Course: Mathematics, Higher Level (HL)

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Longview High School International Baccalaureate Diploma Programme 2010 20 Course Syllabus

1 Longview High School International Baccalaureate Diploma Programme Course Syllabus for Year 1 Student: Grade: Course: Mathematics, Higher Level (HL) Teacher: Larry Cunningham

2 Longview High School International Baccalaureate Diploma Programme Course Syllabus Form Return to Mrs. Spearman by Friday, September 3, 2010 Name: ID Number: Grade: Course: Mathematics Higher Level Teacher: Mr. Cunningham As the student completes this course, the following learner characteristics will be developed: Standards of academic integrity as outlined in the International Baccalaureate Academic Honesty publication: - Personal integrity - Misuse of intellectual property - Authenticity of student work - Understanding of collaboration as working together on a common aim with shared information and does not result in allowing one s work to be copied Respect for classmates Respect for teacher Respect for the classroom environment Respect for the classroom equipment Promptness Preparation Ability to have needed materials on hand Ability to meet deadlines As the teacher leads this course, the following will be developed: Student and teacher as a learning team Climate of caring Climate of support for the student as a learner Help available whenever requested by the student (Students should request help immediately. The teacher will be delighted to provide any support and help necessary.) When major* assignments are graded using an IB rubric, the following conversion will be used: IB Mark Percentage Grade Assignment will be resubmitted by student. *Major assignments graded by IB rubrics will be designated by the teacher. These are not daily grades. I have received and read the IB course syllabus for the course My student has received and read the IB course syllabus shown above. I understand the course requirements and agree to comply by for the course shown above. I have also read the syllabus. I the contents of the syllabus. understand the course requirements and agree to comply by the contents of the syllabus. Last printed 2/25/20 :39:00 AM Page 2 of

3 Student Signature Date Parent Signature Date Last printed 2/25/20 :39:00 AM Page 3 of

4 Longview High School International Baccalaureate Diploma Programme Course Syllabus for Year 1 Student: Grade: Course: Mathematics Standard Level Teacher: Larry Cunningham Course Description: The HL Mathematics Course is a demanding one and is for students with a good background in mathematics who are competent in a range of analytical and technical skills. The majority of these students will be expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology. Others may take this subject because they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems. The nature of the subject is such that it focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way. This is achieved by means of a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solving problems set in a variety of meaningful contexts. Development of each topic should feature justification and proof of results. Students embarking on this course should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. They should also be encouraged to develop the skills needed to continue their mathematical growth in other learning environments. The internally assessed component, the portfolio, offers students a framework for developing independence in their mathematical learning through engaging in mathematical investigation and mathematical modeling. Students will be provided with opportunities to take a considered approach to these activities, and to explore different ways of approaching a problem. The portfolio also allows students to work without the time constraints of a written examination and to develop skills in communicating mathematical ideas. (Adapted from IBO Course Guide, HL Mathematics) Course Topics: Course Outcomes: Students in the Mathematics HL Year 1 Class will study functions and the algebra related to them. There will be detailed study of rational, quadratic, exponential, logarithmic, and absolute value functions. Students will study trigonometric functions, including the unit circle and radian measure. Students will also study arithmetic and geometric sequences and series, the binomial expansion, matrices, and vectors in both 2 and 3 dimensions. Included in the course will be basic counting principles, permutations, and combinations. Having followed any one of the mathematics courses in group 5, students are expected to know and use mathematical concepts and principles. In particular, students must be able to: read, interpret and solve a given problem using appropriate mathematical terms organize and present information and data in tabular, graphical and/or diagrammatic forms know and use appropriate notation and terminology formulate a mathematical argument and communicate it clearly select and use appropriate mathematical strategies and techniques demonstrate an understanding of both the significance and the reasonableness of results Last printed 2/25/20 :39:00 AM Page 4 of

5 Course Assessment: recognize patterns and structures in a variety of situations, and make generalizations recognize and demonstrate an understanding of the practical applications of mathematics use appropriate technological devices as mathematical tools demonstrate an understanding of and the appropriate use of mathematical modeling. (from International Baccalaureate Organization Course Guide, HL Mathematics) IB Assessment: Internal assessment 20% Portfolio A collection of two pieces of work assigned by the teacher and completed by the student during the course. The pieces of work must be based on different areas of the syllabus and represent the two types of tasks: mathematical investigation mathematical modeling. The portfolio is internally assessed by the teacher and externally moderated by the IBO. This assessment will be practiced during year one and will be assessed in year two. External assessment 5 hrs 80% Written papers Paper 1 2 hrs 30% No calculator allowed Section A 15% Compulsory short-response questions based on the compulsory core of the syllabus Section B 15% Compulsory extended-response questions based on the compulsory core of the syllabus Paper 2 2 hrs 30% Graphic display calculator (GDC) required Section A 15% Compulsory short-response questions based on the compulsory core of the syllabus Section B 15% Compulsory extended-response questions based on the compulsory core of the syllabus Paper 3 1 hr 20% Graphic display calculator (GDC) required Extended-response questions based mainly on the syllabus options Throughout the course there will be an emphasis on IB strategies and IB marking schemes. Grades may include quizzes, tests, homework, projects, research and presentations. The course will be designed so that students will have the best opportunity to be successful on the IB exam. Last printed 2/25/20 :39:00 AM Page 5 of

6 Course Resources: Teaching Time: Mathematics for the International Student, Mathematics HL (Core), Second Edition Haese and Harris Publications 2009 Mathematics for the International Student, Mathematics HL (Options), Second Edition Haese and Harris Publications 2009 Year One 150 hours There are many factors that may influence this outline. It is a dynamic document and could change. Last printed 2/25/20 :39:00 AM Page 6 of

