WE ARE MOVING! In order to provide you with a better experience, we've moved to www.jacaranda.com.au where you can purchase or find more information about Jacaranda's latest products. Please note this website is no longer updated regularly and will be inaccessible from August 31st, 2019.

• Jacaranda Shop
• Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 Solutions Manual & eBookPLUS

# Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 Solutions Manual & eBookPLUS

Author/s Rozen 9780730323020 October 2015 552 \$44.95

Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 Solutions Manual with eBookPLUS contains fully worked solutions to every question in the Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 student text.

This resource is a printed student text that includes Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 Solutions Manual eBookPLUS.

Topic 1 — Sketching graphs 1

Exercise 1.2 — An introduction to the modulus function 1

Exercise 1.3 — Sketching graphs of reciprocal functions 2

Exercise 1.4 — Sketching graphs of rational functions 8

Exercise 1.5 — S ketching graphs of y = f (x) and y = f ( x ) from y = f (x) 21

Exercise 1.6 — Circles, ellipses and hyperbolas 26

Topic 2 — Trigonometry 33

Exercise 2.2 — Reciprocal trigonometric functions 33

Exercise 2.3 — Trigonometric identities using reciprocal trigonometric functions 36

Exercise 2.4 — Compound-angle formulas 38

Exercise 2.5 — Double-angle formulas 42

Exercise 2.6 — Inverse trigonometric functions 49

Exercise 2.7 — General solutions of trigonometric equations 59

Exercise 2.8 — Graphs of reciprocal trigonometric functions 65

Exercise 2.9 — Graphs of inverse trigonometric functions 74

Topic 3 — Complex numbers 83

Exercise 3.2 — Complex numbers in rectangular form 83

Exercise 3.3 — Complex numbers in polar form 88

Exercise 3.4 — Solving polynomial equations 100

Exercise 3.5 — Subsets of the complex plane: circles, lines and rays 105

Exercise 3.6 — Roots of complex numbers 114

Topic 4 — Kinematics 121

Exercise 4.2 — Constant acceleration 121

Exercise 4.3 — Motion under gravity 122

Exercise 4.4 — Velocity–time graphs 124

Exercise 4.5 — Variable acceleration 126

Topic 5 — Vectors in three dimensions 131

Exercise 5.2 — Vectors 131

Exercise 5.3 — i j k notation 136

Exercise 5.4 — Scalar product and applications 143

Exercise 5.5 — Vector proofs using the scalar product 152

Exercise 5.6 — Parametric equations 158

Topic 6 — Mechanics 167

Exercise 6.2 — Statics of a particle 167

Exercise 6.3 — Inclined planes and connected particles 175

Exercise 6.4 — Dynamics 180

Exercise 6.5 — Dynamics with connected particles 186

Topic 7 — Differential calculus 193

Exercise 7.2 — Review of differentiation techniques 193

Exercise 7.3 — Applications of differentiation 202

Exercise 7.4 — Implicit and parametric differentiation 209

Exercise 7.5 — Second derivatives 217

Exercise 7.6 — Curve sketching 225

Exercise 7.7 — Derivatives of inverse trigonometric functions 239

Exercise 7.8 — Related rate problems 246

Topic 8 — Integral calculus 253

Exercise 8.2 — Areas under and between curves 253

Exercise 8.3 — Linear substitutions 264

Exercise 8.4 — Other substitutions 275

Exercise 8.5 — Integrals of powers of trigonometric functions 284

Exercise 8.6 — Integrals involving inverse trigonometric functions 291

Exercise 8.7 — Integrals involving partial fractions 302

Topic 9 — Differential equations 315

Exercise 9.2 — Verifying solutions to a differential equation 315

Exercise 9.3 — Solving Type 1 differential equations, = dy dx f (x) 325

Exercise 9.4 — Solving Type 2 differential equations, = dy dx f ( y) 330

Exercise 9.5 — Solving Type 3 differential equations, = dy dx f (x)g(y) 338

Exercise 9.6 — Solving Type 4 differential equations, = d y dx f x ( ) 2 2 344

Topic 10 — Further applications of integration 353

Exercise 10.2 — Integration by recognition 353

Exercise 10.3 — Solids of revolution 365

Exercise 10.4 — Volumes 372

Exercise 10.5 — Arc length, numerical integration and graphs of antiderivatives 381

Exercise 10.6 — Water flow 389

Topic 11 — Applications of first-order differential equations 397

Exercise 11.2 — Growth and decay 397

Exercise 11.3 — Other applications of first-order differential equations 400

Exercise 11.4 — Bounded growth and Newton’s Law of Cooling 406

Exercise 11.5 — Chemical reactions and dilution problems 413

Exercise 11.6 — The logistic equation 425

Exercise 11.7 — Euler’s method 439

Exercise 11.8 — Slope fields 452

Topic 12 — Variable forces 455

Exercise 12.2 — Forces that depend on time 455

Exercise 12.3 — Forces that depend on velocity 461

Exercise 12.4 — Forces that depend on displacement 475

Topic 13 — Vector calculus 483

Exercise 13.2 — Position vectors as functions of time 483

Exercise 13.3 — Differentiation of vectors 489

Exercise 13.4 — Special parametric curves 500

Exercise 13.5 — Integration of vectors 512

Exercise 13.6 — Projectile motion 525

Topic 14 — Statistical inference 539

Exercise 14.2 — Linear combinations of random variables 539

Exercise 14.3 — Sample means 540

Exercise 14.4 — Confidence intervals 542

Exercise 14.5 — Hypothesis testing 543

## Related titles

### StudyOn VCE Specialist Mathematics Units 3 and 4 2E Teacher Edition (Online Purchase)

Author: Jacaranda, Published: 13/01/2016, RRP: \$114.95

### StudyOn VCE Specialist Mathematics Units 3 and 4 (Online Purchase)

Author: Scott, Published: 11/01/2016, RRP: \$20.95

### Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 eGuidePLUS (Online Purchase)

Author: Rozen, Published: 03/12/2015, RRP: \$114.95

### Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 eBookPLUS (Online) + StudyOn VCE Specialist Mathematics Units 3 and 4 (Online)

Author: Rozen, Published: 17/11/2015, RRP: \$59.95

### Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Specialist Mathematics Units 3 and 4

Author: Rozen, Published: 14/11/2015, RRP: \$89.95