IB DP Mathematics: Analysis and Approaches (HL)

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School years: 2019 - 2021
Teacher:  Mr. Aaron Stewart
Teacher contact:  astewart@isb.rs
Google Classroom: Google Classroom
Welcome to Mathematics: Analysis and Approaches HL. This is a demanding two year course that covers the equivalent of at least two semesters of college level mathematics.  Math HL caters 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.
AIMS (as described by the IB Group 5 subject guide)
The aims of all mathematics courses in group 5 are to enable students to:
  1. enjoy mathematics, and develop an appreciation of the elegance and power of mathematics
  2. develop an understanding of the principles and nature of mathematics
  3. communicate clearly and confidently in a variety of contexts
  4. develop logical, critical and creative thinking, and patience and persistence in problem-solving
  5. employ and refine their powers of abstraction and generalization
  6. apply and transfer skills to alternative situations, to other areas of knowledge and to future developments
  7. appreciate how developments in technology and mathematics have influenced each other
  8. appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics
  9. appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives 
  10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.
Problem-solving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP mathematics HL course, students will be expected to demonstrate the following:
  1. Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.
  2. Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.
  3. Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation.
  4. Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.
  5. Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.
  6. Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analyzing information, making conjectures, drawing conclusions and testing their validity.
This Math HL course 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 solve problems set in a variety of meaningful contexts. Development of each topic features 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 will also be encouraged to develop the skills needed to continue their mathematical growth in other learning environments.
This course is a demanding one, requiring students to study a broad range of mathematical topics through a number of different approaches and to varying degrees of depth. Students wishing to study mathematics in a less rigorous environment should therefore opt for one of the standard level courses.
The following list summarizes the topics that will be studied during the course:
YEAR 1  (Grade 11)
YEAR 2 (Grade 12)
Semester 1 
●      Review of prerequisite knowledge
●      Functions
●      Sequences and Series
●      Proof by Induction
●      Trigonometry
Semester 1
●      Review of Year 1
●      Integral Calculus 
●      Complete Internal Assessment
●      Further Calculus
Semester 2
●      Complex Numbers
●      Probability and Statistics
●      Vectors
●      Differential Calculus
●      Internal Assessment
Semester 2 
●      Further Proof
●      Mock exam
●      Review 
●      External Exams, Papers 1, 2, and 3 
What to expect from the teacher:
  1. Pace & pattern: Expect to move through the year’s content following the cycle schedule.
  2. In-class work: Expect to use class time efficiently and productively.
  3. Homework and practice: Expect to have daily homework assignments. When homework is not assigned you should take the initiative to review on your own by doing exercises from the textbook.
What is expected from the student:
  1. Bring the materials necessary for math class each class.  These include your textbook, writing materials, and your graphing calculator.
  2. Arrive on time and participate actively in class, including taking notes and trying practice questions.  All tardies or absences will be noted.
  3. Keep up with assigned work, take notes and meet deadlines.  If a student is absent, the assignment must be turned in on the first day back to receive full credit.  The idea behind this is that students are responsible to check with their teacher to make up missed work.
  4. Follow directions and listen respectfully to others.
  5. Autonomous learning: To become or continue being a proactive self-motivated learner.
  6. Seek assistance when needed.
There are two types of assessments that will be prepared for and completed over the duration of the two-year course:  1. External assessment (prepared for throughout the two-year course and completed/examined in May, 2021) and 2.  Internal assessment (worked on at the end of year one and completed in year two).

External assessment, 5 hours, 80% of DP HL Math grade

Paper 1, 2 hours, no calculator allowed, 110 marks, 30% of DP HL Math grade

This paper does not allow the use of calculator. Problems are designed in a way that checks understanding of concepts without excessive calculations. 
Section A, Compulsory short-response questions based on the syllabus.
Section B, Compulsory extended-response questions based on the syllabus.

Paper 2, 2 hours, Graphic display calculator required, 110 marks, 30% of DP HL Math grade

This paper requires the use of the calculator, and the problems are lengthy, difficult or impossible to solve without a GDC. 
Section A, Compulsory short-response questions based on the syllabus.
Section B, Compulsory extended-response questions based on the syllabus.

Paper 3, 1 hour, Graphic display calculator required, 55 marks, 20% of DP HL Math grade

This paper requires the use of the calculator and consists of two compulsory extended response problem-solving questions.

Internal assessment, Mathematical exploration, 20 marks, 20% of DP HL Math grade

This component is internally assessed by the teacher and externally moderated by the IB at the end of the course.  Internal assessment in mathematics HL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. 
The Internal assessment exploration, offers students the opportunity for developing independence in their mathematical learning. Students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas. The exploration also allows students to work without the time constraints of a written examination and to develop the skills they need for communicating mathematical ideas.
Academic honesty: 
Have in mind that plagiarism will lead to serious consequences. Distinguish between correct paraphrasing, direct quotation, and citation formats. Any notebooks or hoework that looks too similar will also face serious penalties. For more information, please see the ISB Assessment and Academic honesty policy document.
Use of calculators:
Students are expected to have access to a graphic display calculator (GDC) at all times during the course. During the external exams you are required to have them for Papers 2 and 3.  ISB recommends using the TI-84 plus, but other graphic display calculators are acceptable so long as you know how to use it or learn to use it by reading its accompanying directions.
Students will be evaluated based on performance on tests, quizzes and projects. A student’s quarter average with be calculated by dividing the total number of points scored by the total amount of points assigned in the quarter.  
Year 1:
Final grades in Semesters 1 and 2during the Year 1will be scored:
-      40%  quarter 1 
-      40%  quarter 2
-      20%  semester exam
           Year 2: 
            Final grade in Semester 1will be scored:
-      40% quarter 1
-      40% quarter 2
-      20% semester exam
Final grade in Semester 2 will be scored:
-      80% Quarter 3
-      20% overall mock grade
Assignmentswill be given daily and will be checked for completeness and accuracy.  Expect a significant amount of out of class time required to complete assignments.
Quizzes, Tests, and Examswill assess concepts of the course and include past DP Math questions or questions modeled on past DP questions.  Tests will also be timed according to IBDP guidelines.  For these reasons, tests will be marked with a 1 to 7 grade based on approximate grade boundaries from the IBDP.  Grade boundaries are calculated using percentage of correct marks.
Internal Assessmentis internally assessed by the teacher and externally moderated by the IB at the end of the course.  Internal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. It will be given points according to the IBDP rubrics.  These grades will then be converted into a 1 to 7 score based on approximate grade boundaries from the IB.
Contact Information: 
I am here to help you achieve success.  Please ask for help when you feel you may need it.  I am happy to meet with you outside of class time during the school day. Please contact me at the school or by email at astewart@isb.rsto arrange a meeting time or discuss questions or concerns.