7 Major Assignments: Assignment Description Deadline Mathematical Investigation Practice Investigation Final product for IB External Moderation will come in year 2 Mathematical Modeling Practice Modeling Project Final product for IB External Moderation will come in year 2 December, 2010 March, 20 Course Outline: Week Dates: Summary: Readings Assignments /23/2010 8/27/2010 8/30/2010 9/3/2010 9/7/2010 9/20/ /13/2010 9/17/2010 Class Syllabus Class Structure Assumed Knowledge Pretest Chapter 1 Relations and Functions Relations, Functions, and Function Notation Domain and Range Composite Functions Relations and Functions (cont) Composite Functions Sign Charts Rational functions Inverse Functions Chapter 2 Sequences and Series Number Patterns Chapter 1 Test (Functions and Relations) Sequences and Series Number Patterns Sequences of Numbers Arithmetic Sequences Geometric Sequences Series Relations, Functions, and Function Notation Domain and Range Last printed 2/25/20 :39:00 AM Page 7 of

8 5 6 9/20/2010 9/24/2010 9/27/ /1/ /4/ /8/ // /15/2010 Chapter 2 Test (Sequences and Series) Chapter 3 Exponents Exponential Notation Evaluating Powers Laws of Exponents Rational Exponents Expansion and Factoring Exponential Equations and Graphs First Six Weeks Test (cumulative) First Six Weeks Ends Second Six Weeks Begins Growth and Decay The Natural e Chapter 3 Test (Exponents) Chapter 4 Logarithms Base Ten Logarithms Laws of Logarithms Natural Logarithms 9 10/18/ /22/2010 Exponential Equations and Logarithms Change of Base Rule Graphs of Logarithmic Functions Growth and Decay 10 10/25/ /29/2010 Chapter 4 Test (Logarithms) Chapter 5 Graphing and Transforming Functions Families of Functions Transforming Graphs Chapter 6 Quadratic Functions Quadratic Equations The Discriminant Last printed 2/25/20 :39:00 AM Page 8 of

9 12 13 /1/2010 /5/2010 /8/2010 /12/2010 /15/2010 /19/2010 Second Six Weeks Test (cumulative) Quadratic Functions Graphs of Quadratic Functions Finding a Quadratic Function from its Graph Second Six Weeks Ends Third Six Weeks Begins Quadratic Functions Where Functions Meet Quadratic Problem Solving Optimization Chapter 5 (Graphing and Transforming Functions) and Chapter 6 (Quadratic Functions) Test Chapter 7 The Binomial Expansion Binomial Expansions The Binomial Theorem 14 /29/ /3/ /6/ /10/ /13/ /17/ /4/20 1/7/20 Chapter 7 Test (The Binomial Expansion) Mathematical Investigation Mathematical Investigation Third Six Weeks Test (cumulative) Semester Review Mathematical Investigation Due Semester Review Semester Exam Chapter 8 The Unit Circle and Radian Measure Radian Measure Arc length and Sector Area Last printed 2/25/20 :39:00 AM Page 9 of

10 18 1/10/20 1/14/ /18/20 1/21/20 1/24/20 1/28/20 1/31/20 2/4/20 2/7/20 2//20 2/14/20 2/18/20 2/21/20 2/25/20 2/28/ /4/20 The unit circle and basic trigonometric ratios the equation of a line Chapter 8 Test (The Unit Circle and Radian Measure) Chapter 9 Non-Right Angled Trigonometric Geometry Areas of Triangles Law of cosines Law of sines Using the laws of sines and cosines Chapter 9 Test (Non Right Angled Trigonometric Geometry) Chapter 10 Advanced Trigonometry Observing periodic behavior The sine function Modeling using sine functions The cosine function The tangent function general trigonometric functions trigonometric equations using trigonometric models trigonometric relationships Fourth Six Weeks Test (cumulative) Fourth Six Weeks Ends double angle formulae trigonometric equations in quadratic form Chapter 10 Test (Advanced Trigonometry) Mathematical Modeling Project Mathematical Modeling ProjectDue Last printed 2/25/20 :39:00 AM Page 10 of

11 /7/20 3//20 3/21/20 3/25/20 3/28/20 4/1/20 4/4/20 4/8/20 4//20 4/15/20 4/18/20 4/21/ /25/20 4/29/20 Chapter Matrices Matrix Structure Matrix operations and definitions Inverse of a 2 x 2 matrix 3 x 3 matrices Solving systems of linear equations Chapter Test (Matrices) Chapter 12 Vectors in 2 and 3 dimensions Introduction Geometric operations with vectors 2-D vectors in component form 3-D coordinate geometry 3-D vectors in component form Algebraic operations with vectors Parallelism Unit vectors Fifth Six Weeks Test (cumulative) Fifth Six Weeks Ends Scalar product of two vectors Relationships between lines Chapter 12 Test (Vectors in 2 and 3 Dimensions) TAKS Testing Week 33 5/2/20 5/6/20 Chapter 13 Lines and Planes in Space Lines in 2-D and 3-D Applications of a line in space Last printed 2/25/20 :39:00 AM Page of

12 34 5/9/20 5/13/ /16/20 5/20/ /23/20 5/27/20 5/31/ /2/20 Chapter 13 Test (Lines and Planes in Space) Sixth Six Weeks Test (cumulative) The Absolute Value Function Counting Principles, including Permutations and Combinations Counting Principles, including Permutations and Combinations Semester Exam Notes: Last printed 2/25/20 :39:00 AM Page 12 of 12

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.