M4 Basic Mathematics 1 Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2012 Semester: 1

Subject Code: MATH 31101 Subject: Basic Mathematics 1

2 Periods/ Week/ Semester Credit: 1.0

Course Description:

Studying, practicing calculation skill, and practicing solving problem dealing with set theory, real number theory, and mathematical reasoning.

Learning Outcome:

1. Enhance problem solving skills and logical thinking

2. Encourage independent thinking

3. Satisfy Thai requirements for M4 Mathematics

Content Topics:

1. Sets 1.1 Set Writing 1.2 Set Operations 1.3 Diagrams & Problem Solving 2. Real Numbers 2.1 Types of Real Numbers 2.2 Properties of Real Numbers

2.3 Polynomial Factorization

2.4 Single Variable of Equalities & Inequalities with degrees not higher than 2 2.5 Basic Absolute Values 3. Reasoning & Argument 3.1 Proof by Induction 3.2 Proof by Deductions 3.3 Arguments 4. Rational Number Exponents

Teaching & Learning Activities:

1. Classroom activities including lecture, group work and individual work. 2. Self studying at home and in the classroom

Evaluation & Assessment:

During Semester: Final Exam = 80: 20

During Semester = 80 Final Exams = 20 - 1st Minor Test (Set Theory) (Week 4 – End of June) 10

- 2nd Minor Test (Real Numbers) (Week 12 – End of August) 10

- Mid-Term (Set Theory and Real Number Intro) (Week 8 – End of July) 20

- Activities, Worksheets, Presentation, Homework 25 - Analytical Reading & Critical Thinking 5 - Characteristics, Enthusiasm, Creativity, Responsibility, Self-confidence 10 - Final Exam (All topics) (End of Semester) 20

M4 Additional Mathematics 1 Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2012 Semester: 1

Subject Code: MATH 31201 Subject: Additional Mathematics 1

4 Periods/ Week/ Semester Credit: 2

Course Description:

Studying, practicing calculation skill, and practicing solving problem dealing with set theory, real number theory, and mathematical reasoning.

Learning Outcome:

1. Enhance problem solving skills and logical thinking

2. Encourage independent thinking

3. Satisfy Thai requirements for M4 Mathematics

Content Topics:

1. Introduction to Analytic/Coordinate Geometry (20 periods) 1 Projections 2 Distance Formula 3 Midpoint Formula 4 Application 1 5 Slopes 6 Parallel lines 7 Perpendicular lines 8 Line formulas 9 Distances between Line and Point

10 Application 2

2. Introduction to Logic (18 periods) 1 Propositions 2 Conjunctive Propositions 3 Truth-Value Tables 4 Finding Truth-Value of Propositions 5 Equivalent Propositions 6 Tautologies 7 Open Sentences 8 Quantifiers 9 Truth-Values of Sentences which have Single Variable Quantifiers 10 Equivalences & Negations 11 Arguments

3. Real Number System (28 periods) 1 Real Numbers 2 Equality, Addition, Subtraction, Multiplication and Division 3 Property of Real Numbers 4 Solving Polynomial Equations which have Single Variables 5 Property of Inequalities 6 Interval & Equation Solving 7 Absolute Values 8 Solving Equations & Inequalities with Absolute Value

4. Introduction to Theory of Numbers (14 periods) 1 Properties of Integers 2 Applications of Integer Properties

Teaching & Learning Activities:

1. Classroom activities including lecture, group work and individual work. 2. Self studying at home and in the classroom 3. Group Math Projects encompassing the entire school year.

