Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3&4 2E eBookPLUS & Print + StudyOn VCE Mathematical Methods CAS Units 3&4 2E (Book Code)
| Author(s): | Swale |
| ISBN: | 9780730365563 |
| Pub date: | November 2018 |
| RRP: | $89.95 |
This combined print and digital title has been designed to help students at the point of learning, so every student can experience success in VCE Mathematics – in the classroom, at home and thus ultimately in the exam.
The latest editions from the Jacaranda Maths Quest VCE series include these key updates:
• Features in-depth coverage of the Study Design, plus support resources to assist teachers’ implementation of the curriculum
• Jacaranda’s unique exam preparation tool, studyON, is now included free and fully integrated to help prepare students for their exams
• 1000s of new questions written for the series to expand students’ understanding and improve learning outcomes
• Exercises ensure that all students can experience success through the gradation of questions from easier through to more challenging
• Exciting new HTML5 interactivities and videos have been optimised for all devices
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.
About this resource ix
About eBookPLUS and studyON xii
Acknowledgements xiii
1 Functions and graphs 1
1.1 Overview 1
1.2 Linear functions 3
1.3 Solving systems of equations 10
1.4 Quadratic functions 17
1.5 Cubic functions 26
1.6 Higher degree polynomials 36
1.7 Other algebraic functions 47
1.8 Combinations of functions 61
1.9 Modelling and applications 71
1.10 Review: exam practice 75
Answers 79
2 Trigonometric functions 94
2.1 Overview 94
2.2 Trigonometric symmetry properties 96
2.3 Trigonometric equations 108
2.4 General solution of trigonometric equations 115
2.5 Circular functions 120
2.6 The tangent function 127
2.7 Modelling and applications 135
2.8 Review: exam practice 138
Answers 142
3 Composite functions, transformations and inverses 148
3.1 Overview 148
3.2 Composite functions 150
3.3 Functional equations 154
3.4 Transformations 156
3.5 Transformations using matrices 164
3.6 Inverse graphs and relations 171
3.7 Inverse functions 178
3.8 Literal equations 187
3.9 Review: exam practice 190
Answers 194
Revision Topics 1 to 3 205
4 Exponential and logarithmic functions 206
4.1 Overview 206
4.2 Logarithm laws and equations 207
4.3 Logarithmic scales 214
4.4 Indicial equations 217
4.5 Logarithmic graphs 220
4.6 Exponential graphs 228
4.7 Applications 237
4.8 Review: exam practice 242
Answers 247
Revision Topic 4 257
5 Differentiation 258
5.1 Overview 258
5.2 Review of differentiation 260
5.3 Differentiation of exponential functions 275
5.4 Applications of exponential functions 280
5.5 Differentiation of trigonometric functions 285
5.6 Applications of trigonometric functions 290
5.7 Review: exam practice 297
Answers 301
6 Further differentiation and applications 306
6.1 Overview 306
6.2 The chain rule 308
6.3 The product rule 315
6.4 The quotient rule 321
6.5 Curve sketching 325
6.6 Maximum and minimum problems 336
6.7 Rates of change 342
6.8 Review: exam practice 351
Answers 355
7 Anti-differentiation 363
7.1 Overview 363
7.2 Anti-differentiation 365
7.3 Anti-derivatives of exponential and trigonometric functions 372
7.4 Families of curves 376
7.5 Applications 382
7.6 Review: exam practice 388
Answers 392
8 Integration 396
8.1 Overview 396
8.2 The fundamental theorem of integral calculus 398
8.3 Areas under curves 411
8.4 Areas between curves and average values 420
8.5 Applications 427
8.6 Review: exam practice 433
Answers 439
9 Logarithmic functions using calculus 442
9.1 Overview 442
9.2 The derivative of f(x) = loge(x) 444
9.3 The anti-derivative of f(x) =1/X 452
9.4 Applications 464
9.5 Review: exam practice 471
Answers 474
Revision Topics 5 to 9 478
10 Discrete random variables 479
10.1 Overview 479
10.2 Discrete random variables 481
10.3 Measures of centre and spread 491
10.4 Applications 502
10.5 Review: exam practice 509
Answers 513
11 The binomial distribution 517
11.1 Overview 517
11.2 Bernoulli trials 519
11.3 The binomial distribution 523
11.4 Applications 537
11.5 Review: exam practice 540
Answers 544
12 Continuous probability distributions 547
12.1 Overview 547
12.2 Continuous random variables and probability functions 549
12.3 The continuous probability density function 560
12.4 Measures of centre and spread 566
12.5 Linear transformations 580
12.6 Review: exam practice 587
Answers 592
13 The normal distribution 597
13.1 Overview 597
13.2 The normal distribution 599
13.3 Calculating probabilities and the standard normal distribution 606
13.4 The inverse normal distribution 613
13.5 Mixed probability application problems 616
13.6 Review: exam practice 622
Answers 627
14 Statistical inference 629
14.1 Overview 629
14.2 Population parameters and sample statistics 631
14.3 The distribution of 637
14.4 Confidence intervals 644
14.5 Review: exam practice 650
Answers 653
Revision Topics 10 to 14 655
Glossary 657
Index 661
