M4 Core Maths Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2013 Semester: 1

Subject Code: 31101 Subject: Core Maths

2 Period/ Week/ Semester Unit: 1

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. Real Number 1.1 Types of Real Numbers 1.2 Properties of Real Numbers 1.3 Polynomial Factorization

1.4 Single Variable of Equalities & Inequalities with degrees not higher than 2 1.5 Basic Absolute Value 2. Sets

2.1 Set Writing 2.2 Set Operations 2.3 Diagrams & Problem Solving 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 (Real Numbers) (Week 4 – End of June) 10

- 2nd Minor Test (Set Theory) (Week 12 – End of August) 10

- Mid-Term (Real Numbers/Set Theory) (Week 8 – End of July) 15

- Activities, Worksheets, Presentation, Homework 35 - 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: 2013 Semester: 1

Subject Code: 31201 Subject: Additional Mathematics 1

4 Period/ Week/ Semester Unit: 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

M4 Additional Mathematics 2A Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2013 Semester: 1

Subject Code: 31205 Subject: Additional Math 2A

2 Period/ Week/ Semester Unit: 1

Course Description:

This class is intended as a tutorial class for students taking the Math/English track only.

Studying, practicing calculation skill, and practicing solving problem dealing with all of the topics covered in both M4 Core and Additional Math classes.

Learning Outcome:

4. Enhance problem solving skills and logical thinking

5. Encourage independent thinking

6. Satisfy Thai requirements for M4 Mathematics 4. Provide additional time to work on math projects. 5. Provide extra exercises to strengthen math skills where needed.

Teaching & Learning Activities:

1. Classroom activities including lecture, group work and individual work. 2. Extra exercises from both texts and other sources. 3. Self studying at home and in the classroom

Evaluation & Assessment:

There are no set exams for this tutorial course. The grade is determined at the discretion of the instructor. It will be based upon homework, class work, activities, quizzes and tests.

M.5 Basic Mathematics 3 Course Description

Subject Teacher: Andrew Stanford

Matayom: 5 Academic year: 2013 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 2013) 10 points

Midterm (July 29 2013) 20 points

Second Quiz (August 26 2013) 10 points

Final (September 23 2013) 20 points

Activities (classwork, assignments, etc.) 25 points

Effort 10 points

Reading, Analysis, Thinking, and Writing 5 points

Total 100 points

Course Syllabus

Subject Teacher: James Sayer & Stephen Pattenden

Matayom : 5 Academic year: 2013 Semester: 1

Code: MATH 32201 Subject: Additional Math 3 4 Periods / Week Units: 2

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 calculational 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

Trigonometric functions of sum and difference of real numbers or angles

Inverse trig functions

Law of Sine

Law of Cosine

Triangle Areas

Linear Programming

Teaching and Learning Activities:

1. Lecturing 2. Problem solving 3. Challenge Based Learning 4. Project Based Learning

Evaluation and Assessment:

During the Semester: Final Exam 80: 20

Quiz during semester: - Quiz1: (24/06/2013)

Topic: Exponential Functions 10 points

Quiz2: (26/08/2013)

Topic: Analytic Trigonometry . 10 points

Midterm Test: (July)

Topic: Exponential Functions and Analytic Trigonometry 20 points

Class Activities: 5 Points

Project: 10 Points

- Submit project proposal - Submit project outline - Submit complete project 10 points

Activities of Reading, Analyzed Thinking and Writing on Mathematics5 points

Student’s expected characteristics for Mathematics 10 points

(Attitude/ organized / systematic working/ responsibility/ confidence and effort)

Final Exam (September)

Topic: Exponential Functions and Analytic Trigonometry and Linear Programming 20 points

Reference

Pre-Calculus – Sullivan

Course Syllabus

Subject Teacher: Ajarn James Sayer

Matayom: 6 Academic year: 2013 Semester: 1

Code: MATH 33201 Subject: Additional Mathematics 5

Units 2 4 periods / Week / Semester

Course Description:

Studying skill of calculation and reasoning and practicing to solve the problem of permutation & combination, basic rules of enumeration, factorial, binomial theorem, and basic theorems of probability, including random experiment & sample space, probability events and some significant rules of probability. Choosing the method of basic data analysis and explaining the result of data analysis. To utilize the knowledge of data analysis and be able to get the concept of space vector and knowing how to find vector sum, vector product by scalar, scalar product and vector product. Finding size and direction of given vector by setting the experience or creating the situation that being close to the learners, so that they can study, search and practice by reality, demonstration, experiment, discuss, conclusion, reporting. In order to develop skill, mathematic process, the ability of problem solving, reasoning, communication, mathematic communication & presentation, knowledge combination and creative thinking, including realizing on the value and having good attitude to mathematic subject. Learning how to work systematically, orderly, responsible, considerably and creating self-confidence The various methods has been used for evaluation, which base on the situation and reality in accordance with the content and skill that being evaluated.

Objectives:

1. To develop a deeper understanding of mathematics and its importance in all aspects of life.

2. To further one’s ability to think rationally and present opinions in an ordered and logical manner.

3. To improve personal calculating skills.

4. To appreciate the usefulness of mathematics in daily life and to make use of mathematics in one’s quest for knowledge.

Result of expected learning

1. Solving the problem by using basic rules of enumeration, permutation and combination

2. Being able to utilize binomial theorem to use 3. Choosing the method of basic data analysis and explaining the result of data analysis

rightly 4. To be able to utilize the data analysis to use 5. Getting the concept of space vector 6. Being able to find vector sum, vector product by scalar, scalar product and vector

product 7. Being able to find size and direction of the given vector

Content Topics:

1. Probability (40 periods) 1.1. Basic rules of enumeration 1.2. Permutation 1.3. Combination 1.4. Binomial Theorem 1.5. Probability & some significant rules of probability

2. Basic data analysis (20 periods) 2.1. Central value of data 2.2. Measuring the position of data 2.3. Measuring the expansion of data

3. Space Vector (20 periods)

3.1 Vector 3.2 Vector addition 3.3 Vector subtraction 3.4 Vector scalar multiplication 3.5 Scalar product 3.6 Vector product

Instruction Method:

1. Lecture and demonstration methods with student participation wherever possible. 2. Use of work sheets, multi-media and overhead projector where and when deemed

appropriate and beneficial. 3. Interactive computer tutorials both at home and at school. 4. Homework’s aimed at enhancing skills in comprehension and problem solving.

Evaluation:

During semester: Final test 80: 20

During semester: 1.The first minor test Topics in Probability (1.1-1.4) 10 points

2. The second minor test

Topics of vectors (3.1-3.3) 10 points

Midterm Test: Probability / Basic Data Analysis 20 points

Class activities 25 points

Students expected characteristics to Math study 10 points

Reading activity, analytic thinking & writing for

Mathematic communication 5 points

Final Test: Probability / data Analysis / Vectors 20 points

References

Elementary Statistics - Triola

Finite Mathematics – An Applied Approach – Sullivan/Mizrahi

Discrete Mathematics – 4th Ed – McGraw Hill