Phoenix Senior Maths Topics
Differential Calculus
Probability
Series & Sequences
by George Fisher
Phoenix Senior Maths Topics provide thorough and detailed explanations, worked examples, summaries and practice exam questions on essential senior maths topics. Each book is a detailed treatment of a topic selected because of its importance in senior maths. They can be used at school, to supplement the textbook, providing more detail and exercises, and at home, to aid home study and exam preparation.
These books are for senior secondary students, particularly those who:
o want to study a topic in more depth
o are having difficulty with a topic
Phoenix Senior Maths Topics books can be used:
· to learn and understand the topic: a full and detailed treatment of the topic with clear step-by-step explanations and plenty of worked examples.
· as a study and revision aid: a separate summary contains the information which has to be learned, as well as exercises and sample tests with typical examination questions. Solutions are provided.
· as a reference: all the relevant information is easy to find and easy to understand.
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Differential Calculus Contents
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About this book Chapter 1 Limits Definition Properties of limits Chapter 2 Continuity Chapter 3 Gradient of a secant Chapter 4 Gradient of a tangent Chapter 5 The gradient function Chapter 6 Continuity and smoothness Chapter 7 Differentiation The derived function Differentiation from first principles Increment notation Using the delta notation Chapter 8 Rules for differentiation The derivative of xn for n an integer The derivative of cxn The derivative of cx The derivative of a constant The derivative of sums and differences of functions The derivative of xn for negative indices The derivative of xn for fractional indices Differentiation with respect to other variables
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Chapter 9 Further rules for differentiation The function of a function rule The chain rule The product rule The product rule involving the function of a function rule The quotient rule The quotient rule involving the function of a function rule Chapter 10 Geometric applications of differentiation Tangents and normals Higher derivatives Stationary points Turning points Significants of the second derivative Maxima and minima Practical applications of maxima and minima Chapter 11 Miscellaneous examples Summary Sample tests Answers
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Series and Sequences Contents
About this book
Chapter 1 Basic definitions
Definitions, notation
The general term of a series
Sum of a series
Given Sn find Tn
Chapter 2 Arithmetic progression
Definition
The general AP
The sum of an AP
The arithmetic mean
Chapter 3 Geometric progression
Definition
The general GP
The sum of a GP
The geometric mean
Chapter 4 Applications of AP
Chapter 5 Applications of GP
Simple and compound interest
Superannuation, annuities and time payments
Sum to infinity
Recurring decimals
Chapter 6 Miscellaneous problems
Chapter 7 Mathematical induction
Some preliminary results
Mathematical induction
Summary
Sample tests
Answers
Probability Contents
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About this book Chapter 1 Basic definitions and ideas Random experiments. Equally likely outcomes Non-equally likely outcomes Simple events Composite events Sample space Favourable outcomes Chapter 2 Diagrammatic representation of sample spaces Tree diagrams Geometric representation of sample space Contracted form of tree diagrams Chapter 3 The probability of an event Definition Successive outcomes The multiplication principle Probability by tree diagrams Probability that an event does not occur The box-filling technique Chapter 4 Conditional probability |
Chapter 5 Sets and the Venn diagram Intersection Union Chapter 6 The addition principle Mutually exclusive events Events that are not mutually exclusive Using Venn diagrams Chapter 7 The product theorem of probability Multi-stage random experiments Product rule Summary of the 'product theorems' results Using complementary events Chapter 8 Probability trees Chapter 9 Miscellaneous The addition and product theorems Sampling without replacement Chapter 10 Permutations and combinations Permutations Combinations Circular arrangements of unlike things Chapter 11 The binomial theorem Chapter 12 Further probability Application of counting techniques Binomial probability distribution Expected value Summary Sample tests Answers
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