M4 Basic Mathematics 2 Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2012 Semester: 2

Subject Code: 31102 Subject: Core Mathematics

2 Period/ Week/ Semester Unit: 1

Course Description:

The first half of the semester involves the study of basic knowledge of relations, the meaning of ordered pairs, Cartesian products, domain and range, graphs of relations, and inverse relations. The second topic involves trigonometry, its relation to the unit circle, and related identities.

Learning Outcome:

1. Enhance problem solving skills and logical thinking

2. Encourage independent thinking

3. Satisfy Thai requirements for M4 Mathematics

Content Topics:

1. Relations and Functions (28 periods) 1.1 Relationship and Graphs

1.1.1 Ordered Pairs

1.1.2 Cartesian Products

1.1.3 Relations

1.1.4 Domain and Range of Relations

1.1.5 Graphs of Relations

1.1.6 Inverses of Relations

1.2 Meaning of Functions

2. Unit Circle Trigonometry (12 Periods) 2.1 Trigonometry Ratios

2.2 Applications

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 (Relations) (Week 4 – End of November) 10

- 2nd Minor Test (Trigonometry) (Week 12 – End of January) 10

- Mid-Term (Relations/Functions) (Week 8 – End of December) 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 2 Course Description

Subject Teacher: A. Brian Spiegel

Matayom : 4 Academic Year: 2012 Semester: 2

Subject Code: 31203 Subject: Additional Mathematics

4 Period/ Week/ Semester Unit: 2

Course Description:

Study about Translation of Axes and all of the Conic Sections as well as Functions, Graph Theory and Matrices.

Learning Outcome:

4. Enhance problem solving skills and logical thinking

5. Encourage independent thinking

6. Satisfy Thai requirements for M4 Mathematics

Content Topics:

1. Conic Sections (22 periods)

1.1 Translation of Axes

1.2 Circles 1.3 Parabolas

1.4 Ellipses

1.5 Hyperbolas

2. Functions (18 periods) 2.1 Polynomial Functions

2.2 Composite Functions

2.3 Inverse Functions

2.4 Algebra of Functions

2.5 Applications

3. Graph Theory (20 periods) 3.1 Graphs and Definitions

3.2 Euler’s Graph

3.3 The application of Graphs

4. Matrices and Determinants (20 periods)

4.1 Matrix Operations

4.2 Matrix Properties

4.3 Determinants and Inverses

4.4 Using Matrices to solve systems of equations

4.5 Applications

Teaching & Learning Activities:

3. Classroom activities including lecture, group work and individual work. 4. Self studying at home and in the classroom 5. 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 (Conic Sections) (Week 4 – End of November) 10

- 2nd Minor Test (Functions/Graph Theory) (Week 12 – End of Dec.) 10

- Mid-Term (Functions/Conics) (Week 8 – End of December) 15

- Activities, Worksheets, Presentation, Homework 15

- Math Project (Report and Presentation) 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 4 Course Description

Instructor: A. Andrew Stanford

Matayom: 5 Academic year: 2012 Semester: 2

Code: MATH 32102 Subject: Core Mathematics 3 Credit : 1.5

3 Periods / Week / Semester

Subject Characteristic: Core Subject

Course Description

Discovering how to properly collect data, analyze and display data, and make informed decisions based on the data analysis.

Objective

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: Statistics

Types of data and data classifications. Sampling methods. Frequency tables and histograms. Frequency polygons, ogives, pareto charts, pie graphs. Mean, median and mode. Standard deviation.

Instruction Method

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 (November 28 –December 2) 10 points

Midterm (December 17 – December 21) 20 points

Second Quiz (January 23 – January 22) 10 points

Final (February 20 – February 24) 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 4 Course Description

Instructor: Ajarn James & Ajarn Stephen

Matayom 5 Academic year: 2012 Semester: 2

Code: MATH 32201 Subject: Mathematics Credit :2.0

4 periods / Week / Semester

Course Description

This course will cover the mathematics of infinite sequences and series, calculus and Linear Programming. For infinite sequences and series, we study the idea of convergence and infinite geometric series. Calculus extends this to talk about the limit of functions, difference quotients, and the limit of the difference quotients to create the derivative. Study continuity and use the derivative to sketch functions, power and sum-difference rules, instantaneous rates of change, the product and quotient rules, the chain rules, Higher order Derivatives, differentials, derivates of exponentials and logarithm. The derivative is applied to solving real world problems in Physics and economics through optimization, implicit differentiation, and related rates. Finally students study integration by interpreting it as giving the areas between a curve and x-axis. Students will learn complex numbers, graphs and absolute values of complex number, complex number as vectors, polynomial equations. 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 addition, a mathematical project will be involved.

