Cambridge Specialist Mathematics VCE Units 3&4

Cover
Contents
Introduction and overview
Acknowledgements
1 Preliminary topics
1A Circular functions
1B The sine and cosine rules
1C Sequences and series
1D The modulus function
1E Circles
1F Ellipses and hyperbolas
1G Parametric equations
1H Algorithms and pseudocode
Review of Chapter 1
2 Logic and proof
2A Revision of proof techniques
2B Quantifiers and counterexamples
2C Proving inequalities
2D Telescoping series
2E Mathematical induction
Review of Chapter 2
3 Circular functions
3A The reciprocal circular functions
3B Compound and double angle formulas
3C The inverse circular functions
3D Solution of equations
3E Sums and products of sines and cosines
Review of Chapter 3
4 Vectors
4A Introduction to vectors
4B Resolution of a vector into rectangular components
4C Scalar product of vectors
4D Vector projections
4E Collinearity
4F Geometric proofs
Review of Chapter 4
5 Vector equations of lines and planes
5A Vector equations of lines
5B Intersection of lines and skew lines
5C Vector product
5D Vector equations of planes
5E Distances, angles and intersections
Review of Chapter 5
6 Complex numbers
6A Starting to build the complex numbers
6B Modulus, conjugate and division
6C Polar form of a complex number
6D Basic operations on complex numbers in polar form
6E Solving quadratic equations over the complex numbers
6F Solving polynomial equations over the complex numbers
6G Using De Moivre’s theorem to solve equations
6H Sketching subsets of the complex plane
Review of Chapter 6
7 Revision of Chapters 1–6
7A Technology-free questions
7B Multiple-choice questions
7C Extended-response questions
7D Algorithms and pseudocode
8 Differentiation and rational functions
8A Differentiation
8B Derivatives of x = f(y)
8C Derivatives of inverse circular functions
8D Second derivatives
8E Points of inflection
8F Related rates
8G Rational functions
8H A summary of differentiation
8I Implicit differentiation
Review of Chapter 8
9 Techniques of integration
9A Antidifferentiation
9B Antiderivatives involving inverse circular functions
9C Integration by substitution
9D Definite integrals by substitution
9E Use of trigonometric identities for integration
9F Further substitution
9G Partial fractions
9H Integration by parts
9I Further techniques and miscellaneous exercises
Review of Chapter 9
10 Applications of integration
10A The fundamental theorem of calculus
10B Area of a region between two curves
10C Integration using a CAS calculator
10D Volumes of solids of revolution
10E Lengths of curves in the plane
10F Areas of surfaces of revolution
Review of Chapter 10
11 Differential equations
11A An introduction to differential equations
11B Differential equations involving a function of the independent variable
11C Differential equations involving a function of the dependent variable
11D Applications of differential equations
11E The logistic differential equation
11F Separation of variables
11G Differential equations with related rates
11H Using a definite integral to solve a differential equation
11I Using Euler’s method to solve a differential equation
11J Slope field for a differential equation
Review of Chapter 11
12 Kinematics
12A Position, velocity and acceleration
12B Constant acceleration
12C Velocity–time graphs
12D Differential equations of the form v = f(x) and a = f(v)
12E Other expressions for acceleration
Review of Chapter 12
13 Vector functions and vector calculus
13A Vector functions
13B Position vectors as a function of time
13C Vector calculus
13D Velocity and acceleration for motion along a curve
Review of Chapter 13
14 Revision of Chapters 8–13
14A Technology-free questions
14B Multiple-choice questions
14C Extended-response questions
14D Algorithms and pseudocode
15 Linear combinations of random variables and the sample mean
15A Linear functions of a random variable
15B Linear combinations of random variables
15C Linear combinations of normal random variables
15D The sample mean of a normal random variable
15E Investigating the distribution of the sample mean using simulation
15F The distribution of the sample mean
Review of Chapter 15
16 Confidence intervals and hypothesis testing for the mean
16A Confidence intervals for the population mean
16B Hypothesis testing for the mean
16C One-tail and two-tail tests
16D Two-tail tests revisited
16E Errors in hypothesis testing
Review of Chapter 16
17 Revision of Chapters 15–16
17A Technology-free questions
17B Multiple-choice questions
17C Extended-response questions
17D Algorithms and pseudocode
18 Revision of Chapters 1–17
18A Technology-free questions
18B Multiple-choice questions
18C Extended-response questions
Glossary
Answers