Holdet 2022 Map-HL/i - Undervisningsbeskrivelse

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Undervisningsbeskrivelse

Stamoplysninger til brug ved prøver til gymnasiale uddannelser
Termin(er) 2023/24
Institution Herlufsholm Skole
Fag og niveau Matematik -
Lærer(e)
Hold 2022 Map-HL/i (2i Map-HL)

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Titel 1 Study Plan 2023/24

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Titel 1 Study Plan 2023/24

AIMS/OBJECTIVES
1. Develop a deep understanding of mathematical concepts and their applications.
2. Foster computational and problem-solving skills.
3. Encourage logical reasoning and critical thinking.
4. Promote the exploration of mathematical patterns and structures.
5. Integrate technology effectively in the learning process.
6. Appreciate the power, relevance (and beauty) of mathematics in various contexts.
7. Encourage collaborative learning and effective communication in mathematical language.
8. Understand the historical and cultural significance of mathematics.
9. Develop a sense of curiosity and a lifelong love for learning mathematics.

ACADEMICS
● Foundational Mastery
○ Strong grasp of core mathematical concepts like algebra, functions, and calculus.
○ Ability to recall and apply foundational mathematical knowledge in various scenarios.
○ Comprehensive understanding of the basic principles of mathematics.
● Problem-Solving Proficiency
○ Proficiency in applying mathematical concepts to solve complex problems.
○ Mastery of computational techniques and algorithms.
○ Use of logical reasoning to approach and solve challenges.
● Real-World Application
○ Application of mathematical principles to real-world situations.
○ Understanding the practical implications of mathematical concepts.
○ Relating theoretical knowledge to practical experiences and real-life scenarios.
● Progression and Continuity
○ Building on foundational knowledge to delve into advanced mathematical topics.
○ Ensuring a seamless progression from basic to advanced concepts.
○ Integration of various mathematical domains for a holistic understanding.
● Exploration and Inquiry
○ Encouraging exploration of mathematical patterns and structures.
○ Promoting hands-on mathematical investigations.
○ Fostering a culture of inquiry and curiosity in the subject.

TECHNICAL & KNOWLEDGE SKILLS Syllabus topics covered:
● Topic 1—Number and algebra - SL: 16 hrs, HL: 29 hrs
SL & HL (Common Syllabus)
○ SL 1.1: Operations with numbers
○ SL 1.2: Arithmetic sequences and series.
○ SL 1.3: Geometric sequences and series.
○ SL 1.4: Compound interest calculations.
○ SL 1.5: Approximation: decimal places, significant figures.
○ SL 1.6: Introduction to logarithms
○ SL 1.7: Use of technology to solve financial amortization and annuities problems.
○ SL 1.8: Use of technology to solve systems of linear equations & polynomial equations.
HL ONLY
○ AHL 1.9: Laws of logarithms.
○ AHL 1.10: Simplifying expressions, both numerically and algebraically, involving rational exponents.
○ AHL 1.11: The sum of infinite geometric sequences.
○ AHL 1.12: Introduction to complex numbers, specifically i.
○ AHL 1.13: Modulus–argument (polar) form.
○ AHL 1.14: Matrices and matrix manipulation.
○ AHL 1.15: Eigenvalues and eigenvectors.
● Topic 3—Geometry and Trigonometry - SL: 18 hrs, HL: 46 hrs
○ SL 3.1: Area, volume and angles
○ SL 3.2: Geometric ratios in triangles
○ SL 3.3: Applications of right and non-right trigonometry
○ SL 3.4: Circle arc, sectors
○ SL 3.5: Linear equations and graphical representations.
○ SL 3.6: Voronoi diagrams.
○ AHL 3.7: Degrees & radians.
○ AHL 3.8: Graphical methods for trigonometric equations.
○ AHL 3.9: Two-dimensional geometric transformations.
○ AHL 3.10: Introduction to vectors
○ AHL 3.11: Linear vector equations
○ AHL 3.12: Vector applications to kinematics.
○ AHL 3.13: Vector algebra
○ AHL 3.14: Graph theory
○ AHL 3.15: Adjacent matrices
○ AHL 3.16: Tree diagrams and graph algorithms

PERSONAL SKILLS Based on the Approaches to Learning (ATLs), the course focuses on:
● Thinking skills: Logical reasoning, critical thinking, and problem-solving in mathematical contexts.
● Communication skills: Effective communication using mathematical language and notation.
● Research skills: Exploration of mathematical patterns, structures, and historical contexts.
● Self-management skills: Organizing and managing individual and collaborative mathematical tasks.
● Social skills: Collaborative learning, group discussions, and peer evaluations in mathematical contexts.

