4 Mathematics Workbooks cover the Australian Curriculum syllabus for Mathematics Methods year 12
- The workbooks have been written to be used as a text for the Mathematics Methods ATAR course year 12
- Complies with the current (as at 2021) Western Australian Curriculum
- Written by a qualified Teacher with over 40 years of experience teaching Mathematics in Western Australian schools

### CHAPTER 1: Differentiation

- Review of differentiation
- Differentiating products
- Differentiating quotients
- Differentiating a function of a function, chain rule
- Using the chain rule to find derivatives of powers
- Derivative of a derivative
- Chapter 1 Review Exercise

### CHAPTER 2: Applications of Differentiation

- Review of graphical application, firsts derivative test, second derivative test
- Curve sketching
- Rates of change
- Rectilinear motion, displacement, velocity, acceleration
- Optimisation
- The increments formula, small changes, approximations
- Economic applications, marginal analysis
- Chapter 2 Review Exercise

### CHAPTER 3: Anti-differentiation

- Indefinite integral of powers of x
- Linearity properties of integration
- Indefinite integral of (ax + b)
^{n} - Chapter 3 Review Exercise

### CHAPTER 4: Definite Integrals and Fundamental Theorem

- Area under a curve
- Fundamental theorem of calculus
- Properties of definite integrals
- Signed area
- Chapter 4 Review Exercise

### CHAPTER 5: Applications of Integration

- Algebraic functions from the gradient function
- Area under a curve, area between curve and x axis
- Area under a curve and the absolute value function
- Area between curves
- Rectilinear motion
- Time graphs, displacement, velocity, acceleration
- Economic applications,
- Total change
- Chapter 5 Review Exercise

### CHAPTER 6: The Exponential Function

- The number e
- Continuous geometric growth
- The exponential function
- Differentiating exponential functions
- Exponential law of growth and decay
- Integrating exponential functions, integrals of e
^{x}, e^{ax}, e^{ax+b}, e^{f(x)} - Chapter 6 Review Exercise

### CHAPTER 7: Trigonometric Functions

- Differentiating the sine, cosine and tangent functions
- Differentiating trigonometric function involving the chain rule
- Applications of differentiation with trigonometric functions
- Anti-derivatives of trigonometric functions
- Applications of integration with trigonometric functions
- Chapter 7 Review Exercise

### CHAPTER 8: Discrete Random Variables

- Discrete random variables
- Discrete probability distribution, probability mass function
- Uniform discrete probability distributions
- Mean of discrete random variables
- Variance and standard deviation of discrete random variables
- Linear change of origin and scale
- Applications of discrete random variables
- Chapter 8 Review Exercise

### CHAPTER 9: Special Discrete Distributions

- Discrete uniform distribution
- Bernoulli distribution
- Binomial distribution
- Graphs of binomial distributions
- Mean, variance and standard deviation of binomial random variables
- Applications of the binomial distribution
- Chapter 9 Review Exercise