Evaluation & Assessment:

During Semester: Final Exam = 80: 20

During Semester = 80 Final Exams = 20 - 1st Minor Test (Analytical Geometry) (Week 4 – End of June) 10

- 2nd Minor Test (Real Number System) (Week 12 – End of August) 10

- Mid-Term (Analytical Geometry and Logic) (Week 8 – End of July) 15

- Activities, Worksheets, Presentation, Homework 15

- Math Project (Proposal – Week 4) (Completed Report – Week 16) 15 - Analytical Reading & Critical Thinking 5 - Characteristics, Enthusiasm, Creativity, Responsibility, Self-confidence 10 - Final Exam (All topics) (End of Semester) 20

M.5 Basic Mathematics 3 Course Description

Subject Teacher: Andrew Stanford

Matayom: 5 Academic year: 2012 Semester: 1

Code: MATH 32101 Subject: Basic Mathematics 3

3 Periods / Week /Semester Credit : 1.5

Course Description

Exploring properties and relationships, performing calculations, and application of various problem solving methods with regards to factoring polynomials, solving quadratic equations, graphing parabolas, and trigonometry.

Learning Outcomes

1. To gain an understanding of how mathematics is an integral part of all aspects of life.

2. To further develop calculating skills and problem solving strategies.

3. To build a strong mathematical background which can be utilized in future mathematics and science courses.

4. To encourage the application of mathematical concepts and a logical thought process to situations encountered in daily life.

Course Content

Unit 1: Finite Sequences and Series

General term of a sequence Finite arithmetic sequences Finite geometric sequences Finite arithmetic series Finite geometric series

Unit 2: Counting Techniques

The Multiplication Principle Permutations Combinations The Binomial Theorem

Unit 3: Probability

Basic counting principles Probability of mutually exclusive events Probability of independent events Conditional probability Computing odds

Teaching & Learning Activities

1. Lecture and demonstrations of concepts, definitions, properties, and problem solving methods.

2. In class worksheets and group work with an emphasis on student participation.

3. Interactive on-line lessons and virtual manipulatives.

4. Assignments and projects for practicing and applying the concepts and skills learned during class.

Measurement and Evaluation

First Quiz (July 1 2012) 10 points

Midterm (July 29 2012) 20 points

Second Quiz (August 26 2012) 10 points

Final (September 23 2012) 20 points

Activities (classwork, assignments, etc.) 25 points

Effort 10 points

Reading, Analysis, Thinking, and Writing 5 points

Total 100 points

M.5 Additional Mathematic 3 Course Description

Subject Teacher: Ajarn James Sayer

Matayom: 5 Academic Year: 2012 Semester: 1

Subject Code: 32201 Subject: Additional Mathematics 3

4 Period/ Week/ Semester Credit:2.0

Course Description:

This course will cover the mathematics of: exponential functions, logarithms, trigonometric functions of real numbers and angles, roots of polynomials, and complex numbers. We will study the basic mathematical principles in each area and practice calculations important to each of these areas. Solving problems and giving reasons along the way is more important than a correct answer which is unsupported or poorly explained. In this way we hope to understand the subject content, learn mathematical methodology, and build strong calculation skills.

Learning Outcome:

1. To understand the mathematical principles of each topic and to be able to give a reasonable opinion.

2. To develop strong skills in calculating and apply them to problem solving. 3. To create a strong foundation for higher learning in mathematics.

Content Topics:

Exponential functions, logarithmic functions, common logarithms, approximate computation using logarithms, logarithms to different bases, exponential and logarithmic equations. Trig functions of sum and difference of real numbers or angles, inverse trig functions, Law of Sine, Law of Cosine, distance and height. Finding roots of polynomials using the Rational Root Theorem and other results. Linear Programming, graphs and equation solving, linear inequalities.

