Western Australian Mathematics Methods Year 12

Year 12 ATAR Course Textbooks

John Klup Mathematics Methods Units 3 and 4

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

Table of Contents - Unit 3 (Click to expand)

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

ANSWERS

INDEX

Table of Contents - Unit 4 (Click to expand)

CHAPTER 1 Logarithmic Functions

  • Inverse relations
  • Inverse functions
  • Logarithmic functions
  • Common logarithms
  • Laws of logarithms
  • Solving exponential equations using logarithms
  • Graphs of logarithmic functions
  • Logarithmic scales, Richter, Decibel, pH
  • More applications of logarithms
  • Chapter 1 Review Exercise

CHAPTER 2 The Natural Logarithmic Function

  • Natural logarithms
  • Graphs of the natural logarithmic function
  • Derivative of the logarithmic function
  • Applications of the derivative of natural logarithms
  • The indefinite integral of
  • Applications of the integral of natural logarithms
  • Chapter 2 Review Exercise

CHAPTER 3 Continuous Random Variables

  • Distribution of continuous data as a histogram
  • Probability distribution of a continuous random variable
  • Uniform probability distributions
  • Non-uniform probability distributions
  • Cumulative probability function
  • General formulas for mean, variance and standard deviation
  • Linear changes of origin and scale
  • Chapter 3 Review Exercise

CHAPTER 4 The Normal Distribution

  • Normal distribution
  • Standard normal distribution
  • Non standard normal distribution
  • Standardised scores
  • The 68 – 95 – 99.7 rule
  • Quantiles
  • Applications of the normal distribution
  • Modelling data using normal random variables
  • Chapter 4 Review Exercise

CHAPTER 5 Random Sampling

  • Statistical terms
  • Sample vs census
  • Probability sampling methods
  • Non-probability sampling methods
  • Bias
  • Estimation, capture - recapture
  • Variability of random samples
  • Chapter 5 Review Exercise

CHAPTER 6 Sample Proportions

  • Sample proportion, mean and standard deviation
  • Central limit theorem
  • Sample proportion and the standard normal distribution
  • Probability intervals
  • Confidence intervals
  • Margin of error
  • Minimum sample size for estimating a population proportion
  • Variation of confidence intervals
  • Chapter 6 Review Exercise

ANSWERS

INDEX

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Both Unit 3 and Unit 4
Units 3 and 4 Mathematics Workbook


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Unit 3
Unit 3 Mathematics Workbook


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Unit 4
Unit 4 Mathematics Workbook


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