Cambridge Mathematical Methods VCE Units 3/4 - 2nd Edition

Methods34_2ed_full_Part1
	Cover
	Contents
	Introduction and overview
	Acknowledgements
	1 Functions and relations
		1A Set notation and sets of numbers
		1B Identifying and describing relations and functions
		1C Types of functions and implied domains
		1D Sums and products of functions
		1E Composite functions
		1F Inverse functions
		1G Power functions
		1H Applications of functions
		Review of Chapter 1
	2 Coordinate geometry
		2A Linear equations
		2B Linear literal equations and simultaneous linear literal equations
		2C Linear coordinate geometry
		2D Applications of linear functions
		2E The geometry of simultaneous linear equations with two variables
		2F Simultaneous linear equations with more than two variables
		Review of Chapter 2
	3 Transformations
		3A Translations
		3B Dilations
		3C Reflections
		3D Combinations of transformations
		3E Determining transformations
		3F Using transformations to sketch graphs
		3G Transformations of power functions with positive integer index
		3H Determining the rule for a function from its graph
		3I A notation for transformations
		Review of Chapter 3
	4 Polynomial functions
		4A Quadratic functions
		4B Determining the rule for a parabola
		4C The language of polynomials
		4D Division and factorisation of polynomials
		4E The general cubic function
		4F Polynomials of higher degree
		4G Determining the rule for the graph of a polynomial
		4H Solution of literal equations and systems of equations
		Review of Chapter 4
	5 Exponential and logarithmic functions
		5A Exponential functions
		5B The exponential function f(x) = ex
		5C Exponential equations
		5D Logarithms
		5E Graphing logarithmic functions
		5F Determining rules for graphs of exponential and logarithmic functions
		5G Solution of exponential equations using logarithms
		5H Inverses
		5I Exponential growth and decay
		Review of Chapter 5
	6 Circular functions
		6A Measuring angles in degrees and radians
		6B Defining circular functions: sine, cosine and tangent
		6C Further symmetry properties and the Pythagorean identity
		6D Graphs of sine and cosine
		6E Solution of trigonometric equations
		6F Sketch graphs of y = a sin n(t ± ε) and y = a cos n(t ± ε)
		6G Sketch graphs of y = a sin n(t ± ε) ± b and y = a cos n(t ± ε) ± b
		6H Addition of ordinates for circular functions
		6I Determining rules for graphs of circular functions
		6J The tangent function
		6K General solution of trigonometric equations
		6L Applications of circular functions
		Review of Chapter 6
	7 Further functions
		7A More power functions
		7B Composite and inverse functions
		7C Sums and products of functions and addition of ordinates
		7D Function notation and identities
		7E Families of functions and solving literal equations
		Review of Chapter 7
	8 Revision of Chapters 1–7
		8A Technology-free questions
		8B Multiple-choice questions
		8C Extended-response questions
		8D Algorithms and pseudocode
	9 Differentiation
		9A The derivative
		9B Rules for differentiation
		9C Differentiating xn where n is a negative integer
		9D The graph of the derivative function
		9E The chain rule
		9F Differentiating rational powers
		9G Differentiation of ex
		9H Differentiation of the natural logarithm function
		9I Derivatives of circular functions
		9J The product rule
		9K The quotient rule
		9L Limits and continuity
		9M When is a function differentiable?
		Review of Chapter 9
	10 Applications of differentiation
		10A Tangents and normals
		10B Rates of change
		10C Stationary points
		10D Types of stationary points
		10E Absolute maximum and minimum values
		10F Maximum and minimum problems
		10G Families of functions
		10H Newton’s method for finding solutions to equations
		Review of Chapter 10
	11 Integration
		11A Estimating the area under a graph
		11B Antidifferentiation: indefinite integrals
		11C The antiderivative of (ax + b)r
		11E The fundamental theorem of calculus and the definite integral
		11F Finding the area under a curve
		11G Integration of circular functions
		11H Miscellaneous exercises
		11I The area of a region between two curves
		11J Applications of integration
		11K The fundamental theorem of calculus
		Review of Chapter 11
	12 Revision of Chapters 9–11
		12A Technology-free questions
		12B Multiple-choice questions
		12C Extended-response questions
		12D Algorithms and pseudocode
	13 Discrete random variables and their probability distributions
		13A Sample spaces and probability
		13B Conditional probability and independence
		13C Discrete random variables
		13D Expected value (mean), variance and standard deviation
		Review of Chapter 13
	14 The binomial distribution
		14A Bernoulli sequences and the binomial probability distribution
		14B The graph, expectation and variance of a binomial distribution
		14C Finding the sample size
		14D Proofs for the expectation and variance
		Review of Chapter 14
	15 Continuous random variables and their probability distributions
		15A Continuous random variables
		15B Mean and percentiles for a continuous random variable
		15C Measures of spread
		15D Properties of mean and variance
		15E Cumulative distribution functions
		Review of Chapter 15
Methods34_2ed_full_Part2
	16 The normal distribution
		16A The normal distribution
		16B Standardisation and the 68–95–99.7% rule
		16C Determining normal probabilities
		16D Solving problems using the normal distribution
		16E The normal approximation to the binomial distribution
		Review of Chapter 16
	17 Sampling and estimation
		17A Populations and samples
		17B The exact distribution of the sample proportion
		17C Approximating the distribution of the sample proportion
		17D Confidence intervals for the population proportion
		Review of Chapter 17
	18 Revision of Chapters 13–17
		18A Technology-free questions
		18B Multiple-choice questions
		18C Extended-response questions
		18D Algorithms and pseudocode
	19 Revision of Chapters 1–18
		19A Technology-free questions
		19B Multiple-choice questions
		19C Extended-response questions
	A Pseudocode Appendix A
		A1 Introduction to pseudocode
	B Counting methods and the binomial theorem
		B1 Counting methods
		B2 Summation notation
		B3 The binomial theorem
	Glossary
	Answers