Jacaranda Maths Quest 12 Mathematical Methods Units 3&4 for Queensland Second Edition (learnON & Print)

Part of the series Maths Quest for Queensland.

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The Jacaranda Maths Quest for Queensland series has been entirely updated for the revised Queensland Senior Syllabus. Created by experienced Queensland teachers, the new Maths Quest for Queensland series provides all the tools to help your students progress and achieve success.

Available now in learnON, Australia's most powerful online learning platform, which brings trusted Jacaranda content to life.

Visible learning and accessibility

• Each lesson is mapped directly to the revised Queensland Senior Syllabus, ensuring 100% coverage for teachers.
• Lessons clearly labelled [complex] to differentiate complex content from the revised Queensland Senior Syllabus.
• Each lesson is scaffolded using three question types - simple familiar, complex familiar and complex unfamiliar - to prepare students for assessment.

Unparalleled assessment support

• Students access chapter summaries as well as review exercises and unit reviews, each with sample responses.
• Students access auto-marked quick quizzes in every lesson with fully worked solutions.
• A custom test‑builder can be filtered by unit, differentiation and question type.

Step-by-step approach to problem-solving and modelling tasks

• NEW! Practical student guide, stepping them through how to approach and complete problem-solving and modelling tasks.
• Bank of quarantined assessment tasks, including teaching advice to assist teachers to create quality problem‑solving and modelling tasks.

More than a textbook

learnON is everything you need to prepare and deliver effective lessons in one place.

• Engage students with a multimodal learning experience, including videos and interactivities.
• Save time assessing, with ready-made auto-marked question sets, chapter tests and practice assessments with sample responses.
• Identify and act on areas of weakness early, with instant reports and learning data.
• Edit the course content to customise student learning and reduce cognitive load.

Table of Contents

Learning with Learnon ix
Teaching with learnON xv
Acknowledgements xvi
Problem-solving and modelling task guide

Unit 3 Further Calculus and Introduction to Statistics 1

Topic 1 Differentiation of Exponential and Logarithmic Functions

1 Calculus of exponential and logarithmic functions 3

1.1 Overview 4
1.2 Limits 5
1.3 The exponential function 11
1.4 Differentiation of exponential functions 20
1.5 The logarithmic function 25
1.6 Solving equations 34
1.7 Differentiation of logarithmic functions 39
1.8 Modelling and solving with exponential and logarithmic functions 44
1.9 Review 56

Topic 2 Differentiation of Trigonometric Functions and Differentiation Rules

2 Calculus of trigonometric functions 71

2.1 Overview 72
2.2 Review of the unit circle 73
2.3 Review of the trigonometric functions 87
2.4 Differentiation of trigonometric functions 97
2.5 Modelling and solving with trigonometric functions 104
2.6 Review 116

3 Differentiation rules 129

3.1 Overview 130
3.2 The chain rule 131
3.3 The product rule 139
3.4 The quotient rule 144
3.5 Modelling and solving using the differentiation rules 150
3.6 Review 166

Topic 3 Further Applications of Differentiation

4 The second derivative and applications of differentiation 177

4.1 Overview 178
4.2 Second derivatives 179
4.3 Concavity and points of inflection 185
4.4 Curve sketching 191
4.5 Modelling and solving optimisation problems 201
4.6 Review 208

Topic 4 Introduction to Integration

5 Anti-differentiation 219

5.1 Overview 220
5.2 Anti-differentiation of rational functions 221
5.3 Anti-differentiation of exponential functions 228
5.4 Anti-differentiation of logarithmic functions 232
5.5 Anti-differentiation of trigonometric functions 236
5.6 Further integration 240
5.7 Modelling and solving using indefinite integrals 247
5.8 Review 255

Topic 5 Discrete Random Variables

6 General discrete random variables 265

6.1 Overview 266
6.2 Discrete random variables 267
6.3 Expected values 279
6.4 Variance and standard deviation 289
6.5 Modelling and solving with discrete random variables 298
6.6 Review 304

7 Bernoulli and binomial distributions 315

7.1 Overview 316
7.2 Bernoulli distributions 317
7.3 Binomial distributions 323
7.4 The mean and variance of a binomial distribution 333
7.5 Modelling and solving with Bernoulli and binomial distributions 337
7.6 Review 342

Practice Assessment 1
Problem-solving and modelling task

Practice Assessment 2
Unit 3 Examination

Unit 4 Further Calculus, Trigonometry and Statistics 349

Topic 1 Further Integration

8 Further integration 351

8.1 Overview 352
8.2 Estimating the area under a curve 353
8.3 The fundamental theorem of calculus 365
8.4 Areas under a curve 374
8.5 Areas between curves 385
8.6 Modelling and solving with definite integrals 395
8.7 Review 408

Topic 2 Trigonometry

9 Cosine and sine rules 421

9.1 Overview 422
9.2 The sine rule 423
9.3 The cosine rule 432
9.4 Area of a triangle 440
9.5 Modelling and solving with the sine and cosine rules 445
9.6 Review 453

Topic 3 Continuous Random Variables and the Normal Distribution

10 General continuous random variables 461

10.1 Overview 462
10.2 Continuous random variables and the probability density function 463
10.3 Cumulative distribution functions 479
10.4 Measures of centre and spread 490
10.5 Review 499

11 Normal distributions 511

11.1 Overview 512
11.2 The normal distribution 513
11.3 Standardised normal variables 521
11.4 The inverse normal distribution 526
11.5 Modelling and solving with normal distributions 531
1.6 Review 538

Topic 4 Sampling and Proportions

Topic 5 Interval Estimates for Proportions

12 Sampling, proportions and interval estimates 547

12.1 Overview 548
12.2 Random sampling 550
12.3 Sample proportions 557
12.4 Confidence intervals for proportions 562
12.5 Review 568
Answers 573

Practice Assessment 3
Unit 4 Examination

Practice Assessment 4
Units 3 & 4 Examination

Glossary (online only)