Appendix 3 IB Diploma Programme Course Outlines

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1 Appendix 3 IB Diploma Programme Course Outlines The following points should be addressed when preparing course outlines for each IB Diploma Programme subject to be taught. Please be sure to use IBO nomenclature throughout. Name of the course: For example, English A1, HL. Math HL Course description: In two to three paragraphs, describe the course in terms of focus, purpose, aims and objectives, the inclusion of internationalism, the proposed process, and expected assessment. This should be a summary. Description Higher Level Mathematics is a demanding course designed for students who plan to use mathematics as a part of their future studies. The important concepts of rigor and proof are central to this course. Eight compulsory topics are included: Number and Algebra; Functions and Equations; Circular Functions and Trigonometry; Vector Geometry; Matrices and Transformations; Statistics; Probability; and Calculus. The additional topics where one is chosen will be Series and Differential Equations. IB Mathematics Higher Level: The highest level of IB math, this 2-year course is designed for advanced students who are capable of a more rigorous course at an accelerated pace. The course emphasize a multi-representational approach to higher level mathematics, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Higher Level is intended not only to extend students' knowledge of function characteristics but also to introduce them to other modes of mathematical reasoning. Students enrolled in Higher Level are assumed to have mastered algebra, geometry, and pre-calculus. Internationalism Students will learn to appreciate the plethora of historical and cultural perspectives of mathematics by delving into the following: Differences and similarities in worldwide notation Historical impact of mathematicians Mathematics as a universal language Integrated, worldly approach to material taught. Teaching Time Classes meet on an alternating A/B block rotation for 90 minutes every other day. A two year approximation of instructional/contact time will be 180 days or 270 instructional/contact hours. Topics: In narrative or outline form, list what you will cover in your course to meet the IB syllabus requirements. In addition, if IB courses are going to be combined with AP or other curriculums, outlines should address additional non-ib topics to be covered.

2 Topics 1.) Algebra Sequences and Series Exponents and Logarithms Counting Principles and the Binomial Theorem Proof by Mathematical Induction Complex Numbers The Complex Plane DeMoivre s Theorem Conjugate roots of polynomial equations 2.) Functions and Equations Concept of Functions and Domain and Range Composite Functions Graphs of Functions Use of GDC to graph and find asymptotes Transformations of graphs Graphs of absolute values and the Inverses of a function The reciprocal function Quadratic Functions Solutions of quadratics Power functions and the inverse of a power function Exponential and Logarithmic Functions Inequalities in one variable Polynomial Functions 3.) Circular Functions and Trigonometry The Unit Circle and Radians Area of a Sector Definition of all 6 trigonometric functions Pythagorean Identity Compound Angle Identities Double Angle Identities Graphs of trigonometric Functions and their Domain and Range Composite Trigonometric Functions Inverse Functions and their domains and range Solutions of Trigonometric functions in a finite interval Solutions of triangles using Law of Sines and Law of Cosines 4.) Matrices Definition of a matrix Algebra of Matrices Identity and Zero Matrices Determinants of a square matrix Inverse of a matrix Solutions of systems of linear equations 5.) Vectors Vectors as displacements in the plane and in three dimensions Components of a vector Sum and difference of two vectors Multiplication by a scalar Magnitude of a vector Unit vectors in 3-dimensions Position vectors

3 Scalar Product of two vectors Perpendicular and Parallel vectors The angle between two vectors Vector equation of a line The angle between two lines Coincident, parallel, intersecting and skew lines and points of intersection The vector product of two vectors Determinant representation Areas of Triangles and Parallelograms Vector equation of a plane Use of normal vector Cartesian equation of a plane Intersection of a line with a plane, two planes, three planes and the angle between Inverse matrix method and row reduction for finding the intersection of three planes 6.) Statistics and Probability Concepts of Population, sample, random sample and frequency distribution of discrete and continuous data Frequency Tables, diagrams, box and whisker plots, histograms Mean, Median, Mode, quartiles, percentiles, Range Cumulative Frequency Concepts of Trial, outcome, sample space, and event Probability of and event and its complementary Combined Events Conditional Probablity and Independent events Bayes Theorem Use of Venn Diagrams, Tree diagrams and tables to solve problems Discrete and Continuous Random variables Probability Density functions Expected Value Binomial Distribution and Poisson Distribution Normal Distribution and Use of Calculator to find normal probablities 7.) Calculus Limit and Convergence Definition of the derivative Derivative of trigonometric, exponential, logarithmic, and power functions Derivatives of reciprocal trigonometric functions Derivatives of inverse trigonometric functions Chain Rule Differentiation of a sum and multiple functions Product and Quotient rules The second derivative Higher derivatives Local Maximum and Minimum points Use of Derivatives in optimization problems Indefinite integration of power functions, trigonometric functions, exponential functions, and reciprocal functions Anti-differentiation with a boundary condition to determine the constant Definite Integrals Area between curve and the x or y axis or between two curves Volumes of revolution Kinematic problems involving displacement, s, velocity, v, and acceleration, a Graphical behaviour of functions: tangents and normals

