Mathematics Analysis and Approaches new syllabus effective as of September 2019
Group 5 aims
The aims of all mathematics courses are to enable students to:
1. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
2. develop an understanding of the concepts, principles and nature of mathematics
3. communicate mathematics clearly, concisely and confidently in a variety of contexts
4. develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using mathematics
5. employ and refine their powers of abstraction and generalization
6. take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities
7. appreciate how developments in technology and mathematics influence each other
8. appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics
9. appreciate the universality of mathematics and its multicultural, international and historical perspectives
10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course
11. develop the ability to reflect critically upon their own work and the work of others
12. independently and collaboratively extend their understanding of mathematics.
Assessment Objectives
Problemsolving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including nonroutine, openended and realworld problems. Having followed a DP mathematics 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. Problemsolving: recall, select and use their knowledge of mathematical skills, results and models in both realworld 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; use appropriate notation and terminology.
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 realworld, involving organizing and analysing information, making conjectures, drawing conclusions and testing their validity.
ATL Skills
In DP mathematics courses, conceptual understandings are key to promoting deep learning. Concepts play an important role in mathematics, helping students and teachers to think with increasing complexity as they organize and relate facts and topics. Students use conceptual understandings as they solve problems, analyse issues and evaluate decisions that can have an impact on themselves, their communities and the wider world.
Concepts promote the development of a broad, balanced, conceptual and connected curriculum. They represent big ideas that are relevant and facilitate connections within topics, across topics and also to other subjects within the DP. Each topic begins by stating the essential understandings of the topic and highlighting relevant concepts fundamental to the topic.
The course identifies twelve fundamental concepts which relate with varying emphasis to each of the five topics. The twelve concepts identified below support conceptual understanding
Approximation 
This concept refers to a quantity or a representation which is nearly but not exactly correct. 
Change 
This concept refers to a variation in size, amount or behaviour. 
Equivalence 
This concept refers to the state of being identically equal or interchangeable, applied to statements, quantities or expressions. 
Generalization 
This concept refers to a general statement made on the basis of specific examples. 
Modelling 
This concept refers to the way in which mathematics can be used to represent the real world. 
Patterns 
This concept refers to the underlying order, regularity or predictability of the elements of a mathematical system. 
Quantity 
This concept refers to an amount or number. 
Relationships 
This concept refers to the connection between quantities, properties or concepts; these connections may be expressed as models, rules or statements. Relationships provide opportunities for students to explore patterns in the world around them. 
Representation 
This concept refers to using words, formulae, diagrams, tables, charts, graphs and models to represent mathematical information. 
Space 
This concept refers to the frame of geometrical dimensions describing an entity. 
Systems 
This concept refers to groups of interrelated elements. 
Validity 
This concept refers to using wellfounded, logical mathematics to come to a true and accurate conclusion or a reasonable interpretation of results. 
Moreover, throughout the DP mathematics courses, students are encouraged to develop their understanding of the methodology and practice of the discipline of mathematics. The processes of mathematical inquiry, proofs, mathematical modelling and applications and the use of technology is introduced appropriately.
The exploration help students understand the ways in which mathematical discoveries were made and the techniques used to make them and often help them to realize the social and cultural context of mathematics.
Mathematics and theory of knowledge (TOK)
The universality of mathematics as a means of communication is emphasized continually. The international perspective of the students for Mathematics is highly advanced through class discussion and links made with TOK.
As part of their theory of knowledge course, students are encouraged to explore tensions relating to knowledge in mathematics. As an area of knowledge, mathematics seems to supply a certainty perhaps impossible in other disciplines and in many instances provides us with tools to debate these certainties. This may be related to the “purity” of the subject, something that can sometimes make it seem divorced from reality. Yet mathematics has also provided important knowledge about the world and the use of mathematics in science and technology has been one of the driving forces for scientific advances.
Despite all its undoubted power for understanding and change, mathematics is in the end a puzzling phenomenon. A fundamental question for all knowers is whether mathematical knowledge really exists independently of our thinking about it. Is it there, “waiting to be discovered”, or is it a human creation? Indeed, the philosophy of mathematics is an area of study in its own right.
Mathematics and creativity, activity, service (CAS)
CAS and mathematics can complement each other in a number of ways. Mathematical knowledge provides an important key to understanding the world in which we live, and the mathematical skills and techniques students learn in the mathematics courses will allow them to evaluate the world around them which will help them to develop, plan and deliver CAS experiences or projects.
An important aspect of the mathematics courses is that students develop the ability to systematically analyse situations and can recognize the impact that mathematics can have on the world around them. An awareness of how mathematics can be used to represent the truth enables students to reflect critically on the information that societies are given or generate, and how this influences the allocation of resources or the choices that people make. This systematic analysis and critical reflection when problem solving may be inspiring springboards for CAS projects.
Analysis and Approaches
Course description
 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 preuniversity mathematics course (functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof.
 Analysis and approaches is a course aiming to address the needs of students with a strong interest in math and in analytical methods and has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.
 Analysis and approaches at HL is aimed at students who wish to include mathematics as a major component of their university studies or they have a strong interest in Math. This course is a demanding one, requiring students to study a broad range of mathematical topics through a number of different approaches and to varying degrees of depth, with an emphasis on calculus. They will be students who enjoy spending time with problems and get pleasure and satisfaction from solving challenging problems.
 Analysis and approaches at SL is a course aiming to address the needs of students with a strong mathematical background in a less rigorous environment. This course will give emphasis on more traditional math topics to a lesser degree of depth than the HL.
Syllabus outline – HL/SL
Syllabus component 
Suggested teaching hours 

SL 
HL 

Topic 1—Number and algebra 
19 
39 
Topic 2—Functions 
21 
32 
Topic 3— Geometry and trigonometry 
25 
51 
Topic 4—Statistics and probability 
27 
33 
Topic 5 —Calculus 
28 
55 
ExplorationInvestigative, problemsolving and modelling skills development. The exploration is a piece of written work that involves investigating an area of mathematics. 
30 
30 
Total teaching hours 
150 
240 
Assessment outline—HL
Component 
Content 
Overall weighting (%) 
Duration (hours) 
Paper 1 No access to GDC 

30 
2 
Paper 2 GDC REQUIRED 
Compulsory short and extended response questions based on the syllabus 
30 
2 
Paper 3 GDC REQUIRED 
Two compulsory extended response problemsolving questions. 
20 
1 
Internal assessment 
Mathematical Exploration

20 
1015 
Assessment outline—SL
Component 
Content 
Overall weighting (%) 
Duration (hours) 
Paper 1 No access to GDC 

40 
1.5 
Paper 2 GDC REQUIRED 
Compulsory short and extended response questions based on the syllabus 
40 
1.5 
Internal assessment 
Mathematical Exploration

20 
1015 