# Maths Quest 11 Mathematical Methods VCE Units 1 and 2 Solutions Manual & eBookPLUS

Author/s |
Michell |
---|---|

ISBN13 | 9780730322979 |

Pub date | November 2015 |

Pages | 448 |

RRP | $44.95 |

* Maths Quest 11 Mathematical Methods Units 1 and 2 Solutions Manual with eBookPLUS* contains fully worked solutions to every question in the

**Maths Quest 11 Mathematical Methods Units 1 and 2**student text.

This resource is a printed student text that includes the

**Maths Quest 11 Mathematical Methods Units 1 and 2 Solutions Manual**

**eBookPLUS.**

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**Topic 1 — Lines and linear relationships 1**

Exercise 1.2 — Linearly related variables, linear equations and inequations 1

Exercise 1.3 — Systems of 3 × 3 simultaneous linear equations 7

Exercise 1.4 — Linear graphs and their equations 9

Exercise 1.5 — Intersections of lines and their applications 14

Exercise 1.6 — Coordinate geometry of the straight line 18

**Topic 2 — Algebraic foundations 25**

Exercise 2.2 — Algebraic skills 25

Exercise 2.3 — Pascal’s triangle and binomial expansions 29

Exercise 2.4 — The binomial theorem 31

Exercise 2.5 — Sets of real numbers 36

Exercise 2.6 — Surds 37

**Topic 3 — Quadratic relationships 45**

Exercise 3.2 — Quadratic equations with rational roots 45

Exercise 3.3 — Quadratics over R 48

Exercise 3.4 — Applications of quadratic equations 54

Exercise 3.5 — Graphs of quadratic polynomials 57

Exercise 3.6 — Determining the rule from a graph of a quadratic polynomial 65

Exercise 3.7 — Quadratic inequations 68

Exercise 3.8 — Quadratic models and applications 73

**Topic 4 — Cubic polynomials 77**

Exercise 4.2 — Polynomials 77

Exercise 4.3 — The remainder and factor theorems 82

Exercise 4.4 — Graphs of cubic polynomials 87

Exercise 4.5 — Equations of cubic polynomials 96

Exercise 4.6 — Cubic models and applications 102

**Topic 5 — Higher-degree polynomials 109**

Exercise 5.2 — Quartic polynomials 109

Exercise 5.3 — Families of polynomials 116

Exercise 5.4 — Numerical approximations to roots of polynomial equations 122

**Topic 6 — Functions and relations** 129

Exercise 6.2 — Functions and relations 129

Exercise 6.3 — The circle 133

Exercise 6.4 — The rectangular hyperbola and the truncus 140

Exercise 6.5 — The relation y2 = x 149

Exercise 6.6 — Other functions and relations 158

Exercise 6.7 — Transformations of functions 167

**Topic 7 — Matrices and applications to transformations 173**

Exercise 7.2 — Addition, subtraction and scalar multiplication of matrices 173

Exercise 7.3 — Matrix multiplication 178

Exercise 7.4 — Determinants and inverses of 2 × 2 matrices 188

Exercise 7.5 — Matrix equations and solving 2 × 2 linear simultaneous equations 196

Exercise 7.6 — Translations 213

Exercise 7.7 — Reflections 216

Exercise 7.8 — Dilations 221

Exercise 7.9 — Combinations of transformations 225

**Topic 8 — Probability 231**

Exercise 8.2 — Probability review 231

Exercise 8.3 — Conditional probability 238

Exercise 8.4 — Independence 245

Exercise 8.5 — Counting techniques 251

Exercise 8.6 — Binomial coefficients and Pascal’s triangle 260

**Topic 9 — Trigonometric functions 1 269**

Exercise 9.2 — Trigonometric ratios 269

Exercise 9.3 — Circular measure 273

Exercise 9.4 — Unit circle definitions 278

Exercise 9.5 — Symmetry properties 282

Exercise 9.6 — The graphs of the sine and cosine functions 287

**Topic 10 — Trigonometric functions 2 293**

Exercise 10.2 — Trigonometric equations 293

Exercise 10.3 — Transformations of sine and cosine graphs 299

Exercise 10.4 — Applications of sine and cosine functions 311

Exercise 10.5 — The tangent function 317

Exercise 10.6 — Trigonometric relationships 325

**Topic 11 — Exponential functions 331**

Exercise 11.2 — Indices as exponents 331

Exercise 11.3 — Indices as logarithms 335

Exercise 11.4 — Graphs of exponential functions 342

Exercise 11.5 — Applications of exponential functions 349

Exercise 11.6 — Inverses of exponential functions 354

**Topic 12 — Introduction to differential calculus 363**

Exercise 12.2 — Rates of change 363

Exercise 12.3 — Gradients of secants 367

Exercise 12.4 — The derivative function 370

Exercise 12.5 — Differentiation of polynomials by rule 377

**Topic 13 — Differentiation and applications 385**

Exercise 13.2 — Limits, continuity and differentiability 385

Exercise 13.3 — Derivatives of power functions 389

Exercise 13.4 — Coordinate geometry applications of differentiation 394

Exercise 13.5 — Curve sketching 401

Exercise 13.6 — Optimisation problems 411

Exercise 13.7 — Rates of change and kinematics 417

**Topic 14 — Anti-differentiation and introduction to integral calculus 423**

Exercise 14.2 — Anti-derivatives 423

Exercise 14.3 — Anti-derivative functions and graphs 426

Exercise 14.4 — Applications of anti-differentiation 432

Exercise 14.5 — The definite integral 435