3ab Specialist Notes
VCE
Specialist Mathematics Pocket Study Guide
Contents Introduction 1 Vectors in two and three dimensions 2 Complex numbers 3 Coordinate geometry and sketch graphs 4 Circular functions 5 Antidifferentiation 6 Integration 7 Differential equations 8 Kinematics 9 Vector calculus 10 Dynamics iv 1 12 26 40 53 62 70 79 86 92
Introduction What do you really need to know for Specialist Mathematics? We’ve answered that question in this Pocket Study Guide. This handy guide gives you a summary of the entire course in an easy-to-use form. Keep it with you and look through it whenever you get the chance. The guide includes: • diagrams • formulae • graphics calculator and CAS advice • frequently asked questions • study tips • space for you to include your own examples. Also available for Specialist Mathematics in the Leading Edge series: Specialist Mathematics Exam 1 Builder Specialist Mathematics Exam 2 Builder Other Pocket Study Guides available: Further Mathematics Pocket Study Guide Mathematical Methods 3 & 4 Pocket Study Guide Mathematical Methods 1 & 2 Pocket Study Guide Visit us at hi.com.au/theleadingedge
iv
1: Vectors in two and three dimensions
1.1 Vector notation • Vectors are denoted by a directed line segment. The length of the segment represents the magnitude, and the orientation represents its direction. • A vector can be denoted by a bold letter with a tilde beneath; for example, a. An alternative notation is ˜ the form AB , which represents a vector with initial point A and terminal point B. • The magnitude of the vector AB or a is written as ˜ AB or | a|, and is a scalar quantity. ˜ • Two vectors are said to be equal if and only if they have the same magnitude and the same direction. • The negative of a vector AB is a vector of equal magnitude but with opposite direction; that is, − AB = BA. • A vector of zero magnitude, denoted 0 , is ˜ represented as a point and does not have a direction. • Multiplying a vector by a scalar k (k > 0)
Specialist Mathematics Pocket Study Guide
Contents Introduction 1 Vectors in two and three dimensions 2 Complex numbers 3 Coordinate geometry and sketch graphs 4 Circular functions 5 Antidifferentiation 6 Integration 7 Differential equations 8 Kinematics 9 Vector calculus 10 Dynamics iv 1 12 26 40 53 62 70 79 86 92
Introduction What do you really need to know for Specialist Mathematics? We’ve answered that question in this Pocket Study Guide. This handy guide gives you a summary of the entire course in an easy-to-use form. Keep it with you and look through it whenever you get the chance. The guide includes: • diagrams • formulae • graphics calculator and CAS advice • frequently asked questions • study tips • space for you to include your own examples. Also available for Specialist Mathematics in the Leading Edge series: Specialist Mathematics Exam 1 Builder Specialist Mathematics Exam 2 Builder Other Pocket Study Guides available: Further Mathematics Pocket Study Guide Mathematical Methods 3 & 4 Pocket Study Guide Mathematical Methods 1 & 2 Pocket Study Guide Visit us at hi.com.au/theleadingedge
iv
1: Vectors in two and three dimensions
1.1 Vector notation • Vectors are denoted by a directed line segment. The length of the segment represents the magnitude, and the orientation represents its direction. • A vector can be denoted by a bold letter with a tilde beneath; for example, a. An alternative notation is ˜ the form AB , which represents a vector with initial point A and terminal point B. • The magnitude of the vector AB or a is written as ˜ AB or | a|, and is a scalar quantity. ˜ • Two vectors are said to be equal if and only if they have the same magnitude and the same direction. • The negative of a vector AB is a vector of equal magnitude but with opposite direction; that is, − AB = BA. • A vector of zero magnitude, denoted 0 , is ˜ represented as a point and does not have a direction. • Multiplying a vector by a scalar k (k > 0)