# J Klup Methods Year 12 Unit 3

 Members: \$45.00 Others: \$50.00
Categories: Algebra, MAWA, Statistics/Probability, Teacher
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 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