1. Probability (40 periods) 1.1 Basic rules of counting 1.2 Permutation

1.3 Combination 1.4 Binomial Theorem 1.5Probability & some key rules of probability

2. Basic Data Analysis (20 periods) 2.1 Central value of data 2.2 Position measure of data 2.3 Expansion measure of data

3. Three dimensional vector (20 periods) 3.1 Vector 3.2 Vector addition 3.3 Vector subtraction 3.4 Vector multiplication by scalar 3.5 Scalar product 3.6 Vector product Teaching & Learning Activities:

1. Multimedia Presentations 2. Project environments 3. Web 2.0 4. Students centered learning activities 5. In class worksheets and group work with an emphasis on student participation. 6. Interactive online lessons and virtual manipulatives. 7. Assignments and projects for practicing and applying the concepts and skills learned during

class. Evaluation & Assessment:

During semester: Final Exam = 80 : 20

Quiz During semester - 1st Quiz (Mon 2 July 2012) 10 points

Exponential Functions

- 2nd Quiz (Mon. 27 August 2012) 10 points Linear Programming

Midterm Test (Mon.23- 27 July 2012) 20 points

Exponential Functions / Trigonometry

Class Activities 25 points

Student’s expected characteristics to Math study 10 points

(Good attitude to mathematic, orderliness, systematic working, self-responsibility and for public, self-confidence)

Activities of reading, analytic thinking and writing in mathematical communication

5 points

Final Exam (Mon 17 September 2012) 20 points

Exponential Functions / Trigonometry / Linear Programming

References:

PreCalculus - Sullivan

M.6 Additional Mathematic 5 Course Description

Subject Teacher: Ajarn James Sayer

Matayom: 6 Academic Year:2012 Semester: 1

Subject Code: 33201 Subject: Additional Mathematics 5

4 Periods/ Week/ Semester Credit: 2

Course Description:

Skills of calculation, reasoning and practice to solve the problems of permutations & combinations, basic rules of counting, factorials, Binomial Theorem, basic theorem of probability, sampling & sample spaces, probability events, some key rules of probability. Basic methods for data analysis and explain the outcomes of data analysis, apply analysis. Concepts of three dimensional vectors and vector addition, vector product, scalar product, including size & direction of given vectors. Problem solving that is relevant to the learners, demonstrations, experiments, discussions, summary and report, so that students can develop skills, mathematical processes, problem solving ability, reasoning, communication, mathematical communication. To practice working systematically and with disciplined work habits.

Learning Outcome:

1. To solve the problem by using basic rules of counting, permutation and combination 2. To be able to apply the binomial theorem 3. To choose the basic methods of data analysis and explain the outcome of data analysis

rightly. 4. To be able to apply the data analysis to use 5. Having the concept of three dimensional vector 6. To be able to find the vector addition, vector product by scalar, scalar product and vector

product 7. To be able to find size & direction of the given vector

Content Topics:

1. Probability (40 periods) 1.1 Basic rules of counting 1.2 Permutation 1.3 Combination

1.4 Binomial Theorem 1.5Probability & some key rules of probability

2. Basic Data Analysis (20 periods) 2.1 Central value of data 2.2 Position measure of data 2.3 Expansion measure of data

3. Three dimensional vector (20 periods) 3.1 Vector 3.2 Vector addition 3.3 Vector subtraction 3.4 Vector multiplication by scalar 3.5 Scalar product 3.6 Vector product

Teaching & Learning Activities:

1. Multimedia Presentations 2. Interactive computer based learning 3. Project environments 4. Web 2.0 5. Students centered learning activities

Evaluation & Assessment:

During semester: Final Exam = 80 : 20

Quiz During semester - 1st Quiz (Mon 2 July 2012) 10 points

Topics of Probability (1.1 – 1.4)

- 2nd Quiz (Mon. 27 August 2012) 10 points Topic of Three dimensional vector (3.1-3.3)

Midterm Test (Mon.23- 27 July 2012) 20 points

Topics of Probability / Basic Data Analysis

Class Activities 25 points

Student’s expected characteristics to Math study 10 points

(Good attitude to mathematic, orderliness, systematic working, self-responsibility and for public, self-confidence)

Activities of reading, analytic thinking and writing in mathematical communication

5 points

Final Exam (Mon 17 September 2012) 20 points

Topic of Probability/ Basic data analysis/ Three dimensional vectors

References:

Elementary Statistics – Triola

Counting and Probability – David Patrick