IB DP Maths: AI HL復習筆記3.10.4 Chinese Postman Problem
Eulerian Trails & Circuits What are Eulerian trails and circuits? A?trail?is a walk in which?no edge is repeated An?Eulerian trail?is a trail that visits each?edge?in a graph?exactly once A?cir...
IB DP Maths: AI HL復習筆記3.10.3 Minimum Spanning Trees
Kruskal's Algorithm In a situation that can be modelled by a graph,?Kruskal’s algorithm?is a mathematical tool that can be used to?reduce?costs, materials or time. Why do we use Kruskal’s Algorithm...
IB DP Maths: AI HL復習筆記3.10.2 Walks & Adjacency Matrices
Walks & Adjacency Matrices Adjacency matrices?are another way to represent graphs and connections between the different vertices. What is an adjacency matrix? An adjacency matrix can be used to...
IB DP Maths: AI HL復習筆記3.10.1 Introduction to Graph Theory
Parts of a Graph A?graph?is a mathematical structure that is used to represent objects and the connections between them. They can be used in modelling many real-life applications, e.g. electrical c...
IB DP Maths: AI HL復習筆記3.9.2 Constant & Variable Velocity
Vectors & Constant Velocity How are vectors used to model linear motion? If an object is moving with?constant?velocity?it will travel in a?straight line For an object moving in a?straight line?...
IB DP Maths: AI HL復習筆記3.9.1 Kinematics with Vectors
Kinematics using Vectors How are vectors related to kinematics? Kinematics is the use of mathematics to model motion in objects If an object is moving in?one dimension?then its velocity, displaceme...
IB DP Maths: AI HL復習筆記3.8.2 Shortest Distances with Lines
Shortest Distance Between a Point and a Line How do I find the shortest distance from a point to a line? The shortest distance from any point to a line will always be the?perpendicular?distance Not...
IB DP Maths: AI HL復習筆記3.8.1 Vector Equations of Lines
Equation of a Line in Vector Form How do I find the vector equation of a line? The formula for finding the?vector equation?of a line is This is?given in the formula booklet This equation can be use...
IB DP Maths: AI HL復習筆記3.7.7 Geometric Proof with Vectors
Geometric Proof with Vectors How can vectors be used to prove geometrical properties? If two vectors can be shown to be?parallel?then this can be used to prove parallel lines If two vectors are?sca...
IB DP Maths: AI HL復習筆記3.7.6 Components of Vectors
Components of Vectors Why do we write vectors in component form? When working with vectors in context it is often useful to break them down into components acting in a direction that is not one of ...
IB DP Maths: AI HL復習筆記3.7.5 The Vector Product
The?scalar product?is one method of multiplying vectors which results in a scalar and has uses when working with vectors and lines. The?vector product?is a different method, which results in a vect...
IB DP Maths: AI HL復習筆記3.7.4 The Scalar Product
The Scalar ('Dot') Product What is the scalar product? The scalar product (also known as the dot product) is one form in which two vectors can be combined together The result of taking the scalar p...
