#### Mathematics: Analysis and Approaches SL

### Introduction

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL. The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

### Content

- Topic 1 – Number and Algebra
- Topic 2 – Functions
- Topic 3 – Geometry and trigonometry
- Topic 4 – Statistics and probability
- Topic 5 – Calculus
- The toolkit and the mathematical exploration

### Assessment

*Examination 80%*

**Paper 1**

*(1 ½ hours, 40%)*

This paper consists of section A, short-response questions, and section B, extended-response questions.

**Paper 2**

*(1 ½ hours, 40%)*

This paper consists of section A, short-response questions, and section B, extended-response questions. A GDC is required for this paper.

*Internal Assessment 20%*

Internal assessment in mathematics SL is an individual project. This is a report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection. A student should develop his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow the students to develop area(s) of interest to them without a time constraint as in an examination, and allow all students to experience a feeling of success.

#### Mathematics: Analysis and Approaches HL

### Introduction

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL. The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

#### Distinction between Higher and Standard Levels for Analysis and Approaches

Students who choose Mathematics: analysis and approaches at SL or HL should be comfortable in the manipulation of algebraic expressions and enjoy the recognition of patterns and understand the mathematical generalization of these patterns. Students who wish to take Mathematics: analysis and approaches at higher level will have strong algebraic skills and the ability to understand simple proof. They will be students who enjoy spending time with problems and get pleasure and satisfaction from solving challenging problems.

#### Content

- Topic 1 – Number and Algebra
- Topic 2 – Functions
- Topic 3 – Geometry and trigonometry
- Topic 4 – Statistics and probability
- Topic 5 – Calculus
- The toolkit and the mathematical exploration

### Assessment

*Examination 80%*

**Paper 1**

*(2 hours, 30%)*

This paper consists of section A, short-response questions, and section B, extended-response questions. Knowledge of all core topics is required for this paper.

**Paper 2**

*(2 hours, 30%)*

This paper consists of section A, short-response questions, and section B, extended-response questions.

**Paper 3**

*(1 hour, 20%)*

This paper consists of a small number of compulsory extended-response questions based on the option chosen.

*Internal Assessment 20%*

The internally assessed component in this course is a mathematical exploration. This is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection. A student should develop his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow the students to develop areas of interest to them without a time constraint as in an examination, and allow all students to experience a feeling of success.

#### Mathematics: Applications and Interpretation SL

### Introduction

This course recognises the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics. The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.

### Content

- Topic 1 – Number and Algebra
- Topic 2 – Functions
- Topic 3 – Geometry and trigonometry
- Topic 4 – Statistics and probability
- Topic 5 – Calculus
- The toolkit and the mathematical exploration

### Assessment

*Examination 80%*

**Paper 1**

*(1 ½ hours, 40%)*

This paper consists of 15 compulsory short-response questions. Knowledge of all topics is required for this paper. However, not all topics are necessarily assessed in every examination session.

The intention of this paper is to test students’ knowledge and understanding across the breadth of the syllabus.

**Paper 2**

*(1 ½ hours, 40%)*

Knowledge of all topics is required for this paper. The intention of this paper is to test students’ knowledge and understanding of the syllabus in depth. Questions require extended responses involving sustained reasoning. Normally, each question reflects an incline of difficulty, from relatively easy tasks at the start of a question to relatively difficult tasks at the end of a question.

*Internal Assessment 20%*

Internal assessment in mathematical studies SL is an individual project. This is a piece of written work based on personal research involving the collection, analysis and evaluation of data. It is marked according to seven assessment criteria. In developing their projects, students should make use of mathematics learned as part of the course. The level of sophistication of the mathematics should be similar to that suggested by the syllabus.