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

Author/s |
Rozen |
---|---|
ISBN13 | 9780730323020 |
Pub date | October 2015 |
Pages | 552 |
RRP | $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.
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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