# Maths Quest 12 VCE Specialist Mathematics eGuidePLUS (Online Purchase)

ISBN: 978-0-730-32304-4

Jan 2016, Jacaranda

Product not available for purchase

1 Sketching graphs
1.1 Kick off with CAS
1.2 An introduction to the modulus function
1.3 Sketching graphs of reciprocal functions
1.4 Sketching graphs of rational functions
1.5 Sketching graphs of y = |f (x)| and y = f (|x |) from y = f (x)
1.6 Circles, ellipses and hyperbolas
1.7 Review

2 Trigonometry
2.1 Kick off with CAS
2.2 Reciprocal trigonometric functions
2.3 Trigonometric identities using reciprocal trigonometric functions
2.4 Compound angle formulae
2.5 Double angle formulae
2.6 Inverse trigonometric functions
2.7 General solutions of trigonometric equations
2.8 Graphs of reciprocal trigonometric functions
2.9 Graphs of inverse trigonometric functions
2.10 Review

3 Complex numbers
3.1 Kick off with CAS
3.2 Complex numbers in rectangular form
3.3 Complex numbers in polar form
3.4 Solving polynomial equations
3.5 Subsets of the complex plane, circles, lines and rays
3.6 Roots of complex numbers
3.7 Review

4 Kinematics
4.1 Kick off with CAS
4.2 Constant acceleration
4.3 Motion under gravity
4.4 Review

5 Vectors in three dimensions
5.1 Kick off with CAS
5.2 Vectors
5.3 i j k notation
5.4 Scalar product
5.5 Vector proofs using the scalar product
5.6 Parametric equations
5.7 Review

6 Mechanics
6.1 Kick off with CAS
6.2 Statics of a particle
6.3 Inclined planes and connected particles
6.4 Dynamics
6.5 Dynamics with connected particles
6.6 Review

7 Differential Calculus
7.1 Kick off with CAS
7.2 Review of differentiation techniques
7.3 Applications of differentiation
7.4 Implicit and parametric differentiation
7.5 Second derivatives
7.6 Curve sketching
7.7 Derivatives of inverse trigonometric functions
7.8 Related rate problems
7.9 Review

8 Integral calculus
8.1 Kick off with CAS
8.2 Areas and areas between curves
8.3 Linear substitutions
8.4 Non-linear substitutions
8.5 Integrals of powers of trigonometric functions
8.6 Integrals involving inverse trigonometric functions
8.7 Integrals involving partial fractions
8.8 Review

9 Differential equations
9.1 Kick off with CAS
9.2 Verifying solutions to a differential equation
9.3 Solving Type 1
9.4 Solving Type 2
9.5 Solving Type 3
9.6 Solving Type 4
9.7 Review

10 Further applications of integration
10.1 Kick off with CAS
10.2 Integration by recognition
10.3 Solids of revolution
10.4 Volumes
10.5 Arc length and Numerical integration
10.6 Water flow
10.7 Review

11 Applications of first-order differential equations
11.1 Kick off with CAS
11.2 Growth and decay
11.3 Other applications of first order differential equations
11.4 Bounded growth and Newton’s law of cooling
11.5 Chemical reactions and dilution problems
11.6 Logistic equation
11.7 Euler’s method
11.8 Slope fields
11.9 Review

12 Variable forces
12.1 Kick off with CAS
12.2 Forces that depend on time
12.3 Forces that depend on velocity
12.4 Forces that depend on displacement
12.5 Review

13 Vector calculus
13.1 Kick off with CAS
13.2 Position vectors as functions of time
13.3 Differentiation of vectors
13.4 Special parametric curves
13.5 Integration of vectors
13.6 Projectile motion
13.7 Review

14 Statistical Inference
14.1 Kick off with CAS
14.2 Linear combinations of random variables
14.3 Sample means
14.4 Confidence intervals
14.5 Hypothesis testing
14.6 Review