# Jacaranda Maths Quest 12 Specialist Mathematics Units 3&4 for Queensland eBookPLUS & Print + StudyOn Specialist Mathematics U3&4 for Qld (Book Code)

Author(s): |
Smith |

ISBN: |
9780730380030 |

Pub date: |
September 2019 |

RRP: |
$89.95 |

**Jacaranda Maths Quest 12 Specialist Mathematics Units 3 & 4 for Queensland Print & eBookPLUS + studyON**

This combined print and digital title is designed to help teachers unpack the new curriculum and help students at the point of learning, so that every student can experience success in the classroom, at home and thus ultimately in the exam.

An access code for the eBookPLUS comes free on the inside cover of your printed text, so you can make the most of both the print and digital formats.

The latest editions from the

*Jacaranda Maths Quest for Queensland*series include these key updates:

- Inclusion of important language to help frame question sets such as Simple Familiar, Complex Familiar and Complex Unfamiliar
- New assessment practice sections designed as per QCAA guidelines and samples, including Problem Solving and Modelling Tasks
- New chapter questions and activities are aligned with Marzano and Kendall’s new taxonomy: 4 levels of cognitive process – retrieval, comprehension, analysis and knowledge
- Jacaranda’s unique exam preparation tool, studyON, is now included free and fully integrated to help prepare students for their exams
- Provides an unmatched interactive learning experience, through a variety of new interactivities to help students understand challenging concepts
- Free online Fully Worked Solutions with every student text
- Exam practice questions included in every chapter

**EXCLUSIVE OFFER: Get four eBookPLUS and four studyON activation codes free in every print text!**

About this resource vi

About eBookPLUS and studyON ix

Acknowledgements x

**1 Proof by mathematical induction 1**

1.1 Overview 1

1.2 Introduction to proof by mathematical induction 2

1.3 Proof of divisibility 7

1.4 Further proof by induction 9

1.5 Review: exam practice 18

Answers 19

**Revision Unit 3 Mathematical Induction, and Further Vectors, Matrices and Complex Numbers**

Topic 1 Proof by mathematical induction 21

**2 Vectors in three dimensions 22**

2.1 Overview 22

2.2 Introduction to vectors in three dimensions 23

2.3 Geometric proofs using vectors 42

2.4 Cartesian and parametric equations 50

2.5 The vector equation of a straight line 65

2.6 The vector product 73

2.7 Applications of vectors 86

2.8 Review: exam practice 97

Answers 101

**3 Solving systems of linear equations and the application of matrices 106**

3.1 Overview 106

3.2 Solving linear equations using matrix algebra 107

3.3 Solving a system of linear equations using Gaussian elimination 119

3.4 The three cases for solutions of systems of linear equations 126

3.5 Using technology for matrix calculations 147

3.6 Dominance and Leslie matrices 153

3.7 Applications of matrices 162

3.8 Review: exam practice 180

Answers 184

**4 Vector calculus 189**

4.1 Overview 189

4.2 Position vectors as functions of time: circles, ellipses and hyperbolas 190

4.3 Differentiation of vectors 200

4.4 Integration of vectors 211

4.5 Straight line motion with constant and variable acceleration 217

4.6 Projectile motion 228

4.7 Circular motion 242

4.8 Review: exam practice 249

Answers 252

**Revision Unit 3 Mathematical Induction, and Further Vectors, Matrices and Complex Numbers**

Topic 2 Vectors and matrices 260

**5 Complex numbers 261**

5.1 Overview 261

5.2 Complex numbers in Cartesian form 262

5.3 Complex numbers in polar form 268

5.4 De Moivre’s theorem 278

5.5 The complex plane (the Argand plane) 283

5.6 Roots of complex numbers 291

5.7 Factorisation of polynomials 298

5.8 Review: exam practice 304

Answers 306

**Revision Unit 3 Mathematical Induction, and Further Vectors, Matrices and Complex Numbers**

Topic 3 Complex numbers 2 313

Practice Assessment 1 Specialist Mathematics: Problem solving and modelling task 314

Practice Assessment 2 Specialist Mathematics: Unit 3 examination 317

**6 Integration techniques 323**

6.1 Overview 323

6.2 Integration by linear substitution 324

6.3 Integration by non-linear substitutions 333

6.4 Integration using the trigonometric identities 341

6.5 Integration of inverse trigonometric functions 352

6.6 Integration by parts 374

6.7 Integration involving partial fractions 378

6.8 Review: exam practice 387

Answers 389

**7 Applications of integral calculus 395**

7.1 Overview 395

7.2 Area between a function and the axes 396

7.3 Area between functions 403

7.4 Volumes of solids of revolution 413

7.5 Volumes of revolution 421

7.6 Approximation using Simpson’s rule 432

7.7 Exponential probability density function 441

7.8 Review: exam practice 446

Answers 448

**Revision Unit 4 Further Calculus and Statistical Inference**

Topic 1 Integration and applications of integration 451

**8 Rates of change and differential equations 452**

8.1 Overview 452

8.2 Implicit differentiation 453

8.3 Related rates as instances of the chain rule 460

8.4 Solving differential equations of the form *dy/dx *= *f*(*x*) 468

8.5 Solving differential equations of the form *dy/dx*= *g(y*) 475

8.6 Solving differential equations of the form *dy/dx*= *f*(*x*)g*(y*) 482

8.7 Review: exam practice 486

Answers 489

**9 Applications of first-order differential equations 493**

9.1 Overview 493

9.2 Growth and decay 494

9.3 Other applications of first-order differential equations 501

9.4 Bounded growth and Newton’s law of cooling 508

9.5 Chemical reactions and dilution problems 514

9.6 The logistic equation 524

9.7 Slope fields 534

9.8 Review: exam practice 545

Answers 549

**10 Modelling motion 1 554**

10.1 Overview 554

10.2 A body in equilibrium under concurrent forces 555

10.3 Action and reaction forces 568

10.4 Momentum and resultant force 576

10.5 Forces on connected particles 587

10.6 Review: exam practice 595

Answers 599

**11 Modelling motion 2 601**

11.1 Overview 601

11.2 Forces that depend on time 602

11.3 Forces that depend on velocity 608

11.4 Forces that depend on displacement 620

11.5 Simple harmonic motion 626

11.6 Review: exam practice 634

Answers 637

**Revision Unit 4 Further Calculus and Statistical Inference**

Topic 2 Rates of change and differential equations 639

**12 Statistical inference 640**

12.1 Overview 640

12.2 Review of continuous random variables and the normal distribution 641

12.3 Sample means and simulations 644

12.4 Confidence intervals 652

12.5 Applications of confidence intervals 659

12.6 Review: exam practice 672

Answers 675

**Revision Unit 4 Further Calculus and Statistical Inference**

Topic 3 Statistical inference 677

Practice Assessment 3 Specialist Mathematics: Unit 4 examination 678

Practice Assessment 4 Specialist Mathematics: Units 3 & 4 examination 685

Glossary 694

Index 697