Maths in focus. Year 12 : mathematics extension 2

Description

Maths in Focus 12 Mathematics Extension 2 is a new book written for the Mathematics Extension 2 course. Each chapter begins with a table of contents, chapter objectives and a Terminology glossary and graded exercises include HSC-style questions and realistic applications. Investigations explore the syllabus in more detail, providing ideas for research projects and modelling activities and Did you know? sections contain interesting facts and applications of the mathematics learned in a chapter. Each chapter ends with a Test Yourself revision set and Practice sets (after several chapters) include exam-style questions from various chapters. Syllabus gris and codes, answers and an Preface Title page Imprint page Preface Syllabus reference grid About this book Mathematical verbs Contents 1. Complex Numbers Chapter 1: Complex numbers 1.01 Complex numbers 1.02 Square root of a complex number 1.03 The Argand diagram 1.04 Modulus and argument 1.05 Properties of moduli and arguments 1.06 Euler’s formula 1.07 Applying Euler’s formula Test yourself 1 2. Mathematical Proof Chapter 2: Mathematical proof 2.01 The language of proof 2.02 Proof by contradiction 2.03 Proof by counterexample 2.04 Proofs involving numbers 2.05 Proofs involving inequalities Test yourself 2 3. Vectors Chapter 3: 3D Vectors 3.01 Review of 2D vectors 3.02 3D vectors 3.03 Angle between vectors 3.04 Geometry proofs using vectors 3.05 3D space 3.06 Vector equation of a curve 3.07 Vector equation of a straight line 3.08 Parallel and perpendicular lines Test yourself 3 4. Applying Complex Numbers Chapter 4: Applying complex numbers 4.01 De Moivre’s theorem 4.02 Quadratic equations with complex coefficients 4.03 Polynomial equations 4.04 Operations on the complex plane 4.05 Roots of unity 4.06 Roots of complex numbers 4.07 Curves and regions on the complex plane Test yourself 4 4a. Practice Set Practice set 1 5. Further Mathematical Induction Chapter 5: Further mathematical induction 5.01 Review of mathematical induction 5.02 Further mathematical induction 5.03 Series and sigma notation 5.04 Applications of mathematical induction 5.05 Recursive formula proofs 5.06 Proofs involving inequalities and graphs Test yourself 5 6. Further Integration Chapter 6: Further integration 6.01 Integration by substitution 6.02 Rational functions with quadratic denominators 6.03 Partial fractions 6.04 Integration by parts 6.05 Recurrence relations Test yourself 6 7. Mechanics Chapter 7: Mechanics 7.01 Velocity and acceleration in terms of x 7.02 Simple harmonic motion 7.03 Projectile motion 7.04 Forces and equations of motion 7.05 Resisted horizontal motion 7.06 Resisted vertical motion 7.07 Resisted projectile motion Test yourself 7 7a. Practice Set 2 Practice set 2 8. Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Practice Set 1 Chapter 5 Chapter 6 Chapter 7 Practice Set 2 9. Index Index