Expected Outcome

Students should know that all infinite sequences/series converge or diverge. If they converge the the student should be able to find the limiting value using either tables, graphs, or limit laws. Students should have an intuitive idea of continuity (a function in 1 piece) as well as knowledge of its definition. Students should know the definition of derivative of a function and use it to calculate a derivative. Students should know how to take a derivative to sketch functions as well as find the relative min/max and absolute min/max. Students should be able to integrate by substitution.

Topics

1. Infinite sequences and series 1.1 Limits of sequences 1.2 Summation of series

2. Basic of calculus 2.1 Limit of functions 2.2 Limit of continuity functions 2.3 Slope of curve 2.4 Using formula to find derivative 2.5 Derivative of composite functions 2.6 Higher derivative 2.7 Application of derivative 2.8 Integral 2.9 Indefinite integral 2.10 Definite integral 2.11 Area under a curve

3. Complex number 3.1 Complex number 3.2 Graphs and absolute values of complex number 3.3 Complex number as vectors 3.4 Polynomial equations

During the Semester score : Final exam score = 80 : 20

Test 1 (December 2012) 10 points

Test 2 (February 2012) 10 points

Midterm exam (December 2012) 20 points

Activity 15 points

Math Project 10 points

Reading, Analysis thinking and Writing 5 points

Effort 10 points

Final exam (February 2012) 20 points

M.6 Additional Mathematic 5 Course Description

Instructor: Ajarn James

Matayom 5 Academic year: 2012 Semester: 2

Code: MATH33203 Subject: Mathematics Credit :2.0

4 periods / Week / Semester

Course Description:

Studying in quartile, decile and percentile, measure of data expansion, range, quartile deviation, average deviation, standard deviation, properties of the measure of data expansion, variance, measure of relative expansion, frequency curve & data expansion, normal distribution & curve, analysis of functional relation among data, scatter diagram, constant approximation by using the method of the least square, functional relation of time series data, analysis of functional relation among data, diagram and distribution, constant approximation by using the method of the least square, functional relation of time series data. Setting the experience and creating the situations for the learners to study and search by doing, demonstration, experiment, summary and report. In order to develop skill, mathematical process, ability of problem solving, reasoning, communication, mathematical communication and presentation and know how to link the knowledge and have the creative thinking, as well as realizing in the value and having the good attitude to the Mathematics subject. Training learners to work systematically have discipline & responsibility and create self-confidence. Varieties of evaluation & assessment have been used and based on the reality along to the evaluated contents and skills.

Expected Result of Learning

1. To be able to find quartile, decile and percentile of the given data 2. To be able to find range, quartile deviation, average deviation and standard deviation of the

given data 3. Utilizing the properties of the measure of data expansion to use in the given data 4. To be able to find the variance 5. Using the properties of relative expansion in the given data comparison 6. Know how to write frequency curve with the given data expansion 7. Using the standard value in data comparison 8. To be able to find area under normal curve. Understand the meaning of functional relation of

data that consisting of two variables

9. Functional relation of data is used to predict the variable value as the independent variable is given

10. Analyzing the functional relation among data 11. Constant approximation by using the method of the least square 12. Finding the functional relation of the time series data

Content Topics

1. Statistic (2) (20 periods) Quartile, decile and percentile Measure of data expansion Range Quartile deviation Average deviation Standard deviation Properties of the measure of data expansion Variance Measure of relative expansion Frequency curve and data expansion

2. Normal Distribution (30 periods) Standard value Normal distribution and normal curve

3. Statistics (3) (20 Periods) Analyzing the functional relation among data Scatter Diagram Constant approximation by using the method of the least square Functional relation of time series data

Evaluation

During Semester: Final Exam = 80: 20

1st Minor Test Thu.26th November 2012

Topic: Statistic (2) 1.1-1.7 10 points

Midterm Test Mon 16th Dec. 2012

Topic: Statistic(2) / Normal distribution 20 points

2nd Minor Test Thu. 7th Jan. 2012

Topic: Statistics (3) (3.1-3.3) 10 points

Class Activities 25 points

Mathematic activities of reading, creative thinking

and communicative writing 5 points

Student’s expected characteristic to mathematics 10 points

(Good attitude to mathematics, orderliness, systematic working,

self- responsibility and responsibility for public and self-confidence)

Final Exam Mon.15th Feb.- 2013 20 points Topic: Normal distribution

Functional relation among data

Statistics (3)