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Wednesday 21.4.2010
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1. Introduction and basic concepts
Time: 13:20 - 14:50
Definition of vector
Magnitude and direction of vector
Zero vector
Equality of vectors
Parallel vectors
Angle between vectors
Chapter 15:
A: Directed line segment representation
B: Vector equality
Exercises 15A1, 15B1 and 15B2.
Pages 5-15 in Pyramidi: Exercises 201, 202, 203, 206, 208.
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Friday 23.4.2010
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2.2. Addition and subtraction of vectors
Time: 09:50 - 11:20
Geometrical addition of vectors
Geometrical subtraction of vectors
Commutative law
Associative law
Distributive law
2.2 Vektoreiden summa ja erotus, pages 20-32.
15 C: Vector addition and 15D Vector subtraction
Exercises: 211, 212,
Homework exercises: 213, 214 and 215.
Have a nice weekend.
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Monday 26.4.2010
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2.3 Multiplication by a real number
Time: 08:00 - 09:30
2.3 Vektorin kertominen reaaliluvulla
Multiplication by a real number
Associative and commutative laws for multiplication by a real number (page 36 in Pyramidi)
Side of a triangle using adjacent sides and ratio p:q
Unit vector
Exercises 225, 226, 227, 228, 229 and 230.
Homework exercises: 240, 244, 245 and 246.
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Wednesday 28.4.2010
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2.4 Parallelism
Time: 13:25 - 14:55
Homework discussion.
2.4 Vektoreiden yhdensuuntaisuus on pages 51-55.
Exercises 258-264 on page 55.
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Friday 30.4.2010
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2.5 Base vectors
Time: 09:50 - 11:20
2.5 Kantavektorit on pages 56-67.
Exercises 267-273 on page66.
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Monday 3.5.2010
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2.6 Scalar Product
Time: 08:00 - 09:30
Exercises 286-287.
Homework exercises 288, 289 and 290.
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Wednesday 5.5.2010
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3 Vectors in XY-coordinate system
Time: 13:25 - 14:55
3.1 Basic concepts
Unit vectors i and j.
Postion vector
Exercises 301, 302, 303, 307 and 311.
3.2 Length of a Vector
Exercises 314, 315, 316 and 320.
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Friday 7.5.2010
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3.3 Vector between two points 3.4 Scalar product in XY-coordinate system
Time: 09:50 - 11:20
3.3 Kahden pisteen välinen vektori
Distance revisited
Midpoint of a line revisited
(Exercises 328, 329, 330, 339, and 341 skipped for the moment).
3.4 Pistetulo xy-koordinaatistossa
Homework exercises: 349, 351, 354, 355, and 357.
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Monday 10.5.2010
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3.5 Direction Vector of a Line
Time: 08:00 - 09:30
About IB mathematics
Aims
Structure of the syllabus
Nature of core
Command terms
Contents if Topic 5: Vectors
The importance of simulations in mathematics
Lesson notes on the board.
3.5 Suoran suuntavektori
Direction vector of a line
Direction vector and gradient
Exercise: 373
Homework exercises: 374, 375, 376, 377 and 379 on page 112.
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Wednesday 12.5.2010
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3.6 Normal vector 4 Vectors in 3D
Time: 13:25 - 14:55
3.6 Suoran normaalivektori
Vector representation of normal of a line
Exercises 384 and 385 on page 118.
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Monday 17.5.2010
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4.3 Vectors in xyz-coordinate system (3D space)
Time: 08:00 - 09:30
4 Vectors in Three Dimensions
4.1 Introduction
4.2 xyz-coordinate system
4.3 Vectors in xyz-coordinate system
xyz-coordinate system. We do not consider left and right handed systems.
Orthogonal base in 3D
Length of vector in 3D
Position vector in 3D
Vector between points in 3D
Parallel vectors
Exercises 419 and 420.
Homework exercises: 425, 426, 428, 430, 431, 432, and 436 on pages 138-139.
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Wednesday 19.5.2010
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4.4 Vector between two points in 3D
Time: 13:25 - 14:55
4.4 Kahden pisteen välinen vektori
Vector connecting two points in 3D
Distance in 3D
Ball in 3D
Midpoint in 3D
Exercises 448 and 449.
Homework exercises: 450 and 452.
On pages 150-151.
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Friday 21.5.2010
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4.5 Scalar product in 3D 5 Vector representation of a line in 3D
Time: 09:50 - 11:20
4.3 Pistetulo xyz-koordinaatistossa
Exercises 468, 469 and 470 on page 156.
Line in coordinate form
Line in normal form
Exercises 501, 502 and 504 on page 169.
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Monday 24.5.2010
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Revision
Time: 08:00 - 09:30
Revision for the test.
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