Jacaranda Maths Quest 11 Mathematical Methods VCE Units 1&2 2e eBookPLUS & Print + StudyON VCE Mathematical Methods Units 1&2 (Book Code) | Zookal Textbooks | Zookal Textbooks
  • Author(s) Sue Michell
  • Edition2
  • Published19th November 2018
  • PublisherJohn Wiley & Sons Australia
  • ISBN9780730365464

About this resource vii


About eBookPLUS and studyON x


Acknowledgements xi


1 Lines and linear relationships 1


1.1 Overview 1


1.2 Linearly related variables, linear equations and inequations 3


1.3 Systems of 3 × 3 simultaneous linear equations 16


1.4 Linear graphs and their equations 21


1.5 Intersections of lines and their applications 34


1.6 Coordinate geometry of the straight line 40


1.7 Bisection and lengths of line segments 47


1.8 Review: exam practice 53


Answers 56


2 Algebraic foundations 63


2.1 Overview 63


2.2 Algebraic skills 65


2.3 Pascal’s triangle and binomial expansions 73


2.4 The binomial theorem 77


2.5 Sets of real numbers 85


2.6 Surds 91


2.7 Review: exam practice 102


Answers 106


3 Quadratic relationships 110


3.1 Overview 110


3.2 Quadratic equations with rational roots 112


3.3 Quadratics over R 117


3.4 Applications of quadratic equations 130


3.5 Graphs of quadratic polynomials 134


3.6 Determining the rule of a quadratic polynomial from a graph 146


3.7 Quadratic inequations 152


3.8 Quadratic models and applications 159


3.9 Review: exam practice 163


Answers 167


4 Cubic polynomials 178


4.1 Overview 178


4.2 Polynomials 180


4.3 The remainder and factor theorems 192


4.4 Graphs of cubic polynomials 201


4.5 Equations of cubic polynomials 212


4.6 Cubic models and applications 223


4.7 Review: exam practice 228


Answers 232


5 Higher-degree polynomials 247


5.1 Overview 247


5.2 Quartic polynomials 249


5.3 Families of polynomials 258


5.4 Numerical approximations to roots of polynomial equations 267


5.5 Review: exam practice 276


Answers 280


6 Functions and relations 289


6.1 Overview 289


6.2 Functions and relations 291


6.3 The circle 301


6.4 The rectangular hyperbola and the truncus 312


6.5 The relation y2 = x 330


6.6 Other functions and relations 343


6.7 Transformations of functions 356


6.8 Review: exam practice 366


Answers 371


Revision Topics 1 to 6 393


7 Matrices and applications to transformations 394


7.1 Overview 394


7.2 Addition, subtraction and scalar multiplication of matrices 396


7.3 Matrix multiplication 403


7.4 Determinants and inverses of 2 × 2 matrices 408


7.5 Matrix equations and solving 2 × 2 linear simultaneous equations 414


7.6 Translations 424


7.7 Reflections 431


7.8 Dilations 438


7.9 Combinations of transformations 443


7.10 Review: exam practice 446


Answers 451


Revision Topic 7 458


8 Probability 459


8.1 Overview 459


8.2 Probability review 461


8.3 Conditional probability 472


8.4 Independence 481


8.5 Counting techniques 487


8.6 Binomial coefficients and Pascal’s triangle 500


8.7 Review: exam practice 509


Answers 513


Revision Topic 8 517


9 Trigonometric functions 1 518


9.1 Overview 518


9.2 Trigonometric ratios 519


9.3 Circular measure 529


9.4 Unit circle definitions 538


9.5 Symmetry properties 548


9.6 Graphs of the sine and cosine functions 559


9.7 Review: exam practice 570


Answers 573


10 Trigonometric functions 2 580


10.1 Overview 580


10.2 Trigonometric equations 582


10.3 Transformations of sine and cosine graphs 591


10.4 Applications of sine and cosine functions 605


10.5 The tangent function 612


10.6 Trigonometric relationships 622


10.7 Review: exam practice 629


Answers 634


11 Exponential functions 648


11.1 Overview 648


11.2 Indices as exponents 650


11.3 Indices as logarithms 658


11.4 Graphs of exponential functions 668


11.5 Applications of exponential functions 677


11.6 Inverses of exponential functions 684


11.7 Review: exam practice 697


Answers 701


Revision Topics 9 to 11 712


12 Introduction to differential calculus 713


12.1 Overview 713


12.2 Rates of change 715


12.3 Gradients of secants 723


12.4 The derivative function 728


12.5 Differentiation of polynomials by rule 735


12.6 Review: exam practice 746


Answers 750


13 Differentiation and applications 757


13.1 Overview 757


13.2 Limits, continuity and differentiability 759


13.3 Derivatives of power functions 769


13.4 Coordinate geometry applications of differentiation 777


13.5 Curve sketching 786


13.6 Optimisation problems 796


13.7 Rates of change and kinematics 803


13.8 Review: exam practice 812


Answers 815


14 Anti-differentiation and introduction to integral calculus 824


14.1 Overview 824


14.2 Anti-derivatives 826


14.3 Anti-derivative functions and graphs 833


14.4 Application of anti-differentiation 841


14.5 The definite integral 847


14.6 Review: exam practice 858


Answers 862


Revision Topics 12 to 14 868


Glossary 869


Index 878

Jacaranda Maths Quest 11 Mathematical Methods VCE Units 1&2 2e eBookPLUS & Print + StudyON VCE Mathematical Methods Units 1&2 (Book Code)

