New senior mathematics extension 1 for years 11 & 12

Description

New Senior Mathematics, 3rd Edition offers a series of student books and worked solutions designed to help you prepare for your classes with ease and ensure students reach their potential. It’s the new edition built for New South Wales on a solid foundation. Reader+ is the home of your eBooks. It gives you more options, more flexibility and more control when it comes to the classroom materials you use. It comes with features like in-text note taking, bookmarking, highlighting, interactive videos, audio tools, presentation tools and more. It's all about giving teachers and learners more options and more opportunities to make progress in the classroom, and beyond. Click here to learn more. How do I activate my eBook? When you purchase your eBook, it will come with an access code. This code will be emailed to you. If you purchase a printed book with eBook, it will come with its eBook access code inside the cover. To activate your code, you'll need to log in to pearsonplaces.com.au. 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Preliminary pages Introduction and dedication Features of the third edition Contents Year 11 Chapter 1 Further work with functions 1.1 Quadratic inequalities 1.2 Rational function inequalities (x in denominator) 1.3 Inequalities involving absolute value and square roots 1.4 Circular and simultaneous inequalities Chapter review 1 Chapter 2 Polynomials 2.1 Polynomials 2.2 Division of polynomials and the remainder theorem 2.3 The factor theorem 2.4 Relationship between roots and coefficients 2.5 Multiple roots of a polynomial equation 2.6 Polynomial functions Chapter review 2 Chapter 3 Graphing functions 3.1 Reciprocal functions 3.2 Square root functions 3.3 Absolute value functions 3.4 Graphing polynomials by adding ordinates 3.5 Graphing polynomials by multiplying ordinates 3.6 Parametric form of a function or relation Chapter review 3 Chapter 4 Further trigonometric identities 4.1 Sum and difference of two angles 4.2 Double angle formulae 4.3 Half-angle formulae—the t formulae 4.4 Using identities to simplify expressions and prove results 4.5 Trigonometric products as sums or differences 4.6 Overview of trigonometric equations 4.7 Simple trigonometric equations 4.8 Trigonometric equations involving angle formulae Chapter review 4 Chapter 5 Inverse functions 5.1 Inverse functions 5.2 Inverse trigonometric functions Chapter review 5 Chapter 6 Permutations and combinations 6.1 Fundamental counting principle 6.2 Pigeonhole principle 6.3 Permutations 6.4 Arrangement of n objects when some are identical 6.5 Combinations 6.6 Counting techniques in probability 6.7 Expansion of (1 + x)ⁿ, Pascal’s triangle 6.8 More Pascal’s triangle expansions 6.9 Pascal’s triangle relations and the binomial theorem Chapter review 6 Chapter 7 Rates of change and their application 7.1 Rates of change with respect to time 7.2 Velocity and acceleration as rates of change 7.3 Exponential growth and decay 7.4 Harder exponential growth and decay 7.5 Related rates of change Chapter review 7 Year 12 Chapter 8 Trigonometric equations 8.1 Solving trigonometric equations using the auxiliary angle method 8.2 Solving quadratic trigonometric equations 8.3 Solving equations using angle formulae, including the t formulae Chapter review 8 Chapter 9 Proof by mathematical induction 9.1 Mathematical induction involving series 9.2 Proving divisibility by induction 9.3 When induction doesn’t work Chapter review 9 Chapter 10 Vectors in two dimensions 10.1 Introduction to vectors 10.2 Vectors in two dimensions 10.3 Vectors in component form 10.4 Scalar product of vectors 10.5 Projections of vectors 10.6 Vectors in geometric proofs Chapter review 10 Chapter 11 Applications of calculus 11.1 Volumes of solids of revolution 11.2 Indefinite integrals and substitution 11.3 Definite integrals and substitution 11.4 Integration of sin² x and cos² x 11.5 Integrals of the type ∫ f’(x) (f(x))ⁿ dx 11.6 Integrals involving trigonometric substitution 11.7 Differentiation of inverse trigonometric functions 11.8 Integration involving inverse trigonometric functions Chapter review 11 Chapter 12 Differential equations 12.1 Introduction to differential equations 12.2 Direction fields 12.3 Solving differential equations of the form dy/dx = f(x) 12.4 Solving differential equations of the form dy/dx = g(y) 12.5 Solving differential equations of the form dy/dx = f(x) g(y) using separation of variables 12.6 Modelling with first order differential equations Chapter review 12 Chapter 13 Motion, forces and projectiles 13.1 Problems involving displacement and velocity 13.2 Problems involving forces 13.3 Projectile motion Chapter review 13 Chapter 14 The binomial distribution 14.1 Bernoulli trials 14.2 Binomial distribution 14.3 Mean and variance of the binomial distribution 14.4 Normal approximation for the sample proportion Chapter review 14 Summary Mathematics Extension 1 course outcomes Answers Answers for Chapter 1 Further work with functions Answers for Chapter 2 Polynomials Answers for Chapter 3 Graphing functions Answers for Chapter 4 Further trigonometric identities Answers for Chapter 5 Inverse functions Answers for Chapter 6 Permutations and combinations Answers for Chapter 7 Rates of change and their application Answers for Chapter 8 Trigonometric equations Answers for Chapter 9 Proof by mathematical induction Answers for Chapter 10 Vectors in two dimensions Answers for Chapter 11 Applications of calculus Answers for Chapter 12 Differential equations Answers for Chapter 13 Motion, forces and projectiles Answers for Chapter 14 The binomial distribution Glossary