Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3 and 4 3e learnON and P

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Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3 and 4

Everything your students need to succeed.

The best Mathematics series for the new VCE Study Design. Developed by expert Victorian teachers for, VCE students.  Get exam ready: past VCAA exam questions (all since 2013) Students can start preparing from lesson one, with past VCAA exam questions embedded in every lesson.  Practice, customisable SACs available for all Units to build student competence and confidence.  Learn online with Australia's most powerful learning platform, learnON Be confident your students can get unstuck and progress, in class or at home. For every question online they receive immediate feedback and fully worked solutions. Teacher-led videos to learn and re-learn. Instant reports make tracking progress simple.  Combine units flexibly with the Jacaranda Supercourse An Australian first, build the course you've always wanted with the Jacaranda Supercourse. You can combine all Methods Units 1 to 4, so students can move backwards and forwards freely. Or Methods and General Units 1 & 2 for when students switch courses. The possibilities are endless!

Table of Contents

About This Resource v Acknowledgements xii 1 Functions and graphs 1 1.1 Overview 2 1.2 Linear functions 3 1.3 Solving systems of equations 11 1.4 Quadratic functions 18 1.5 Cubic functions 28 1.6 Higher degree polynomials 40 1.7 Other algebraic functions 50 1.8 Combinations of functions 66 1.9 Modelling and applications 77 1.10 Review 82 Answers 87 2 Trigonometric (circular) functions 103 2.1 Overview 104 2.2 Trigonometric symmetry properties 105 2.3 Trigonometric equations 118 2.4 General solutions of trigonometric equations 125 2.5 The sine and cosine functions 130 2.6 The tangent function 139 2.7 Modelling and applications 148 2.8 Review 154 Answers 159 3 Composite functions, transformations and inverses 167 3.1 Overview 168 3.2 Composite functions 169 3.3 Transformations 174 3.4 Inverse graphs 182 3.5 Inverse functions 192 3.6 Literal equations 201 3.7 Review 206 Answers 211 4 Exponential and logarithmic functions 223 4.1 Overview 224 4.2 Logarithm laws and equations 225 4.3 Logarithmic scales 234 4.4 Indicial equations 238 4.5 Logarithmic graphs 242 4.6 Exponential graphs 250 4.7 Applications 262 4.8 Review 270 Answers 276 5 Differentiation 287 5.1 Overview 288 5.2 Review of differentiation 289 5.3 Differentiation of exponential functions 304 5.4 Applications of exponential functions 310 5.5 Differentiation of trigonometric functions 316 5.6 Applications of trigonometric functions 322 5.7 Differentiation and application of logarithmic functions 330 5.8 Review 338 Answers 345 6 Further differentiation and applications 353 6.1 Overview 354 6.2 The chain rule 355 6.3 The product rule 363 6.4 The quotient rule 370 6.5 Curve sketching 375 6.6 Maximum and minimum problems 387 6.7 Rates of change 394 6.8 Newton's method 403 6.9 Review 408 Answers 415 7 Anti-differentiation 425 7.1 Overview 426 7.2 Anti-differentiation 427 7.3 Anti-derivatives of exponential and trigonometric functions 435 7.4 The anti-derivative of f(x) = 1 /x 440 7.5 Families of curves 444 7.6 Applications 452 7.7 Review 458 Answers 464 8 Integral calculus 471 8.1 Overview 472 8.2 The fundamental theorem of integral calculus 473 8.3 Areas under curves 484 8.4 Areas between curves and average values 497 8.5 Applications 507 8.6 Review 522 Answers 529 9 Discrete random variables 535 9.1 Overview 536 9.2 Probability review 537 9.3 Discrete random variables 544 9.4 Measures of centre and spread 554 9.5 Applications 565 9.6 Review 572 Answers 577 10 The binomial distribution 583 10.1 Overview 584 10.2 Bernoulli trials 585 10.3 The binomial distribution 590 10.4 Applications 604 10.5 Review 608 Answers 614 11 Continuous probability distributions 617 11.1 Overview 618 11.2 Continuous random variables and probability functions 619 11.3 The continuous probability density function 631 11.4 Measures of centre and spread 638 11.5 Linear transformations 651 11.6 Review 657 Answers 664 12 The normal distribution 671 12.1 Overview 672 12.2 The normal distribution 673 12.3 Calculating probabilities and the standard normal distribution 681 12.4 The inverse normal distribution 688 12.5 Mixed probability applications 693 12.6 Review 702 Answers 709 13 Statistical inference 713 13.1 Overview 714 13.2 Population parameters and sample statistics 715 13.3 The distribution of the sample proportion 721 13.4 Confidence intervals 729 13.5 Review 736 Answers 744 Algorithms and Pseudocode Glossary 747 Index 751

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