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- 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 ex, eax, eax+b, ef(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