TOK:
● Is all knowledge concerned with identification and use of patterns? Consider Fibonacci numbers and connections with the golden ratio.
● Is mathematics invented or discovered? For instance, consider the number e or logarithms–did they already exist before man defined them?
● What is meant by the terms “law” and “theory” in mathematics. How does this compare to how these terms are used in different areas of knowledge?
● Is it possible to know about things of which we can have no experience, such as infinity?
● Mathematics can be used successfully to model real-world processes. Is this because mathematics was created to mirror the world or because the world is intrinsically mathematical?
● What is it about models in mathematics that makes them effective? Is simplicity a desirable characteristic in models?

BOOKS & STUDY
BOOK: Mathematics: Application and Interpretation, Suzanne Doering et al., Oxford.
● SL 1.1: Operations with numbers
● SL 1.2: Arithmetic sequences and series.
○ Pages 178-189
● SL 1.3: Geometric sequences and series.
○ Pages 290-301
● SL 1.4: Compound interest calculations.
○ Pages 302-309
● SL 1.5: Approximation: decimal places, significant figures.
○ Pages 4-12
● SL 1.6: Introduction to logarithms
○ Pages 190-197
● SL 1.7: Use of technology to solve financial amortization and annuities problems.
○ Pages 302-209
● SL 1.8: Linear equations & polynomial equations.
○ Pages 155-168 & Pages 232 -269
● AHL 1.9: Laws of logarithms.
○ Pages 310-329
● AHL 1.10: Simplifying expressions, both numerically and algebraically, involving rational exponents.
○ Pages 4-12
● AHL 1.11: The sum of infinite geometric sequences.
○ Pages 290-301
● AHL 1.12: Introduction to complex numbers.
○ Pages 356-367
● AHL 1.13: Modulus–argument (polar) form.
○ Pages 13-38
● AHL 1.14: Matrices and matrix manipulation.
● AHL 1.15: Eigenvalues and eigenvectors.
○ Pages 372-413
—----------------------------------------------------------------------------
● SL 3.1: Area, volume and angles
○ Pages 13-38
● SL 3.2: Trigonometric functions  & ratios
○ Pages 338-352
● SL 3.3: Applications of right and non-right trigonometry
● SL 3.4: Circle arc, sectors
○ Pages 13-42
● SL 3.5: Linear equations and graphical representations.
○ Pages 82-95
● SL 3.6: Voronoi diagrams.
○ Pages 96-103
● AHL 3.7: Degrees & radians.
○ Pages 13-27
● AHL 3.8: Graphical methods for trigonometric equations.
○ Pages 342-351 & Pages 112-129
● AHL 3.9: Two-dimensional geometric transformations.
○ Pages 391-401
● AHL 3.10: Introduction to vectors
● AHL 3.11: Linear vector equations
● AHL 3.12: Vector applications to kinematics.
● AHL 3.13: Vector algebra
○ Pages 82-133
● AHL 3.14: Graph theory
○ Pages 690-733
● AHL 3.15: Adjacent matrices
○ Pages 377-382
● AHL 3.16: Tree diagrams and graph algorithms
○ Pages 690-733

ASSESSMENT/EVALUATION Students will be assessed using:
● Small Quizzes: Regular quizzes to test understanding of recent topics with prompt feedback.
● Individual Projects and Reports: Assignments to delve deeper into specific mathematical areas.
● Laboratory Work: Practical sessions for hands-on mathematical exploration.
● Group Projects: Collaborative tasks to foster teamwork and collective problem-solving.
● Written Examinations: Including the final trimester exam to assess cumulative knowledge.
ASSESSMENT METHODOLOGY
● Knowledge Demonstration:
○ Students should display a clear understanding of terminology, facts, concepts, skills, techniques, and methodologies related to physics.
● Formative Assessment: Regular feedback mechanisms to help students understand their strengths and areas for improvement. It aims to shape ongoing teaching and learning strategies to meet the desired outcomes.
○ Regular assignments and quizzes that provide continuous feedback.
○ Group discussions and collaborative projects to foster peer learning and reflection.
○ Problem-solving tasks that simulate real-world applications of mathematical principles.
● Summative Assessment: Periodic assessments that encapsulate the learning of a particular duration.
○ Periodic written assessments to gauge students' grasp over the conceptual understandings of each topic.
○ Semester and final examinations to evaluate the overall grasp over the entire course content.
● Analysis and Synthesis:
○ Learners are expected to critically analyze and evaluate experimental procedures, data (both primary and secondary), and discern patterns and predictions.
● External & Internal Assessments:
○ Work for external assessment marked by IB examiners.
○ Internal assessment tasks marked by teachers and externally moderated by the IB.
● Assessment Principles:
○ Adhering to the IB's criterion-related assessment approach, focusing on students’ performance in relation to identified levels of attainment, and not in relation to the work of others.
○ Encouraging the dual use of summative assessment tools for formative purposes throughout the teaching and learning process.
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 45 moduler
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