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  • Author(s) Sue Michell
  • Edition2
  • Published19th November 2018
  • PublisherJohn Wiley & Sons Australia
  • ISBN9780730365464

About this resource vii


About eBookPLUS and studyON x


Acknowledgements xi


1 Lines and linear relationships 1


1.1 Overview 1


1.2 Linearly related variables, linear equations and inequations 3


1.3 Systems of 3 × 3 simultaneous linear equations 16


1.4 Linear graphs and their equations 21


1.5 Intersections of lines and their applications 34


1.6 Coordinate geometry of the straight line 40


1.7 Bisection and lengths of line segments 47


1.8 Review: exam practice 53


Answers 56


2 Algebraic foundations 63


2.1 Overview 63


2.2 Algebraic skills 65


2.3 Pascal’s triangle and binomial expansions 73


2.4 The binomial theorem 77


2.5 Sets of real numbers 85


2.6 Surds 91


2.7 Review: exam practice 102


Answers 106


3 Quadratic relationships 110


3.1 Overview 110


3.2 Quadratic equations with rational roots 112


3.3 Quadratics over R 117


3.4 Applications of quadratic equations 130


3.5 Graphs of quadratic polynomials 134


3.6 Determining the rule of a quadratic polynomial from a graph 146


3.7 Quadratic inequations 152


3.8 Quadratic models and applications 159


3.9 Review: exam practice 163


Answers 167


4 Cubic polynomials 178


4.1 Overview 178


4.2 Polynomials 180


4.3 The remainder and factor theorems 192


4.4 Graphs of cubic polynomials 201


4.5 Equations of cubic polynomials 212


4.6 Cubic models and applications 223


4.7 Review: exam practice 228


Answers 232


5 Higher-degree polynomials 247


5.1 Overview 247


5.2 Quartic polynomials 249


5.3 Families of polynomials 258


5.4 Numerical approximations to roots of polynomial equations 267


5.5 Review: exam practice 276


Answers 280


6 Functions and relations 289


6.1 Overview 289


6.2 Functions and relations 291


6.3 The circle 301


6.4 The rectangular hyperbola and the truncus 312


6.5 The relation y2 = x 330


6.6 Other functions and relations 343


6.7 Transformations of functions 356


6.8 Review: exam practice 366


Answers 371


Revision Topics 1 to 6 393


7 Matrices and applications to transformations 394


7.1 Overview 394


7.2 Addition, subtraction and scalar multiplication of matrices 396


7.3 Matrix multiplication 403


7.4 Determinants and inverses of 2 × 2 matrices 408


7.5 Matrix equations and solving 2 × 2 linear simultaneous equations 414


7.6 Translations 424


7.7 Reflections 431


7.8 Dilations 438


7.9 Combinations of transformations 443


7.10 Review: exam practice 446


Answers 451


Revision Topic 7 458


8 Probability 459


8.1 Overview 459


8.2 Probability review 461


8.3 Conditional probability 472


8.4 Independence 481


8.5 Counting techniques 487


8.6 Binomial coefficients and Pascal’s triangle 500


8.7 Review: exam practice 509


Answers 513


Revision Topic 8 517


9 Trigonometric functions 1 518


9.1 Overview 518


9.2 Trigonometric ratios 519


9.3 Circular measure 529


9.4 Unit circle definitions 538


9.5 Symmetry properties 548


9.6 Graphs of the sine and cosine functions 559


9.7 Review: exam practice 570


Answers 573


10 Trigonometric functions 2 580


10.1 Overview 580


10.2 Trigonometric equations 582


10.3 Transformations of sine and cosine graphs 591


10.4 Applications of sine and cosine functions 605


10.5 The tangent function 612


10.6 Trigonometric relationships 622


10.7 Review: exam practice 629


Answers 634


11 Exponential functions 648


11.1 Overview 648


11.2 Indices as exponents 650


11.3 Indices as logarithms 658


11.4 Graphs of exponential functions 668


11.5 Applications of exponential functions 677


11.6 Inverses of exponential functions 684


11.7 Review: exam practice 697


Answers 701


Revision Topics 9 to 11 712


12 Introduction to differential calculus 713


12.1 Overview 713


12.2 Rates of change 715


12.3 Gradients of secants 723


12.4 The derivative function 728


12.5 Differentiation of polynomials by rule 735


12.6 Review: exam practice 746


Answers 750


13 Differentiation and applications 757


13.1 Overview 757


13.2 Limits, continuity and differentiability 759


13.3 Derivatives of power functions 769


13.4 Coordinate geometry applications of differentiation 777


13.5 Curve sketching 786


13.6 Optimisation problems 796


13.7 Rates of change and kinematics 803


13.8 Review: exam practice 812


Answers 815


14 Anti-differentiation and introduction to integral calculus 824


14.1 Overview 824


14.2 Anti-derivatives 826


14.3 Anti-derivative functions and graphs 833


14.4 Application of anti-differentiation 841


14.5 The definite integral 847


14.6 Review: exam practice 858


Answers 862


Revision Topics 12 to 14 868


Glossary 869


Index 878

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