# Jacaranda Maths Quest 9 Stage 5 NSW Australian Curriculum 2E LearnON & Print

Author(s): | Elms |

ISBN: | 9780730347187 |

Pub date: | November 2017 |

RRP: | $69.95 |

*Jacaranda Maths Quest 9 Stage 5 NSW Australian curriculum, 2nd Edition learnON & Print*This combined print and digital title provides 100% coverage of the NSW Australian curriculum for Mathematics. The textbook comes with a complimentary activation code for learnON, the powerful digital learning platform making learning personalised and visible for both students and teachers.

The latest editions of

*Jacaranda Maths Quest NSW Australian curriculum*series include these key features:

**Worked examples**featuring the familiar THINK/WRITE columns providing exemplary solutions and explanations**Carefully graded questions in each exercise**and individual pathway interactivities providing questions for learners at three levels**Worked solutions for every question**providing immediate feedback and help resolve misconceptions at the point of learning**Features a new exercise structure based on**, with two exercise sets per sub-topic to test knowledge and put theory into practice*Working Mathematically***The reading content contains embedded videos**addressing the 50 common maths misconceptions and hundreds of interactivities at the point of learning**Completely new curriculum grids**, work programs and even a poster for schools show complete coverage of every dot point in the curriculum

For teachers, learnON includes additional teacher resources such as quarantined questions and answers, curriculum grids and work programs.

To complement the Maths Quest series,

*assessON Maths Quest*is available for Years 7–10.

Overview ix

Acknowledgments xi

**1 NAPLAN practice 1**

1.1 Overview 1

1.2 NAPLAN practice 1 2

1.3 NAPLAN practice 2 8

1.4 NAPLAN practice 3 15

1.5 Review 22

Answers 23

**2 Financial mathematics [5.1] 25**

2.1 Overview 25

NSW 2.2 [Stage 5.1] Salaries and wages 26

NSW 2.3 [Stage 5.1] Special rates 29

NSW 2.4 [Stage 5.1] Piecework 35

NSW 2.5 [Stage 5.1] Commissions and royalties 38

NSW 2.6 [Stage 5.1] Loadings and bonuses 41

NSW 2.7 [Stage 5.1] Taxation and net earnings 45

ACMNA211 2.8 [Stage 5.1] Simple interest 49

ACMNA229 2.9 [Stage 5.1] Compound interest 55

2.10 Review 61

Answers 65

**3 Similar figures and scale drawings [5.1 and 5.3] 71**

3.1 Overview 71

ACMMG201 3.2 [Stage 4] Congruent figures 72

ACMMG221 3.3 [Stage 5.1] Scale drawings 79

ACMMG220 | ACMMG221 3.4 [Stage 5.1] Similar figures 90

ACMMG244 3.5 [Stage 5.3] Area and volume of similar figures 102

3.6 Review 108

Answers 114

**4 Right-angled triangles (trigonometry) [5.1] 119**

4.1 Overview 119

ACMMG222 4.2 [Stage 4] Pythagoras’ theorem 120

ACMMG222 4.3 [Stage 4] Applications of Pythagoras’ theorem 129

ACMMG223 4.4 [Stage 5.1] Similarity and the sine, cosine and tangent ratios 136

ACMMG224 4.5 [Stage 5.1] Calculating unknown side lengths 144

ACMMG224 4.6 [Stage 5.1] Calculating unknown angles 152

ACMMG245 4.7 [Stage 5.1] Angles of elevation and depression 158

4.8 Review 164

Answers 171

**5 Single variable data analysis [5.1 and 5.2] 177**

5.1 Overview 177

ACMSP284 5.2 [Stage 4] Collecting data 178

ACMSP282 | ACMSP228 5.3 [Stage 5.1] Stem-and-leaf plots and dot plots 188

ACMSP282 5.4 [Stage 5.1] Comparing and displaying data 195

ACMSP283 5.5 [Stage 5.1] Mean, median and mode 206

ACMSP248 5.6 [Stage 5.2] Quartiles, interquartile range and distributions 214

5.7 Review 222

Answers 228

**6 Indices, scientific notation and surds [5.1, 5.2 and 5.3] 241**

6.1 Overview 241

ACMNA186 6.2 [Stage 5.3] Rational and irrational numbers 242

ACMMG219 6.3 [Stage 5.3] Simple operations with surds 248

ACMNA264 6.4 [Stage 5.1] Rounding and significant figures 254

ACMNA210 6.5 [Stage 5.1] Scientific notation 258

ACMNA212 6.6 [Stage 5.1] Applying the index laws to variables 264

ACMNA231 6.7 [Stage 5.1] Using index laws to simplify algebraic products and quotients 270

ACMNA209 | ACMNA231 6.8 [Stage 5.2] Applying index laws to algebraic expressions involving integer indices 273

ACMNA264 6.9 [Stage 5.3] Introduction to fractional indices 278

6.10 Review 281

Answers 287

**7 Area, surface area and volume [5.1 and 5.2] 297**

7.1 Overview 297

ACMMG219 7.2 [Stage 5.1] Time scales and units of measurement 298

ACMMG216 7.3 [Stage 5.1] Area of composite shapes 307

ACMMG216 7.4 [Stage 5.1] Area and perimeter of semicircles and sectors 318

ACMMG218 7.5 [Stage 5.1] Surface area of rectangular and triangular prisms 324

ACMMG217 | ACMMG242 7.6 [Stage 5.2] Surface area of cylinders and composite solids 330

ACMMG217 | ACMMG242 7.7 [Stage 5.2] Volume of prisms, cylinders and composite solids 335

