Maths+HL

=Mathematics HL in the IB Diploma Programme = toc This course caters for students with a very 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.

All mathematics courses share the same general aims, which are to enable students to
 * Aims**


 * Appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives;
 * Foster enjoyment from engaging in mathematical pursuits, and to develop an appreciation of the beauty, power and usefulness of mathematics;
 * Develop logical, critical and creative thinking in mathematics
 * Develop mathematical knowledge, concepts and principles;
 * Employ and refine the powers of abstraction and generalisation;
 * Develop patience and persistence in problem-solving;
 * Have an enhanced awareness of, and utilise the potential of, technological developments in a variety of mathematical situations; and
 * Communicate mathematically, both clearly and confidently, in a variety of contexts.

Course Requirements
A high amount of background knowledge is presumed. Students must have a genuine interest and ability in mathematics. They should have sustained at least a grade level 6 in grades 9 and 10 Mathematics; conforming to BIS recommendations. Exceptions to this are considered on a case-by-case basis.

**Topics Studied in Grades 11 and 12**
Eight topic areas are offered at Higher Level; seven of which are compulsory //core// topics. Topic eight is selected from four //options//, all of which are further mathematics. All eight topics must be covered.

Core topics


 * 1) Algebra
 * 2) Functions and equations
 * 3) Circular functions and trigonometry
 * 4) Matrices
 * 5) Vectors
 * 6) Statistics and probability
 * 7) Calculus

Option topic (One area selected from the following)
 * 1) Statistics and probability
 * 2) Sets, relations and groups
 * 3) Series and differential equations
 * 4) Discrete mathematics

Recommended time allocation: Core topics 190 hours Option topic 40 hours

Two pieces of work, based on different areas of the syllabus, representing the following two types of task:
 * The Portfolio**


 * Type I: Mathematical investigation
 * Type II: Mathematical modelling

Recommended time allocation for the portfolio: 10 hours

__Essential Resources __
Mathematics for the International Student Mathematics Higher Level (Core) Haese & Harris Publications, 2007 ISBN 1 876543 09 4
 * Text 1**

Mathematics for the International Student Mathematics Higher Level (Options) Haese & Harris Publications, 2007 ISBN 1 876543 33 7
 * Text 2**

__**Graphical Display Calculator (GDC)**__ In 2004 the GDC became compulsory in all DP mathematics courses. Students taking any mathematics examinations will be at a disadvantage if they do not have access to a suitable GDC.

__Recommended / approved models__ __NOTE__ Students at BIS are recommended to purchase the **Casio CFX-9850G Plus**, available through the school office.
 * **//Texas Instruments//** || **//Casio//** ||
 * TI-84 Plus Silver Edition || CFX-9850G Plus/Graph 65 Plus ||
 * TI-84 Plus || FX1.0 Plus ||
 * TI-83 Plus Silver Edition || CFX-9950 Plus ||
 * TI-83 Plus || FX-9750G Plus/Graph 35 Plus ||

__Assessment and Grading __
Mathematics Higher Level is assessed by external examination, which comprises 80% of the final grade. The examination is in three parts, Paper 1 (40%), Paper 2 (30%) and Paper 3 (10%). Paper 1 is a non-calculator paper; Paper 3 examines the //option// topic followed by higher level students. A full description of Paper 1, Paper 2 and Paper 3 may be found by following the link.
 * IB External Assessment**

Each portfolio contributes 10% of the final grade (20% in total). Tasks are set and internally assessed by the teacher and moderated externally. The IBO assessment criteria for portfolio tasks may be found by following the link.
 * IB Internal Assessment**

All student attainment requires positive performance assessment; whatever the level of individual ability. Attainment grades for all BIS Mathematics courses comprise 20% semester exam, 40% continuous assessment, 20% written assignments, 15% homework and 5% participation. Students are encouraged to routinely examine their attainment against the following IBO recommended grade descriptors in order to understand and monitor their own progress.
 * BIS Continuous Assessment in Mathematics**