4 Points of inflection and significance of second derivative Implicit Differentiation Further Integration Integration by substitution Integration by parts Solution of first order differential equations by separation of variables 8.) Option: Series and Differential Equations Infinite sequences of real numbers Limit Theorems and n approaches infinity Limit of a Sequence Improper integrals The integral as a limit of a sum Convergence of infinite series Partial fractions Tests for convergence: comparison test, limit comparison test, ratio test, integral test The p-series Use of integrals to estimate sums of series Series that converge absolutely Series that converge conditionally Alternating series Power series: radius of convergence and interval of convergence Taylor polynomials and series, including the error term Maclaurin series for e x,sin x,cos x,arctan x,ln( 1+ x),( 1+ x) p The evaluation of limits using l Hopital s Rule and or the Taylor series First order differential equations: geometric interpretation using slope fields Numerical Solutions using Euler s method Homogeneous differential equation

5 Assessment: Knowledge of IBO-required assessments and descriptors should be evident. All parts of IB assessment should be addressed, both internal and external. In addition, examples of non-ib monitoring should be given, if they are part of the course. Internal Assessment Portfolio Mathematical investigation Mathematical Modelling External Assesment Paper 1 No calculator Paper 2 Calculator Paper 3 Option

6 Resources: List the books and other resource materials and software that will be used in the course. Information should include what is currently available as well as what is being ordered. Bruce M., Haese R., Haese S., Martin O., Owen J., Urban P. Mathematics HL (CORE). Haese and Harris Pub Bruce M., Haese R., Haese S., Martin O., Owen J., Urban P. Mathematics HL (Option). Haese and Harris Pub Buckle N., Dunbar I. Mathematics Higher Level (Core). IBID Press Stewart J. Single Variable Calculus 4 th edition. Brooks/Cole Pub

7 Teaching time: List all classroom teaching hours for each HL and SL course. HL/SL course HL Year One HL Year Two Teaching hours 135 Hours 135 Hours (add rows as necessary)

8 In addition: For group 1 subjects: Does the course provide adequate preparation in oral and written expression and in analytical and critical thought? List the works for language A1 and explain how these works reinforce internationalism. Does your list of works reflect the requirements of both genres and periods, as explained in the language A1 syllabus and in the prescribed booklist (PBL) for your language A1? Are there adequate materials, particularly in literature, criticism, and literary history?

9 For group 2 subjects: Does the course provide adequate preparation in oral and written expression and in analytical and critical thought? Is provision made for individual practice in speaking and listening over and above what is possible within regular class hours, whether through a language laboratory or by other means? Is each language level grouped appropriately, allowing the teachers to provide specialized, intense instruction for each group? Explain how the resources and themes chosen will highlight or reinforce internationalism. Is the school well stocked with general high-interest reading material at all levels of proficiency in the languages being offered? Does the school subscribe to newspapers and periodicals in the language(s) being offered for student and staff use?

10 For group 3 subjects: Where history will be offered at higher level, please indicate the regional option selected. Have the teachers organized appropriate optional topics for study where applicable? Does the course provide adequate preparation in oral and written expression and in analytical and critical thought? Explain how the topics chosen will be used to reinforce internationalism. Does the school subscribe to newspapers, periodicals, and current reference materials providing upto-date information, for both staff and student needs, relevant to the group 3 courses offered at the school? Where history will be offered at higher level, are there adequate reference materials in the library to support the study of the regional option, as well as to provide sources for in-depth study?

11 For group 4 subjects: Have the teachers organized appropriate laboratory exercises and optional topics for study that conform to IBO requirements for the specific science course? Does the course provide adequate training in analytical and critical thought? Have science teachers collaborated and planned for the group 4 project? How do you envision that the methodology and resources with which the sciences are presented will enhance the international perspective of your students? Has there been an assessment of the laboratory facilities? Is there adequate instructional space for the group 4 courses? Are the science laboratories adequately equipped to perform those exercises required by the IB curriculum? Does the school subscribe to appropriate scientific periodicals and journals and maintain balanced, current and adequate stocks in the life and physical sciences?

12 For group 5 subjects: Does the course provide adequate training in analytical and critical thought? Have courses been sequenced to provide appropriate preparation for the various mathematics options and computer science? How do you envision the methodology and resources with which mathematics/computer science are presented will enhance the international perspective of your students? Does the classroom and/or library contain a variety of modern mathematics textbooks, technical reference materials and other supplementary instructional materials to support the course(s) in IB mathematics? Does the classroom and/or library contain sufficient materials to support the computer science courses?

13 For group 6 subjects: Are all group 6 courses adequately supported with materials and laboratory/studio space? Does the course outline adequately demonstrate that the school has prepared for the required internal assessments for the subject(s)?

14 For Theory of Knowledge: Is the TOK course designed to conform to IBO requirements in substance and classroom hours? Indicate the distribution of TOK topics over the two years of the IB Diploma Programme. Does the course provide adequate training in analytical and critical thought?

15 For all subjects: Has a thorough review of the available resource materials and equipment (both within the department and in the library/media centre) been conducted? Are instructional materials available in sufficient quality, quantity and variety to give effective support to the aims and methods of the courses? Are community resources used both within the classroom and as part of regular field trips? Are the needs and projected costs of acquiring all necessary materials and equipment for each subject group clearly stated? Is an international perspective included?

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