7.8 Review 346

Answers 352

**8 Algebraic techniques 1 [5.2] 359**

8.1 Overview 359

ACMNA175 | ACMNA176 8.2 [Stage 4] Variables 360

ACMNA177 8.3 [Stage 4] Algebra in worded problems 366

ACMNA177 8.4 [Stage 4] Simplifying algebraic expressions 370

ACMNA232 8.5 [Stage 5.2] Simplifying algebraic fractions 1 375

ACMNA213 | ACMNA233 8.6 [Stage 5.2] Expanding algebraic expressions 380

ACMNA230 8.7 [Stage 5.2] The highest common factor 387

ACMNA233 8.8 [Stage 5.2] Factorising monic quadratics 390

8.9 Review 394

Answers 399

**9 Probability [5.1 and 5.2] 407**

9.1 Overview 407

ACMSP226 9.2 [Stage 5.1] Theoretical probability 408

ACMSP226 9.3 [Stage 5.1] Experimental probability 415

ACMSP226 9.4 [Stage 5.1] Venn diagrams and two-way tables 421

ACMSP225 9.5 [Stage 5.2] Two-step experiments 431

ACMSP246 9.6 [Stage 5.2] Mutually exclusive and independent events 439

ACMSP247 9.7 [Stage 5.2] Conditional probability 447

9.8 Review 454

Answers 459

**10 Linear equations [5.2] 471**

10.1 Overview 471

ACMNA215 | ACMNA240 10.2 [Stage 5.2] Solving linear equations 472

ACMNA215 10.3 [Stage 5.2] Solving linear equations with brackets 479

ACMNA215 10.4 [Stage 5.2] Solving linear equations with pronumerals on both sides 482

ACMNA235 10.5 [Stage 5.2] Solving problems with linear equations 486

ACMNA234 10.6 [Stage 5.2] Substituting values into formulas 490

10.7 Review 494

Answers 499

**11 Linear and non-linear relationships [5.1 and 5.2] 503**

11.1 Overview 503

ACMNA215 11.2 [Stage 5.1] Sketching linear graphs using the coordinates of two points 504

ACMNA294 | ACMNA214 11.3 [Stage 5.1] Midpoint of a line segment and distance between two points 509

ACMNA294 11.4 [Stage 5.1] The gradient of a straight line 514

ACMNA215 11.5 [Stage 5.2] Using the gradient–intercept form to graph linear relationships 522

ACMNA238 11.6 [Stages 5.1 and 5.2] Parallel and perpendicular lines 526

NSW 11.7 [Stage 5.2] Finding the equation of a straight line 529

NSW 11.8 [Going further] Practical applications of linear graphs 535

ACMNA296 | ACMNA239 11.9 [Stages 5.1 and 5.2] Non-linear relationships (parabolas, exponentials, circles) 540

11.10 Review 550

Answers 555

**12 Quadratic equations [5.2] 571**

12.1 Overview 571

ACMNA241 12.2 [Stage 5.2] Quadratic equations 572

ACMNA241 12.3 [Stage 5.2] The Null Factor Law 576

ACMNA241 12.4 [Stage 5.2] Solving the quadratic equation *ax*^{2 }+ *bx *+ *c *= 0 579

ACMNA241 12.5 [Stage 5.2] Solving quadratic equations with two terms 582

ACMNA241 12.6 [Stage 5.2] Applications of quadratic equations 585

12.7 Review 589

Answers 592

**13 Proportion and rates [5.2 and 5.3] 595**

13.1 Overview 595

ACMNA208 13.2 [Stage 5.2] Direct proportion 596

ACMNA208 13.3 [Stage 5.2] Direct proportion and ratio 600

ACMNA208 13.4 [Stage 5.2] Inverse proportion 604

ACMNA208 13.5 [Stage 5.2] Simple rate problems 607

ACMNA208 13.6 [Stage 5.3] Constant and variable rates 610

ACMNA208 13.7 [Stage 5.3] Rates of change 616

13.8 Review 621

Answers 627

**14 Algebraic techniques 2 [5.3] 635**

14.1 Overview 635

ACMNA233 14.2 [Stage 5.3] Special binomial products 636

ACMNA233 14.3 [Stage 5.3] Further expansions 641

ACMNA269 14.4 [Stage 5.3] The highest common binomial factor 642

ACMNA269 14.5 [Stage 5.3] Factorisation patterns 645

ACMNA269 14.6 [Stage 5.3] Factorising non-monic quadratics 649

NSW 14.7 [Stage 5.3] Simplifying algebraic fractions 2 652

ACMNA233 14.8 [Stage 5.3] Applications of binomial products 657

14.9 Review 665

Answers 669

**15 Quadratic relationships [5.3] 677**

15.1 Overview 677

ACMNA267 15.2 [Stage 5.3] Graphs of quadratic functions 678

ACMNA267 15.3 [Stage 5.3] Plotting points to graph quadratic functions 683

ACMNA267 15.4 [Stage 5.3] Sketching parabolas of the form *y *= *ax*^{2 }689

ACMNA267 15.5 [Stage 5.3] Sketching parabolas of the form *y *= *ax*^{2 }+ *k *693

ACMNA267 15.6 [Stage 5.3] Sketching parabolas of the form *y *= (*x *− *h*)^{2 }697

ACMNA267 15.7 [Stage 5.3] Sketching parabolas of the form *y *= (*x *− *h*)^{2 }+ *k *701

ACMNA267 15.8 [Stage 5.3] Sketching parabolas of the form *y *= (*x *+ *a*) (*x *+ *b*) 705

ACMNA267 15.9 [Stage 5.3] Applications 709

15.10 Review 714

Answers 719

Glossary 739

Index 749