Demonstrates a thorough knowledge and understanding of the syllabus; successfully applies mathematical principles at a sophisticated level in a wide variety of contexts; successfully uses problem-solving techniques in challenging situations; recognises patterns and structures; makes generalisations and justifies conclusions; understands and explains the significance and reasonableness of results; and draws full and relevant conclusions; communicates mathematics in a clear, effective and concise manner, using correct techniques, notation and terminology; demonstrated the ability to integrate knowledge, understanding and skills from different areas of the course; uses technology proficiently.
 * Grade 7 Excellent performance**

Demonstrates a broad knowledge and understanding of the syllabus; successfully applies mathematical principles in a variety of contexts; uses problem-solving techniques in challenging situations; recognises patterns and structures, and makes some generalisations; understands and explains the significance and reasonableness of results, and draws relevant conclusions; communicates mathematics in a clear and effective manner, using correct techniques, notation and terminology; demonstrates some ability to integrate knowledge, understanding and skills from different areas of the course; uses technology proficiently.
 * Grade 6 Very good performance**

Demonstrates a broad knowledge and understanding of the syllabus; successfully applies mathematical principles in performing routine tasks; successfully carries out mathematical processes in a variety of contexts; and recognises patterns and structures; understands the significance of results and draws some conclusions; successfully uses problem-solving techniques in routine situations; communicates mathematics effectively, using suitable notation and terminology; demonstrates and awareness of the links between different areas of the course; uses technology appropriately.
 * Grade 5 Good performance**

Demonstrates a satisfactory knowledge of the syllabus; applies mathematical principles in performing some routine tasks; successfully carries out mathematical principles in straightforward context; shows some ability to recognise patterns and structures; uses problem-solving techniques in routine situation; has limited understanding of the significance of results and attempts to draw some conclusions; communicates mathematics adequately, using some appropriate techniques, notation and terminology; uses technology satisfactory.
 * Grade 4 Satisfactory performance**

Demonstrates partial knowledge of the syllabus and limited understanding of mathematical principles in performing some routine tasks; attempts to carry out mathematical processes in straightforward contexts; communicates some mathematics, using appropriate techniques, notation or terminology; uses technology to a limited extent.
 * Grade 3 Mediocre performance**

Demonstrates limited knowledge of the syllabus; attempts to carry out mathematical processes at a basic level; communicates some mathematics, but often uses inappropriate techniques, notation or terminology; uses technology inadequately.
 * Grade 2 Poor performance**

Demonstrates minimal knowledge of the syllabus; demonstrates little or no ability too use mathematical processes, even when attempting routine tasks; is unable to make effective use of technology.
 * Grade 1 Very poor performance**


 * Approximate grade boundaries used at BIS relative to the IBO grade level descriptors**
 * Grade Level || **1** || **2** || **3** || **4** || **5** || **6** || **7** ||
 * Boundary (%) || 0 - 9 || 10 - 24 || 25 - 39 || 40 - 54 || 55 - 69 || 70 - 84 || 85 -100 ||
 * GPA Contribution || 0 || 0 || 0 || 1 || 2 || 3 || 4 ||

Pre-Diploma Course (Grade 10 preparation)
The BIS Grade 10 curriculum is now aligned to best meet the needs of students in grades 11 and 12 - both diploma and non-diploma students. Emphasis is on consolidation of basic number rules and processes; algebraic manipulation skills; functions and graphs; understanding and applying the laws of probability and statistics; trigonometry; furthering knowledge of plane geometry and 3D vector space; and kinematics. In addition students will complete and in-depth mathematical investigation concentrating on structure and content; accurate communication; correct terminology and notation, and demonstrating sound logical reasoning and analysis while working towards a generalised mathematical statement. If time permits, students will begin studying approaches to rates of change and the Calculus.

Semester 1 Content (Grade 11)

 * Topic 1 Algebra
 * Topic 2 Functions
 * Portfolio 1

Semester 2 Content (Grade 11)

 * Topic 3 Trigonometric Function
 * Topic 7 Calculus
 * Portfolio 2

Semester 3 Content (Grade 12)

 * Topic 4 Matrics
 * Topic 5 Vectors
 * Topic 6 Statistics & Probability
 * Topic 8 Statistics & Probability

Semester 4 Content (Grade 12)
---
 * Topic 8 Statistics & Probability
 * Mock Exam
 * Portfolio 3
 * Revision