IB DP Mathematics: Analysis and Approaches (SL)

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School years: 2019 - 2021
Teacher:  Mr. John Pollard
Teacher contact:  jpollard@isb.rs
Google Classroom: www.classroom.google.com
 
I.INTRODUCTION
 
Welcome to Mathematics: Analysis and Approaches (SL). Analysis and approaches at SL is appropriate for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. They will also be fascinated by exploring real and abstract applications of these ideas, with and without the use of technology. Students who take Mathematics: Analysis and approaches will be those who enjoy the thrill of mathematical problem solving and generalization. This subject is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics for example.
 
II.CURRICULUM GOALS
 
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.
OBJECTIVES:
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.
III.COURSE CONTENT
 
Number and algebra: scientific notation, arithmetic and geometric sequences and series and their applications including financial applications, laws of logarithms and exponentials, solving exponential equations, simple proof, approximations and errors, and the binomial theorem.
 
Functions: equations of straight lines, concepts and properties of functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions. Solving equations both analytically and graphically, and transformation of graphs.
 
Geometry and trigonometry: volume and surface area of 3d solids, right-angled and non-right-angled trigonometry including bearings and angles of elevation and depression, radian measure, the unit circle and Pythagorean identity, double angle identities for sine and cosine, composite trigonometric functions, solving trigonometric equations.
 
Statistics and probability: collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation, regression, calculating probabilities, probability diagrams, the normal distribution with standardization of variables, and the binomial distribution.
Calculus: informal ideas of limits and convergence, differentiation including analysing graphical behaviour of functions, finding equations of normals and tangents, optimisation, kinematics involving displacement, velocity, acceleration and total distance travelled, the chain, product and quotient rules, definite and indefinite integration.
 
COURSE SYLLABUS DETAIL:
 
The following list summarizes the topics that will be studied during the course:
 
YEAR 1 (Grade 11)
 
YEAR 2 (Grade 12)
 
Semester 1 
●      Sequences and Series
●      Functions
●      Linear and Quadratic Functions
●      Rational Functions
●      Measuring Change - Differentiation
 
Semester 1
●      Internal Assessment
●      Integral Calculus 
●      Periodic Functions
●      Modelling Change
 
Semester 2
●      Statistics – Univariate Data
●      Statistics – Bivariate Data
●      Trigonometry
●      Exponentials and Logarithms
●      Probability
Semester 2 
●      Probability Distributions
●      Mock exam
●      Review 
●      External Exams: Papers 1 and 2 
 
 
IV. EXPECTATIONS:
 
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. 10% will be deducted from the grade of any work submitted after the due date. Work submitted substantially late will have a percentage deducted in accordance with the period of delay. 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.
V. ASSESSMENT
 
Mathematics: Analysis and approaches SL assessment:
 
External assessment
Mathematics: Analysis and approaches SL will be assessed with two written papers. Each paper will consist of a section A (short questions) and a section B (long questions). Paper 1 will be without the use technology and paper 2 will allow the use of a graphical calculator.
 
Internal assessment (IA – 20%) 
The internal assessment task will be the same for both HL and SL and will be based on a piece of research which interests the student and models the type of mathematical activity undertaken in the modern world.
 
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 homework 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.  ISB recommends using the TI-84 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.
 
VI. ISB GRADING POLICY:
 
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
 
 
Homework Assignments will 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 jpollard@isb.rsto arrange a meeting time or discuss questions or concerns.

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