Description

Maths Quest 11 Mathematical Methods Units 1 and 2 provides comprehensive coverage of the new VCE Study Design for 2016-2018. It includes Jacaranda's unique exam preparation tool, studyON, which has been fully integrated with the text to maximise every student's opportunity for exam success. Features and benefits * Many HTML5 interactivities are available. These are designed to engage, excite and enhance understanding by bringing difficult concepts to life. * The theory is written by highly experienced and successful teachers with a proven and fundamental understanding of how students learn mathematics and succeed in exams. * Every exercise contains three levels of carefully graded questions which allow students to practise, consolidate and master their knowledge independently. * Thousands of new questions have been written exclusively for this series, including many higher level questions that stretch students' understanding of mathematics for improved learning outcomes. * CAS support is provided within the student text through activities and questions. Additionally, students can obtain detailed step-by-step instructions by accessing the TI-Nspire CAS or the Casio ClassPad II Calculator Manuals in the Prelim section of their eBookPLUS. * studyON VCE Mathematical Methods Units 1 and 2 is fully integrated with the student text. studyON is Jacaranda's unique study, revision and exam preparation tool. Students can rely on Jacaranda's dedicated customer service and support. This resource is a hard-copy student text that includes the eBookPLUS and studyON VCE Mathematical Methods Units 1 and 2. studyON for Units 1 and 2 is a comprehensive study, revision and exam preparation tool that delivers proven learning outcomes. Features and benefits * Sit exams: VCAA exam-style questions along with marking guides. Students receive instant feedback and can track their results at a concept, topic or whole-course level. * Concepts: Concept summary screens provide concise, in-depth explanations supported by relevant examples. * Read more: Hyperlinks direct students to more information in the Jacaranda eBookPLUS.

Table of contents

Introduction vii About eBookPLUS and studyON x Acknowledgements xi Topic 1 Lines and linear relationships 2 1.1 Kick off with CAS 3 1.2 Linearly related variables, linear equations and inequations 4 1.3 Systems of 3 x 3 simultaneous linear equations 16 1.4 Linear graphs and their equations 21 1.5 Intersections of lines and their applications 33 1.6 Coordinate geometry of the straight line 40 1.7 Review 52 Answers 53 Topic 2 Algebraic foundations 58 2.1 Kick off with CAS 59 2.2 Algebraic skills 60 2.3 Pascal's triangle and binomial expansions 67 2.4 The binomial theorem 72 2.5 Sets of real numbers 80 2.6 Surds 86 2.7 Review 97 Answers 98 Topic 3 Quadratic relationships 104 3.1 Kick off with CAS 105 3.2 Quadratic equations with rational roots 106 3.3 Quadratics over R 110 3.4 Applications of quadratic equations 122 3.5 Graphs of quadratic polynomials 127 3.6 Determining the rule of a quadratic polynomial from a graph 138 3.7 Quadratic inequations 142 3.8 Quadratic models and applications 149 3.9 Review 154 Answers 155 Topic 4 Cubic polynomials 164 4.1 Kick off with CAS 165 4.2 Polynomials 166 4.3 The remainder and factor theorems 177 4.4 Graphs of cubic polynomials 185 4.5 Equations of cubic polynomials 195 4.6 Cubic models and applications 202 4.7 Review 209 Answers 210 Topic 5 Higher-degree polynomials 222 5.1 Kick off with CAS 223 5.2 Quartic polynomials 224 5.3 Families of polynomials 231 5.4 Numerical approximations to roots of polynomial equations 240 5.5 Review 250 Answers 251 Topic 6 Functions and relations 258 6.1 Kick off with CAS 259 6.2 Functions and relations 260 6.3 The circle 269 6.4 The rectangular hyperbola and the truncus 278 6.5 The relation y2 = x 294 6.6 Other functions and relations 305 6.7 Transformations of functions 319 6.8 Review 328 Answers 329 Topic 7 Matrices and applications to transformations 348 7.1 Kick off with CAS 349 7.2 Addition, subtraction and scalar multiplication of matrices 350 7.3 Matrix multiplication 357 7.4 Determinants and inverses of 2 x 2 matrices 362 7.5 Matrix equations and solving 2 x 2 linear simultaneous equations 367 7.6 Translations 376 7.7 Reflections 383 7.8 Dilations 389 7.9 Combinations of transformations 394 7.10 Review 397 Answers 398 Topic 8 Probability 404 8.1 Kick off with CAS 405 8.2 Probability review 406 8.3 Conditional probability 417 8.4 Independence 425 8.5 Counting techniques 430 8.6 Binomial coefficients and Pascal's triangle 443 8.7 Review 451 Answers 452 Topic 9 Trigonometric functions 1 456 9.1 Kick off with CAS 457 9.2 Trigonometric ratios 458 9.3 Circular measure 465 9.4 Unit circle definitions 473 9.5 Symmetry properties 482 9.6 Graphs of the sine and cosine functions 493 9.7 Review 503 Answers 504 Topic 10 Trigonometric functions 2 510 10.1 Kick off with CAS 511 10.2 Trigonometric equations 512 10.3 Transformations of sine and cosine graphs 521 10.4 Applications of sine and cosine functions 533 10.5 The tangent function 540 10.6 Trigonometric relationships 550 10.7 Review 558 Answers 559 Topic 11 Exponential functions 570 11.1 Kick off with CAS 571 11.2 Indices as exponents 572 11.3 Indices as logarithms 579 11.4 Graphs of exponential functions 587 11.5 Applications of exponential functions 596 11.6 Inverses of exponential functions 604 11.7 Review 618 Answers 619 Topic 12 Introduction to differential calculus 630 12.1 Kick off with CAS 631 12.2 Rates of change 632 12.3 Gradients of secants 640 12.4 The derivative function 645 12.5 Differentiation of polynomials by rule 652 12.6 Review 662 Answers 663 Topic 13 Differentiation and applications 668 13.1 Kick off with CAS 669 13.2 Limits, continuity and differentiability 670 13.3 Derivatives of power functions 679 13.4 Coordinate geometry applications of differentiation 686 13.5 Curve sketching 695 13.6 Optimisation problems 704 13.7 Rates of change and kinematics 710 13.8 Review 720 Answers 721 Topic 14 Anti-differentiation and introduction to integral calculus 728 14.1 Kick off with CAS 729 14.2 Anti-derivatives 730 14.3 Anti-derivative functions and graphs 736 14.4 Applications of anti-differentiation 742 14.5 The definite integral 748 14.6 Review 758 Answers 759 Index 765